uscrime_data <- read.table('C:/Users/mjpearl/Desktop/omsa/ISYE-6501-OAN/hw8/data/uscrime.txt',header = TRUE, stringsAsFactors = FALSE)
head(uscrime_data)## M So Ed Po1 Po2 LF M.F Pop NW U1 U2 Wealth Ineq
## 1 15.1 1 9.1 5.8 5.6 0.510 95.0 33 30.1 0.108 4.1 3940 26.1
## 2 14.3 0 11.3 10.3 9.5 0.583 101.2 13 10.2 0.096 3.6 5570 19.4
## 3 14.2 1 8.9 4.5 4.4 0.533 96.9 18 21.9 0.094 3.3 3180 25.0
## 4 13.6 0 12.1 14.9 14.1 0.577 99.4 157 8.0 0.102 3.9 6730 16.7
## 5 14.1 0 12.1 10.9 10.1 0.591 98.5 18 3.0 0.091 2.0 5780 17.4
## 6 12.1 0 11.0 11.8 11.5 0.547 96.4 25 4.4 0.084 2.9 6890 12.6
## Prob Time Crime
## 1 0.084602 26.2011 791
## 2 0.029599 25.2999 1635
## 3 0.083401 24.3006 578
## 4 0.015801 29.9012 1969
## 5 0.041399 21.2998 1234
## 6 0.034201 20.9995 682#Remove So feature from the dataset as this is not required to normalize as it's a binary or
stepwise_x_colnames = colnames(uscrime_data[,names(uscrime_data) != "So" & names(uscrime_data) != "Crime"])
scale <- function(dataframe, cols) {
result <- dataframe # make a copy of the input data frame
for (j in cols) {
m <- mean(dataframe[,j])
std <- sd(dataframe[,j])
result[,j] <- sapply(result[,j], function(x) (x - m) / std)
}
return(result)
}
uscrime_data.norm <- scale(uscrime_data, stepwise_x_colnames)We will now fit the variable using AIC as the validation critiera, and cross validation to split the relevant data into training, validation and test. We will use backward step-wise regression to start with the full feature set and determine based on the iterative p-value scores which features to keep.
ctrl <- trainControl(method = "repeatedcv", number = 5, repeats = 5)
step_fit <- train(Crime ~ ., data = uscrime_data.norm, "lmStepAIC", scope =
list(lower = Crime~1, upper = Crime~.), direction = "backward",
trControl=ctrl)## Start: AIC=436.65
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 3 1250739 434.65
## - Pop 1 1468 1252204 434.70
## - LF 1 7264 1257999 434.88
## - Wealth 1 23397 1274133 435.37
## - M.F 1 31670 1282406 435.63
## - Po2 1 35985 1286721 435.76
## - NW 1 40372 1291108 435.89
## - U1 1 47815 1298550 436.11
## - Time 1 52895 1303631 436.27
## <none> 1250736 436.65
## - Po1 1 112926 1363662 438.02
## - U2 1 119494 1370230 438.21
## - M 1 125217 1375953 438.37
## - Prob 1 132024 1382760 438.57
## - Ineq 1 326905 1577641 443.71
## - Ed 1 447722 1698458 446.59
##
## Step: AIC=434.65
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 1517 1252256 432.70
## - LF 1 9461 1260200 432.95
## - Wealth 1 23508 1274247 433.38
## - M.F 1 32034 1282773 433.64
## - Po2 1 36020 1286759 433.76
## - NW 1 49231 1299970 434.16
## - Time 1 53146 1303885 434.27
## - U1 1 58889 1309628 434.45
## <none> 1250739 434.65
## - Po1 1 112924 1363663 436.02
## - M 1 126586 1377325 436.41
## - Prob 1 132323 1383062 436.57
## - U2 1 134790 1385529 436.64
## - Ineq 1 350118 1600857 442.28
## - Ed 1 450871 1701610 444.66
##
## Step: AIC=432.7
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 8525 1260781 430.96
## - Wealth 1 23698 1275955 431.43
## - M.F 1 31288 1283544 431.66
## - Po2 1 34871 1287128 431.77
## - NW 1 47762 1300019 432.16
## - Time 1 55742 1307998 432.40
## - U1 1 57551 1309807 432.45
## <none> 1252256 432.70
## - Po1 1 113527 1365783 434.08
## - M 1 128780 1381036 434.52
## - Prob 1 130880 1383136 434.58
## - U2 1 136032 1388288 434.72
## - Ineq 1 354963 1607219 440.43
## - Ed 1 454662 1706919 442.78
##
## Step: AIC=430.96
## .outcome ~ M + Ed + Po1 + Po2 + M.F + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 22858 1283639 429.66
## - Wealth 1 26106 1286887 429.76
## - Po2 1 27842 1288623 429.82
## - NW 1 44149 1304930 430.31
## - U1 1 49152 1309933 430.46
## - Time 1 58632 1319413 430.74
## <none> 1260781 430.96
## - Po1 1 105020 1365801 432.08
## - Prob 1 122511 1383292 432.58
## - U2 1 135851 1396632 432.95
## - M 1 145635 1406416 433.23
## - Ineq 1 364133 1624914 438.86
## - Ed 1 459057 1719838 441.07
##
## Step: AIC=429.66
## .outcome ~ M + Ed + Po1 + Po2 + NW + U1 + U2 + Wealth + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - U1 1 30116 1313755 428.57
## - Wealth 1 36098 1319737 428.75
## - Po2 1 44695 1328334 429.00
## - NW 1 44937 1328576 429.01
## <none> 1283639 429.66
## - Time 1 102217 1385856 430.65
## - U2 1 120154 1403792 431.15
## - Prob 1 131848 1415487 431.48
## - Po1 1 141167 1424806 431.73
## - M 1 193289 1476927 433.13
## - Ineq 1 447474 1731113 439.33
## - Ed 1 618558 1902197 443.00
##
## Step: AIC=428.57
## .outcome ~ M + Ed + Po1 + Po2 + NW + U2 + Wealth + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 33273 1347029 427.54
## - NW 1 55105 1368860 428.17
## - Wealth 1 60972 1374727 428.34
## <none> 1313755 428.57
## - Time 1 87196 1400951 429.07
## - Prob 1 108525 1422280 429.66
## - Po1 1 126961 1440716 430.17
## - U2 1 138065 1451820 430.47
## - M 1 175793 1489548 431.47
## - Ineq 1 543956 1857711 440.08
## - Ed 1 589961 1903716 441.03
##
## Step: AIC=427.54
## .outcome ~ M + Ed + Po1 + NW + U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 40412 1387440 426.70
## <none> 1347029 427.54
## - Time 1 70948 1417977 427.55
## - Wealth 1 75567 1422596 427.67
## - Prob 1 85433 1432462 427.94
## - U2 1 135653 1482682 429.29
## - M 1 180929 1527958 430.46
## - Ed 1 597096 1944124 439.85
## - Ineq 1 676779 2023807 441.42
## - Po1 1 799408 2146437 443.71
##
## Step: AIC=426.7
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 44121 1431562 425.92
## - Wealth 1 56953 1444394 426.27
## - Prob 1 65252 1452692 426.49
## <none> 1387440 426.70
## - U2 1 146141 1533581 428.60
## - M 1 316631 1704071 432.71
## - Ed 1 557726 1945166 437.87
## - Ineq 1 692713 2080154 440.49
## - Po1 1 1374239 2761679 451.54
##
## Step: AIC=425.92
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Prob 1 38903 1470465 424.96
## - Wealth 1 47113 1478675 425.18
## <none> 1431562 425.92
## - U2 1 163316 1594877 428.13
## - M 1 302456 1734018 431.39
## - Ed 1 636963 2068524 438.27
## - Ineq 1 648939 2080501 438.50
## - Po1 1 1346190 2777751 449.77
##
## Step: AIC=424.96
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq
##
## Df Sum of Sq RSS AIC
## <none> 1470465 424.96
## - U2 1 143419 1613883 426.59
## - Wealth 1 155026 1625490 426.87
## - M 1 292606 1763070 430.04
## - Ed 1 624333 2094797 436.76
## - Ineq 1 886541 2357006 441.36
## - Po1 1 1457183 2927647 449.82
## Start: AIC=414.67
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 2532 1150359 412.75
## - Time 1 2649 1150475 412.76
## - So 1 3384 1151210 412.78
## - Wealth 1 4409 1152235 412.81
## - Po1 1 6773 1154599 412.89
## - NW 1 9773 1157599 412.98
## - M.F 1 18900 1166726 413.28
## - LF 1 19841 1167667 413.31
## - Pop 1 21634 1169460 413.36
## - U1 1 45424 1193251 414.11
## - Ed 1 50695 1198521 414.27
## <none> 1147826 414.67
## - M 1 92725 1240551 415.55
## - Ineq 1 132426 1280252 416.71
## - Prob 1 173373 1321199 417.88
## - U2 1 201924 1349750 418.67
##
## Step: AIC=412.75
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 2922 1153280 410.85
## - Time 1 4546 1154905 410.90
## - Wealth 1 6646 1157004 410.97
## - NW 1 14511 1164870 411.22
## - LF 1 17966 1168325 411.33
## - M.F 1 18196 1168555 411.33
## - Pop 1 24013 1174372 411.52
## - U1 1 50633 1200992 412.35
## <none> 1150359 412.75
## - Ed 1 79655 1230014 413.23
## - M 1 92707 1243065 413.62
## - Ineq 1 146375 1296734 415.18
## - Prob 1 195612 1345970 416.56
## - U2 1 199414 1349773 416.67
## - Po1 1 387526 1537884 421.50
##
## Step: AIC=410.85
## .outcome ~ M + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 4887 1158167 409.00
## - Wealth 1 6877 1160157 409.07
## - LF 1 15205 1168485 409.33
## - NW 1 18489 1171770 409.43
## - Pop 1 21534 1174815 409.53
## - M.F 1 26614 1179895 409.69
## <none> 1153280 410.85
## - U1 1 70253 1223533 411.03
## - Ed 1 79257 1232537 411.31
## - M 1 91508 1244789 411.67
## - Ineq 1 175015 1328296 414.07
## - Prob 1 197175 1350456 414.69
## - U2 1 212153 1365434 415.09
## - Po1 1 384928 1538209 419.50
##
## Step: AIC=409
## .outcome ~ M + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 6129 1164296 407.20
## - LF 1 12735 1170902 407.41
## - NW 1 14553 1172720 407.46
## - M.F 1 30136 1188303 407.95
## - Pop 1 30160 1188327 407.95
## <none> 1158167 409.00
## - U1 1 68131 1226298 409.12
## - M 1 86957 1245124 409.68
## - Ed 1 87379 1245546 409.69
## - Ineq 1 188131 1346298 412.57
## - U2 1 207402 1365569 413.10
## - Prob 1 244402 1402569 414.09
## - Po1 1 412736 1570903 418.28
##
## Step: AIC=407.2
## .outcome ~ M + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 11463 1175758 405.56
## - LF 1 13137 1177432 405.61
## - Pop 1 25903 1190199 406.01
## - M.F 1 38448 1202744 406.40
## <none> 1164296 407.20
## - U1 1 75615 1239911 407.53
## - M 1 83344 1247640 407.76
## - Ed 1 86023 1250318 407.84
## - U2 1 222832 1387127 411.68
## - Ineq 1 224992 1389288 411.74
## - Prob 1 255437 1419732 412.54
## - Po1 1 492168 1656464 418.24
##
## Step: AIC=405.56
## .outcome ~ M + Ed + Po1 + LF + M.F + Pop + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 15437 1191196 404.04
## - Pop 1 24059 1199818 404.31
## - M.F 1 31322 1207080 404.53
## <none> 1175758 405.56
## - U1 1 67199 1242957 405.62
## - Ed 1 82239 1257998 406.06
## - M 1 113769 1289527 406.98
## - U2 1 213964 1389723 409.75
## - Prob 1 249767 1425525 410.69
## - Ineq 1 353911 1529669 413.30
## - Po1 1 709788 1885546 421.04
##
## Step: AIC=404.04
## .outcome ~ M + Ed + Po1 + M.F + Pop + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 16372 1207568 402.55
## <none> 1191196 404.04
## - M 1 105247 1296443 405.18
## - Ed 1 118715 1309911 405.56
## - M.F 1 129674 1320870 405.87
## - U1 1 137033 1328229 406.07
## - U2 1 226506 1417702 408.48
## - Prob 1 271188 1462384 409.63
## - Ineq 1 365929 1557125 411.96
## - Po1 1 786728 1977924 420.81
##
## Step: AIC=402.55
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1207568 402.55
## - Ed 1 112584 1320152 403.85
## - M 1 134818 1342387 404.46
## - U1 1 147919 1355487 404.82
## - M.F 1 219777 1427345 406.74
## - U2 1 226569 1434138 406.91
## - Prob 1 254824 1462392 407.63
## - Ineq 1 354038 1561606 410.06
## - Po1 1 847976 2055545 420.23
## Start: AIC=399.57
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 46 603504 397.57
## - M.F 1 1215 604673 397.64
## - U1 1 5758 609216 397.93
## - So 1 9047 612505 398.13
## - LF 1 12164 615622 398.33
## - Pop 1 26995 630453 399.23
## <none> 603458 399.57
## - Time 1 33816 637274 399.64
## - Prob 1 94003 697461 403.07
## - Po2 1 112160 715618 404.05
## - U2 1 145068 748526 405.75
## - Wealth 1 155552 759010 406.28
## - Po1 1 218722 822180 409.32
## - Ed 1 300731 904189 412.93
## - Ineq 1 474630 1078088 419.62
## - M 1 492082 1095540 420.23
##
## Step: AIC=397.57
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 1332 604836 395.65
## - U1 1 5730 609234 395.93
## - So 1 12516 616020 396.35
## - LF 1 13117 616621 396.39
## - Pop 1 28128 631632 397.30
## <none> 603504 397.57
## - Time 1 39065 642569 397.95
## - Prob 1 105905 709409 401.71
## - Po2 1 137139 740643 403.35
## - U2 1 148655 752159 403.94
## - Wealth 1 155774 759278 404.30
## - Po1 1 248501 852005 408.67
## - Ed 1 305864 909368 411.15
## - Ineq 1 548417 1151922 420.14
## - M 1 553037 1156541 420.29
##
## Step: AIC=395.65
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + Pop + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - U1 1 13511 618347 394.49
## - So 1 13686 618522 394.51
## - LF 1 21577 626413 394.99
## - Pop 1 27904 632741 395.37
## <none> 604836 395.65
## - Time 1 37954 642790 395.97
## - Prob 1 104716 709553 399.72
## - Po2 1 136652 741488 401.40
## - Wealth 1 154735 759571 402.31
## - U2 1 163864 768701 402.77
## - Po1 1 252705 857542 406.92
## - Ed 1 305463 910300 409.19
## - Ineq 1 557434 1162270 418.48
## - M 1 577494 1182330 419.13
##
## Step: AIC=394.49
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + Pop + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 8111 626458 392.99
## - LF 1 17021 635368 393.53
## - Time 1 27479 645826 394.15
## - Pop 1 29767 648114 394.28
## <none> 618347 394.49
## - Prob 1 99277 717624 398.15
## - Po2 1 126053 744400 399.54
## - Wealth 1 167935 786282 401.62
## - Po1 1 241935 860282 405.04
## - U2 1 287723 906070 407.01
## - Ed 1 293232 911579 407.24
## - Ineq 1 560154 1178501 417.00
## - M 1 565624 1183971 417.18
##
## Step: AIC=392.99
## .outcome ~ M + Ed + Po1 + Po2 + LF + Pop + U2 + Wealth + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 11944 638402 391.71
## - Pop 1 31690 658148 392.86
## - Time 1 32000 658458 392.88
## <none> 626458 392.99
## - Po2 1 129772 756231 398.14
## - Prob 1 169429 795887 400.09
## - Wealth 1 172468 798926 400.23
## - Po1 1 251147 877606 403.80
## - U2 1 293626 920085 405.60
## - Ed 1 343778 970236 407.61
## - M 1 633899 1260358 417.55
## - Ineq 1 659151 1285610 418.31
##
## Step: AIC=391.71
## .outcome ~ M + Ed + Po1 + Po2 + Pop + U2 + Wealth + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 26893 665296 391.28
## - Time 1 28119 666521 391.35
## <none> 638402 391.71
## - Po2 1 117886 756289 396.15
## - Prob 1 157545 795947 398.09
## - Wealth 1 168512 806914 398.61
## - Po1 1 240398 878801 401.85
## - U2 1 358405 996807 406.64
## - Ed 1 359859 998262 406.70
## - M 1 646234 1284636 416.28
## - Ineq 1 662926 1301329 416.77
##
## Step: AIC=391.28
## .outcome ~ M + Ed + Po1 + Po2 + U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## <none> 665296 391.28
## - Time 1 61148 726444 392.62
## - Po2 1 148608 813903 396.94
## - Prob 1 156045 821341 397.28
## - Wealth 1 172623 837918 398.04
## - Po1 1 262098 927394 401.90
## - U2 1 344447 1009743 405.13
## - Ed 1 375538 1040833 406.28
## - Ineq 1 637077 1302373 414.80
## - M 1 777823 1443118 418.70
## Start: AIC=401.05
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 7 794278 399.05
## - Wealth 1 293 794564 399.06
## - M.F 1 10048 804319 399.51
## - Time 1 11894 806165 399.60
## - So 1 12373 806644 399.62
## - Po1 1 20509 814780 399.99
## - NW 1 28324 822595 400.34
## - LF 1 30240 824511 400.43
## - Pop 1 38548 832819 400.80
## <none> 794271 401.05
## - Prob 1 66454 860725 402.02
## - M 1 93370 887641 403.16
## - U1 1 176560 970831 406.47
## - U2 1 293495 1087766 410.68
## - Ineq 1 327968 1122239 411.84
## - Ed 1 674691 1468962 421.80
##
## Step: AIC=399.05
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 293 794571 397.06
## - M.F 1 10609 804887 397.54
## - Time 1 11996 806275 397.60
## - So 1 12372 806650 397.62
## - NW 1 31183 825461 398.47
## - LF 1 31523 825801 398.49
## - Pop 1 38583 832861 398.80
## <none> 794278 399.05
## - Prob 1 67623 861901 400.07
## - M 1 95319 889597 401.24
## - U1 1 177000 971279 404.49
## - U2 1 294327 1088605 408.71
## - Ineq 1 335250 1129528 410.08
## - Po1 1 461151 1255429 413.99
## - Ed 1 680134 1474412 419.94
##
## Step: AIC=397.06
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 11359 805930 395.59
## - So 1 12141 806711 395.62
## - Time 1 13550 808121 395.69
## - NW 1 30902 825473 396.47
## - LF 1 31230 825801 396.49
## - Pop 1 38495 833066 396.81
## <none> 794571 397.06
## - Prob 1 67351 861921 398.07
## - M 1 95527 890098 399.26
## - U1 1 177176 971747 402.51
## - U2 1 302411 1096982 406.99
## - Ineq 1 516102 1310673 413.58
## - Po1 1 577234 1371805 415.27
## - Ed 1 729036 1523606 419.15
##
## Step: AIC=395.59
## .outcome ~ M + So + Ed + Po1 + LF + Pop + NW + U1 + U2 + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 7233 813162 393.92
## - So 1 9697 815626 394.03
## - LF 1 21092 827021 394.54
## - NW 1 22291 828221 394.60
## <none> 805930 395.59
## - Pop 1 50903 856833 395.85
## - Prob 1 83991 889920 397.25
## - M 1 142249 948179 399.60
## - U1 1 169207 975137 400.64
## - U2 1 293101 1099030 405.06
## - Ineq 1 551796 1357725 412.88
## - Po1 1 645671 1451601 415.36
## - Ed 1 745303 1551233 417.81
##
## Step: AIC=393.92
## .outcome ~ M + So + Ed + Po1 + LF + Pop + NW + U1 + U2 + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - So 1 10621 823783 392.40
## - NW 1 24266 837429 393.01
## - LF 1 24798 837960 393.03
## - Pop 1 43677 856839 393.85
## <none> 813162 393.92
## - M 1 167507 980669 398.85
## - U1 1 205859 1019022 400.27
## - Prob 1 217120 1030282 400.67
## - U2 1 330426 1143588 404.53
## - Ineq 1 546309 1359472 410.93
## - Po1 1 651450 1464613 413.69
## - Ed 1 747575 1560737 416.04
##
## Step: AIC=392.4
## .outcome ~ M + Ed + Po1 + LF + Pop + NW + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 14651 838433 391.05
## - NW 1 14939 838722 391.06
## - Pop 1 38659 862442 392.09
## <none> 823783 392.40
## - M 1 171030 994812 397.38
## - U1 1 207796 1031579 398.72
## - Prob 1 257738 1081521 400.47
## - U2 1 323355 1147138 402.65
## - Ineq 1 626261 1450044 411.32
## - Po1 1 671978 1495761 412.47
## - Ed 1 756112 1579895 414.49
##
## Step: AIC=391.05
## .outcome ~ M + Ed + Po1 + Pop + NW + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 13412 851845 389.64
## - Pop 1 40916 879349 390.81
## <none> 838433 391.05
## - M 1 177586 1016019 396.16
## - U1 1 200272 1038706 396.98
## - Prob 1 243411 1081844 398.48
## - U2 1 348906 1187340 401.92
## - Ineq 1 611646 1450080 409.32
## - Po1 1 736043 1574477 412.37
## - Ed 1 844365 1682798 414.83
##
## Step: AIC=389.64
## .outcome ~ M + Ed + Po1 + Pop + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 37215 889060 389.22
## <none> 851845 389.64
## - Prob 1 230453 1082298 396.50
## - U1 1 231961 1083806 396.55
## - M 1 248683 1100528 397.11
## - U2 1 382719 1234564 401.37
## - Ineq 1 737906 1589751 410.72
## - Ed 1 841385 1693230 413.06
## - Po1 1 875604 1727449 413.80
##
## Step: AIC=389.22
## .outcome ~ M + Ed + Po1 + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 889060 389.22
## - Prob 1 199414 1088474 394.71
## - U1 1 213498 1102557 395.18
## - M 1 299016 1188076 397.95
## - U2 1 356187 1245246 399.69
## - Ineq 1 703103 1592163 408.78
## - Ed 1 893135 1782195 412.95
## - Po1 1 1006237 1895297 415.23
## Start: AIC=396.13
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - U2 1 656 696107 394.17
## - Time 1 3241 698692 394.30
## - So 1 3245 698696 394.30
## - Pop 1 3855 699305 394.34
## - NW 1 12250 707700 394.78
## - M 1 14016 709467 394.87
## - Po2 1 16134 711585 394.98
## - LF 1 20891 716342 395.23
## - U1 1 22660 718111 395.32
## - Ed 1 25376 720827 395.46
## <none> 695451 396.13
## - Wealth 1 48381 743832 396.62
## - M.F 1 103636 799087 399.27
## - Po1 1 117681 813132 399.92
## - Prob 1 180006 875457 402.65
## - Ineq 1 310951 1006402 407.81
##
## Step: AIC=394.17
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 2734 698841 392.31
## - Pop 1 3768 699874 392.37
## - Time 1 3816 699922 392.37
## - NW 1 12605 708712 392.83
## - Po2 1 16583 712689 393.04
## - M 1 17150 713256 393.07
## - LF 1 20756 716862 393.25
## - Ed 1 34984 731091 393.98
## <none> 696107 394.17
## - Wealth 1 47738 743845 394.62
## - U1 1 62580 758686 395.35
## - M.F 1 104817 800923 397.36
## - Po1 1 117269 813376 397.93
## - Prob 1 179351 875458 400.65
## - Ineq 1 310580 1006686 405.82
##
## Step: AIC=392.31
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 3499 702340 390.50
## - Time 1 5591 704432 390.61
## - Po2 1 19820 718660 391.35
## - M 1 20669 719510 391.39
## - NW 1 22365 721206 391.48
## - Ed 1 36492 735332 392.19
## <none> 698841 392.31
## - LF 1 40374 739215 392.39
## - Wealth 1 65597 764437 393.63
## - U1 1 82042 780882 394.42
## - M.F 1 110165 809006 395.73
## - Po1 1 126293 825133 396.46
## - Prob 1 176672 875512 398.65
## - Ineq 1 446453 1145293 408.59
##
## Step: AIC=390.5
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + NW + U1 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 4548 706887 388.74
## - Po2 1 20014 722353 389.54
## - M 1 20093 722433 389.54
## - NW 1 23229 725569 389.70
## - Ed 1 37157 739497 390.40
## - LF 1 37686 740025 390.43
## <none> 702340 390.50
## - Wealth 1 73546 775885 392.18
## - U1 1 78573 780913 392.42
## - M.F 1 110969 813309 393.92
## - Po1 1 130134 832473 394.79
## - Prob 1 183263 885603 397.07
## - Ineq 1 515603 1217943 408.86
##
## Step: AIC=388.74
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + NW + U1 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 15636 722523 387.54
## - M 1 18770 725657 387.70
## - NW 1 19496 726383 387.74
## <none> 706887 388.74
## - LF 1 40738 747625 388.81
## - Ed 1 43643 750530 388.95
## - Wealth 1 69374 776261 390.20
## - U1 1 78223 785110 390.62
## - Po1 1 130709 837596 393.01
## - M.F 1 145606 852493 393.67
## - Prob 1 221148 928035 396.81
## - Ineq 1 531893 1238780 407.49
##
## Step: AIC=387.54
## .outcome ~ M + Ed + Po1 + LF + M.F + NW + U1 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 12804 735327 386.19
## - M 1 17039 739561 386.41
## - LF 1 28714 751236 386.99
## - Ed 1 30830 753353 387.09
## <none> 722523 387.54
## - Wealth 1 64659 787182 388.72
## - U1 1 65832 788354 388.77
## - M.F 1 136214 858737 391.94
## - Prob 1 209709 932232 394.97
## - Ineq 1 557946 1280469 406.72
## - Po1 1 1062848 1785370 419.02
##
## Step: AIC=386.19
## .outcome ~ M + Ed + Po1 + LF + M.F + U1 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 22879 758206 385.33
## - Ed 1 25932 761259 385.48
## - M 1 28825 764152 385.62
## <none> 735327 386.19
## - Wealth 1 56628 791955 386.94
## - U1 1 58645 793972 387.03
## - M.F 1 123449 858776 389.94
## - Prob 1 202690 938017 393.20
## - Ineq 1 632251 1367578 407.15
## - Po1 1 1580899 2316226 426.65
##
## Step: AIC=385.33
## .outcome ~ M + Ed + Po1 + M.F + U1 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Ed 1 13855 772061 384.00
## - M 1 24646 782852 384.51
## - U1 1 36763 794969 385.08
## <none> 758206 385.33
## - Wealth 1 46406 804612 385.53
## - M.F 1 103803 862010 388.08
## - Prob 1 180660 938866 391.24
## - Ineq 1 609713 1367919 405.16
## - Po1 1 1764480 2522686 427.81
##
## Step: AIC=384
## .outcome ~ M + Po1 + M.F + U1 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - M 1 16092 788153 382.76
## <none> 772061 384.00
## - Wealth 1 52816 824877 384.45
## - U1 1 61947 834008 384.85
## - Prob 1 181364 953425 389.81
## - M.F 1 208287 980348 390.84
## - Ineq 1 634095 1406156 404.18
## - Po1 1 1765627 2537688 426.03
##
## Step: AIC=382.76
## .outcome ~ Po1 + M.F + U1 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 38368 826521 382.52
## <none> 788153 382.76
## - U1 1 92219 880372 384.86
## - Prob 1 175372 963525 388.20
## - M.F 1 227882 1016036 390.16
## - Ineq 1 643454 1431607 402.85
## - Po1 1 1885733 2673886 425.96
##
## Step: AIC=382.52
## .outcome ~ Po1 + M.F + U1 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 826521 382.52
## - U1 1 87075 913597 384.23
## - Prob 1 220415 1046937 389.27
## - M.F 1 238569 1065090 389.90
## - Ineq 1 1006531 1833052 409.99
## - Po1 1 3380168 4206689 440.73
## Start: AIC=410.2
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 2956 1020072 408.31
## - Time 1 5020 1022137 408.38
## - Wealth 1 7230 1024347 408.46
## - So 1 13311 1030428 408.68
## - Po2 1 24893 1042010 409.09
## - NW 1 37418 1054535 409.53
## - LF 1 41442 1058559 409.68
## - M.F 1 49426 1066543 409.95
## - U1 1 50222 1067339 409.98
## <none> 1017117 410.20
## - M 1 64258 1081375 410.46
## - Prob 1 74399 1091516 410.81
## - U2 1 74420 1091537 410.81
## - Po1 1 127083 1144200 412.55
## - Ineq 1 274413 1291530 417.04
## - Ed 1 342226 1359343 418.93
##
## Step: AIC=408.31
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 3963 1024035 406.45
## - Wealth 1 6300 1026372 406.53
## - So 1 13527 1033599 406.79
## - Po2 1 23428 1043501 407.15
## - NW 1 35765 1055837 407.58
## - LF 1 46333 1066406 407.95
## - U1 1 50929 1071001 408.11
## <none> 1020072 408.31
## - M.F 1 67336 1087409 408.67
## - U2 1 71817 1091889 408.82
## - Prob 1 72487 1092559 408.85
## - M 1 72687 1092759 408.85
## - Po1 1 124184 1144257 410.56
## - Ineq 1 271658 1291730 415.04
## - Ed 1 343935 1364008 417.06
##
## Step: AIC=406.45
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 12019 1036054 404.88
## - So 1 14491 1038526 404.97
## - Po2 1 37266 1061301 405.77
## - NW 1 37526 1061562 405.78
## - LF 1 45518 1069553 406.06
## <none> 1024035 406.45
## - U1 1 57271 1081307 406.46
## - M.F 1 63680 1087715 406.68
## - U2 1 84913 1108948 407.40
## - M 1 95129 1119165 407.74
## - Po1 1 155825 1179860 409.69
## - Prob 1 174109 1198144 410.26
## - Ineq 1 289291 1313327 413.65
## - Ed 1 343971 1368006 415.16
##
## Step: AIC=404.88
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - So 1 8626 1044679 403.19
## - NW 1 34830 1070884 404.10
## - Po2 1 35075 1071128 404.11
## - LF 1 37968 1074021 404.21
## <none> 1036054 404.88
## - U1 1 59230 1095283 404.94
## - M.F 1 65794 1101848 405.16
## - M 1 83207 1119260 405.74
## - U2 1 91353 1127406 406.01
## - Po1 1 160452 1196505 408.21
## - Prob 1 197186 1233240 409.33
## - Ed 1 338570 1374624 413.34
## - Ineq 1 394956 1431009 414.83
##
## Step: AIC=403.19
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 26397 1071077 402.11
## - Po2 1 30781 1075460 402.26
## - LF 1 31217 1075896 402.28
## - U1 1 51069 1095748 402.95
## - M.F 1 57210 1101889 403.16
## <none> 1044679 403.19
## - M 1 79813 1124493 403.91
## - U2 1 82933 1127612 404.01
## - Po1 1 153871 1198550 406.27
## - Prob 1 229127 1273807 408.52
## - Ed 1 343222 1387902 411.70
## - Ineq 1 430757 1475436 413.96
##
## Step: AIC=402.11
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 19396 1090473 400.77
## - LF 1 20953 1092030 400.83
## - M.F 1 40382 1111459 401.48
## - U1 1 45497 1116574 401.65
## <none> 1071077 402.11
## - U2 1 90112 1161189 403.10
## - Po1 1 140146 1211223 404.66
## - M 1 159604 1230681 405.25
## - Prob 1 205292 1276369 406.60
## - Ed 1 321557 1392634 409.82
## - Ineq 1 648941 1720018 417.64
##
## Step: AIC=400.77
## .outcome ~ M + Ed + Po1 + LF + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 11496 1101969 399.16
## - M.F 1 38614 1129087 400.06
## - U1 1 40860 1131333 400.14
## <none> 1090473 400.77
## - U2 1 91351 1181824 401.75
## - M 1 158406 1248878 403.79
## - Prob 1 199275 1289747 404.98
## - Ed 1 303041 1393513 407.85
## - Ineq 1 669526 1759999 416.49
## - Po1 1 1184856 2275328 425.99
##
## Step: AIC=399.16
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - M.F 1 27353 1129322 398.07
## - U1 1 32335 1134304 398.23
## <none> 1101969 399.16
## - U2 1 92772 1194741 400.15
## - M 1 174798 1276767 402.61
## - Prob 1 187905 1289874 402.99
## - Ed 1 294197 1396166 405.92
## - Ineq 1 659752 1761721 414.52
## - Po1 1 1210697 2312666 424.59
##
## Step: AIC=398.07
## .outcome ~ M + Ed + Po1 + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - U1 1 12059 1141381 396.46
## <none> 1129322 398.07
## - U2 1 70320 1199642 398.30
## - Prob 1 184898 1314220 401.68
## - M 1 213495 1342817 402.48
## - Ed 1 410205 1539527 407.53
## - Ineq 1 811850 1941172 416.11
## - Po1 1 1468739 2598061 426.90
##
## Step: AIC=396.46
## .outcome ~ M + Ed + Po1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1141381 396.46
## - U2 1 105272 1246653 397.73
## - Prob 1 193977 1335359 400.27
## - M 1 212014 1353395 400.77
## - Ed 1 416554 1557936 405.97
## - Ineq 1 862060 2003441 415.28
## - Po1 1 2430506 3571887 436.67
## Start: AIC=420.46
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 68 1045901 418.47
## - NW 1 1498 1047331 418.52
## - LF 1 2324 1048157 418.55
## - Pop 1 2395 1048229 418.55
## - So 1 5141 1050974 418.65
## - Po2 1 10101 1055935 418.83
## - M.F 1 14201 1060035 418.98
## - U1 1 36286 1082119 419.76
## - Po1 1 46319 1092153 420.11
## <none> 1045834 420.46
## - Wealth 1 91888 1137721 421.66
## - Prob 1 102549 1148382 422.02
## - U2 1 105878 1151711 422.13
## - M 1 107176 1153009 422.17
## - Ed 1 235506 1281339 426.18
## - Ineq 1 380798 1426632 430.26
##
## Step: AIC=418.47
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 1590 1047491 416.52
## - LF 1 2398 1048299 416.55
## - Pop 1 3681 1049582 416.60
## - So 1 5393 1051294 416.66
## - Po2 1 10187 1056088 416.83
## - M.F 1 15024 1060925 417.01
## - U1 1 36456 1082357 417.77
## - Po1 1 47444 1093345 418.15
## <none> 1045901 418.47
## - Wealth 1 93714 1139615 419.73
## - U2 1 107256 1153157 420.18
## - M 1 107425 1153326 420.18
## - Prob 1 135989 1181890 421.11
## - Ed 1 236606 1282507 424.22
## - Ineq 1 381056 1426957 428.27
##
## Step: AIC=416.52
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 1833 1049324 414.59
## - Pop 1 3879 1051370 414.66
## - Po2 1 9131 1056622 414.85
## - So 1 9405 1056896 414.86
## - M.F 1 13501 1060992 415.01
## - U1 1 34967 1082458 415.77
## - Po1 1 46262 1093753 416.17
## <none> 1047491 416.52
## - Wealth 1 92286 1139777 417.73
## - U2 1 106464 1153955 418.20
## - M 1 116434 1163925 418.53
## - Prob 1 134489 1181979 419.11
## - Ed 1 238108 1285599 422.31
## - Ineq 1 400353 1447843 426.82
##
## Step: AIC=414.59
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + Pop + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 5739 1055063 412.80
## - Po2 1 7521 1056845 412.86
## - M.F 1 13023 1062347 413.06
## - So 1 17706 1067030 413.23
## - U1 1 34630 1083954 413.82
## - Po1 1 44474 1093798 414.17
## <none> 1049324 414.59
## - Wealth 1 90584 1139908 415.74
## - U2 1 108081 1157405 416.32
## - Prob 1 142747 1192071 417.44
## - M 1 151837 1201161 417.73
## - Ed 1 254361 1303685 420.84
## - Ineq 1 432301 1481625 425.70
##
## Step: AIC=412.8
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 4001 1059064 410.94
## - So 1 19897 1074960 411.51
## - M.F 1 19922 1074985 411.51
## - U1 1 32140 1087203 411.94
## - Po1 1 39237 1094300 412.19
## <none> 1055063 412.80
## - Wealth 1 93434 1148497 414.02
## - U2 1 102344 1157407 414.32
## - Prob 1 137675 1192738 415.46
## - M 1 147083 1202146 415.76
## - Ed 1 253633 1308696 418.98
## - Ineq 1 427805 1482868 423.73
##
## Step: AIC=410.94
## .outcome ~ M + So + Ed + Po1 + M.F + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - So 1 17352 1076416 409.56
## - M.F 1 20099 1079162 409.66
## - U1 1 29150 1088214 409.97
## <none> 1059064 410.94
## - U2 1 98847 1157910 412.33
## - Wealth 1 100502 1159566 412.39
## - Prob 1 134036 1193100 413.47
## - M 1 143228 1202292 413.76
## - Ed 1 251050 1310114 417.03
## - Ineq 1 487870 1546934 423.34
## - Po1 1 521546 1580610 424.16
##
## Step: AIC=409.56
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - M.F 1 19079 1095495 408.23
## - U1 1 45622 1122038 409.14
## <none> 1076416 409.56
## - Wealth 1 102037 1178453 411.00
## - Prob 1 116684 1193100 411.47
## - U2 1 129990 1206406 411.89
## - M 1 170600 1247016 413.15
## - Ed 1 239334 1315750 415.19
## - Po1 1 554937 1631353 423.36
## - Ineq 1 564391 1640807 423.58
##
## Step: AIC=408.23
## .outcome ~ M + Ed + Po1 + U1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - U1 1 28893 1124389 407.22
## <none> 1095495 408.23
## - Prob 1 105283 1200778 409.71
## - U2 1 112504 1207999 409.94
## - Wealth 1 147693 1243188 411.03
## - M 1 172151 1267646 411.77
## - Ed 1 449167 1544662 419.28
## - Po1 1 539118 1634613 421.43
## - Ineq 1 841861 1937356 427.89
##
## Step: AIC=407.22
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1124389 407.22
## - Prob 1 103897 1228285 408.57
## - U2 1 121445 1245833 409.11
## - M 1 158255 1282644 410.22
## - Wealth 1 170451 1294839 410.58
## - Ed 1 447271 1571659 417.94
## - Po1 1 659616 1784005 422.76
## - Ineq 1 897131 2021519 427.51
## Start: AIC=424.7
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 13 1169259 422.70
## - Time 1 17 1169263 422.70
## - NW 1 1884 1171129 422.76
## - Pop 1 2650 1171896 422.79
## - LF 1 2675 1171920 422.79
## - Po2 1 29852 1199097 423.66
## - Wealth 1 43990 1213236 424.11
## - M.F 1 44843 1214089 424.13
## - U1 1 62732 1231978 424.69
## <none> 1169245 424.70
## - Prob 1 63480 1232725 424.71
## - Po1 1 105464 1274709 425.98
## - U2 1 154315 1323560 427.41
## - M 1 236819 1406064 429.71
## - Ineq 1 267163 1436408 430.52
## - Ed 1 292816 1462062 431.20
##
## Step: AIC=422.7
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 22 1169281 420.70
## - NW 1 2248 1171507 420.78
## - Pop 1 2669 1171928 420.79
## - LF 1 3381 1172640 420.81
## - Po2 1 29841 1199100 421.66
## - M.F 1 45008 1214267 422.14
## - Wealth 1 54190 1223449 422.42
## <none> 1169259 422.70
## - Prob 1 65634 1234893 422.78
## - U1 1 68087 1237345 422.85
## - Po1 1 105731 1274989 423.99
## - U2 1 157130 1326389 425.49
## - M 1 244098 1413356 427.91
## - Ed 1 296352 1465610 429.29
## - Ineq 1 351474 1520733 430.69
##
## Step: AIC=420.7
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 2230 1171511 418.78
## - Pop 1 2951 1172232 418.80
## - LF 1 3360 1172641 418.81
## - Po2 1 33636 1202917 419.78
## - M.F 1 46855 1216136 420.20
## - Wealth 1 54228 1223509 420.43
## <none> 1169281 420.70
## - U1 1 70640 1239921 420.93
## - Prob 1 100936 1270217 421.85
## - Po1 1 118173 1287454 422.36
## - U2 1 163122 1332403 423.67
## - M 1 249527 1418808 426.05
## - Ed 1 296392 1465673 427.29
## - Ineq 1 351456 1520738 428.69
##
## Step: AIC=418.78
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 2516 1174027 416.86
## - Pop 1 2835 1174345 416.87
## - Po2 1 31439 1202950 417.78
## - M.F 1 44863 1216374 418.20
## - Wealth 1 53645 1225156 418.48
## <none> 1171511 418.78
## - U1 1 79381 1250891 419.27
## - Prob 1 104737 1276248 420.03
## - Po1 1 115945 1287456 420.36
## - U2 1 191920 1363430 422.54
## - Ed 1 299374 1470885 425.42
## - M 1 325577 1497088 426.09
## - Ineq 1 445563 1617074 429.02
##
## Step: AIC=416.86
## .outcome ~ M + Ed + Po1 + Po2 + M.F + Pop + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 3835 1177862 414.98
## - Po2 1 29343 1203370 415.80
## - M.F 1 47521 1221548 416.37
## - Wealth 1 56796 1230823 416.65
## <none> 1174027 416.86
## - U1 1 79806 1253833 417.36
## - Prob 1 102452 1276479 418.04
## - Po1 1 113444 1287471 418.36
## - U2 1 190075 1364102 420.56
## - Ed 1 315352 1489379 423.90
## - M 1 340564 1514591 424.54
## - Ineq 1 446468 1620495 427.10
##
## Step: AIC=414.98
## .outcome ~ M + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 28292 1206154 413.88
## - Wealth 1 54854 1232716 414.71
## <none> 1177862 414.98
## - M.F 1 79035 1256897 415.45
## - U1 1 84868 1262729 415.63
## - Prob 1 99586 1277448 416.07
## - Po1 1 109802 1287664 416.37
## - U2 1 192761 1370623 418.74
## - Ed 1 313621 1491483 421.95
## - M 1 361762 1539624 423.16
## - Ineq 1 469591 1647453 425.73
##
## Step: AIC=413.88
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 55900 1262054 413.61
## <none> 1206154 413.88
## - U1 1 84409 1290563 414.45
## - M.F 1 97901 1304055 414.85
## - Prob 1 103906 1310060 415.02
## - U2 1 195527 1401681 417.59
## - Ed 1 293999 1500153 420.17
## - M 1 365520 1571674 421.94
## - Ineq 1 479144 1685298 424.59
## - Po1 1 745982 1952136 430.18
##
## Step: AIC=413.61
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1262054 413.61
## - M.F 1 129798 1391852 415.33
## - Prob 1 141364 1403418 415.64
## - U1 1 143814 1405868 415.71
## - U2 1 291518 1553572 419.50
## - M 1 316817 1578871 420.12
## - Ed 1 428745 1690798 422.72
## - Ineq 1 466941 1728995 423.57
## - Po1 1 1336004 2598058 439.04
## Start: AIC=421.63
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 2497 853372 419.74
## - M.F 1 9990 860865 420.08
## - LF 1 10413 861288 420.10
## - Wealth 1 15833 866708 420.35
## - U1 1 29866 880742 420.97
## - Pop 1 37336 888211 421.30
## - NW 1 41479 892354 421.48
## <none> 850875 421.63
## - Time 1 52571 903447 421.97
## - M 1 76288 927163 422.98
## - U2 1 101862 952737 424.04
## - Po2 1 110156 961031 424.38
## - Prob 1 222913 1073788 428.70
## - Po1 1 263907 1114783 430.16
## - Ineq 1 309553 1160428 431.73
## - Ed 1 344425 1195300 432.88
##
## Step: AIC=419.74
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 10088 863460 418.20
## - Wealth 1 15256 868628 418.43
## - LF 1 16020 869392 418.47
## - Pop 1 35143 888516 419.32
## - U1 1 39959 893331 419.53
## - NW 1 44132 897505 419.71
## <none> 853372 419.74
## - Time 1 55240 908612 420.19
## - M 1 95819 949191 421.89
## - Po2 1 115510 968883 422.69
## - U2 1 126781 980153 423.14
## - Prob 1 240970 1094342 427.44
## - Po1 1 273499 1126872 428.58
## - Ineq 1 330582 1183955 430.51
## - Ed 1 352174 1205546 431.22
##
## Step: AIC=418.2
## .outcome ~ M + Ed + Po1 + Po2 + LF + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 8349 871809 416.58
## - Wealth 1 12916 876377 416.78
## - U1 1 29994 893455 417.53
## - NW 1 36403 899863 417.81
## <none> 863460 418.20
## - Pop 1 48943 912403 418.35
## - Time 1 75569 939029 419.47
## - U2 1 122565 986025 421.38
## - Po2 1 127035 990495 421.55
## - M 1 164169 1027629 422.99
## - Prob 1 232559 1096019 425.50
## - Po1 1 311166 1174626 428.20
## - Ineq 1 337981 1201442 429.08
## - Ed 1 395960 1259420 430.92
##
## Step: AIC=416.58
## .outcome ~ M + Ed + Po1 + Po2 + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 9184 880994 414.98
## - U1 1 25760 897569 415.71
## - NW 1 29206 901015 415.86
## - Pop 1 44146 915955 416.50
## <none> 871809 416.58
## - Time 1 67254 939063 417.47
## - Po2 1 122094 993904 419.69
## - U2 1 130347 1002156 420.01
## - M 1 181695 1053504 421.96
## - Prob 1 231126 1102935 423.75
## - Po1 1 315758 1187568 426.63
## - Ineq 1 330558 1202367 427.11
## - Ed 1 420806 1292615 429.94
##
## Step: AIC=414.98
## .outcome ~ M + Ed + Po1 + Po2 + Pop + NW + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - NW 1 20330 901324 413.87
## - U1 1 26720 907714 414.15
## - Pop 1 37565 918559 414.61
## <none> 880994 414.98
## - Time 1 62571 943565 415.66
## - Po2 1 123845 1004839 418.11
## - U2 1 151300 1032294 419.17
## - Prob 1 222396 1103390 421.76
## - M 1 230969 1111963 422.06
## - Po1 1 342819 1223813 425.80
## - Ineq 1 379935 1260929 426.97
## - Ed 1 560722 1441716 432.19
##
## Step: AIC=413.87
## .outcome ~ M + Ed + Po1 + Po2 + Pop + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - U1 1 24631 925955 412.93
## - Pop 1 30650 931974 413.18
## - Time 1 45395 946719 413.79
## <none> 901324 413.87
## - Po2 1 105010 1006334 416.17
## - U2 1 149643 1050967 417.86
## - Prob 1 228767 1130091 420.70
## - Po1 1 322567 1223890 423.81
## - M 1 429938 1331262 427.08
## - Ineq 1 545219 1446543 430.32
## - Ed 1 549925 1451249 430.45
##
## Step: AIC=412.93
## .outcome ~ M + Ed + Po1 + Po2 + Pop + U2 + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 31790 957745 412.24
## - Pop 1 32874 958829 412.29
## <none> 925955 412.93
## - Po2 1 93176 1019131 414.67
## - U2 1 207373 1133328 418.81
## - Prob 1 215809 1141764 419.10
## - Po1 1 314800 1240755 422.34
## - M 1 421075 1347030 425.54
## - Ed 1 528487 1454442 428.54
## - Ineq 1 593546 1519501 430.24
##
## Step: AIC=412.24
## .outcome ~ M + Ed + Po1 + Po2 + Pop + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 957745 412.24
## - Po2 1 71101 1028846 413.04
## - Pop 1 72318 1030063 413.08
## - Prob 1 184188 1141933 417.10
## - U2 1 202750 1160495 417.73
## - Po1 1 284986 1242731 420.40
## - M 1 389285 1347031 423.54
## - Ed 1 636319 1594064 430.11
## - Ineq 1 687953 1645698 431.35
## Start: AIC=394.41
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 22 847908 392.41
## - Wealth 1 79 847965 392.41
## - Po1 1 2117 850003 392.50
## - Po2 1 4204 852091 392.59
## - So 1 5481 853367 392.64
## - Pop 1 10443 858329 392.85
## - NW 1 10956 858842 392.87
## - M.F 1 14783 862670 393.03
## - Time 1 36387 884273 393.92
## <none> 847886 394.41
## - U1 1 159188 1007075 398.61
## - M 1 175480 1023366 399.18
## - Prob 1 184660 1032547 399.50
## - Ineq 1 195760 1043646 399.89
## - U2 1 250956 1098842 401.74
## - Ed 1 276734 1124621 402.58
##
## Step: AIC=392.41
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 78 847986 390.42
## - Po1 1 2171 850079 390.50
## - Po2 1 4990 852898 390.62
## - So 1 6618 854526 390.69
## - Pop 1 11184 859092 390.88
## - NW 1 12338 860246 390.93
## - M.F 1 17463 865371 391.15
## - Time 1 37133 885041 391.96
## <none> 847908 392.41
## - U1 1 184343 1032251 397.49
## - M 1 185267 1033175 397.53
## - Ineq 1 199398 1047306 398.02
## - Prob 1 200046 1047954 398.04
## - U2 1 251386 1099294 399.76
## - Ed 1 296225 1144133 401.20
##
## Step: AIC=390.42
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + Pop + NW + U1 + U2 +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po1 1 2200 850186 388.51
## - Po2 1 4946 852932 388.62
## - So 1 6742 854729 388.70
## - Pop 1 12337 860323 388.94
## - NW 1 12506 860492 388.94
## - M.F 1 17799 865786 389.16
## - Time 1 37056 885042 389.96
## <none> 847986 390.42
## - M 1 192116 1040102 395.77
## - U1 1 200856 1048843 396.07
## - Prob 1 241551 1089537 397.44
## - U2 1 275267 1123254 398.54
## - Ineq 1 316090 1164076 399.82
## - Ed 1 316588 1164575 399.84
##
## Step: AIC=388.51
## .outcome ~ M + So + Ed + Po2 + M.F + Pop + NW + U1 + U2 + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 8332 858518 386.86
## - NW 1 11653 861839 387.00
## - Pop 1 14035 864221 387.10
## - M.F 1 23831 874017 387.50
## - Time 1 37298 887484 388.05
## <none> 850186 388.51
## - M 1 204814 1055000 394.28
## - U1 1 237379 1087565 395.37
## - Prob 1 245158 1095344 395.63
## - Ineq 1 332493 1182679 398.39
## - Ed 1 350529 1200715 398.94
## - U2 1 378178 1228364 399.76
## - Po2 1 431466 1281652 401.29
##
## Step: AIC=386.86
## .outcome ~ M + Ed + Po2 + M.F + Pop + NW + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - NW 1 5994 864512 385.11
## - Pop 1 12342 870860 385.37
## - M.F 1 26753 885271 385.96
## - Time 1 31096 889614 386.14
## <none> 858518 386.86
## - M 1 198894 1057412 392.36
## - U1 1 232076 1090594 393.47
## - Prob 1 241347 1099865 393.78
## - Ineq 1 326664 1185182 396.47
## - Ed 1 361347 1219865 397.51
## - U2 1 381247 1239765 398.09
## - Po2 1 446556 1305074 399.94
##
## Step: AIC=385.11
## .outcome ~ M + Ed + Po2 + M.F + Pop + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 14967 879478 383.73
## - M.F 1 23282 887794 384.07
## - Time 1 26943 891454 384.22
## <none> 864512 385.11
## - U1 1 227006 1091517 391.50
## - Prob 1 245982 1110494 392.12
## - M 1 254012 1118524 392.38
## - Ed 1 355358 1219870 395.51
## - U2 1 375289 1239801 396.09
## - Ineq 1 449618 1314130 398.19
## - Po2 1 665780 1530291 403.67
##
## Step: AIC=383.73
## .outcome ~ M + Ed + Po2 + M.F + U1 + U2 + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 44343 923821 383.50
## - M.F 1 50099 929578 383.72
## <none> 879478 383.73
## - M 1 258065 1137544 390.99
## - Prob 1 261564 1141043 391.10
## - U1 1 263569 1143048 391.16
## - Ed 1 341823 1221302 393.55
## - U2 1 395423 1274901 395.09
## - Ineq 1 441834 1321312 396.38
## - Po2 1 877909 1757388 406.65
##
## Step: AIC=383.5
## .outcome ~ M + Ed + Po2 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 923821 383.50
## - M.F 1 86827 1010648 384.73
## - Prob 1 228385 1152206 389.45
## - M 1 234012 1157833 389.63
## - U1 1 241843 1165664 389.87
## - Ed 1 370124 1293945 393.63
## - U2 1 381617 1305439 393.95
## - Ineq 1 419036 1342858 394.96
## - Po2 1 892867 1816688 405.84
## Start: AIC=399.46
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 176 761177 397.47
## - LF 1 311 761312 397.48
## - M.F 1 2358 763359 397.58
## - NW 1 6056 767057 397.76
## - Time 1 18418 779419 398.35
## - Wealth 1 20134 781135 398.43
## - U1 1 25039 786040 398.66
## <none> 761001 399.46
## - Pop 1 93721 854722 401.76
## - Prob 1 113716 874718 402.62
## - U2 1 119889 880891 402.88
## - Po2 1 128511 889512 403.24
## - M 1 172304 933306 405.02
## - Ed 1 241898 1002900 407.68
## - Po1 1 264520 1025521 408.50
## - Ineq 1 309390 1070392 410.09
##
## Step: AIC=397.47
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 695 761872 395.51
## - M.F 1 2207 763384 395.58
## - NW 1 7896 769073 395.85
## - Time 1 18499 779676 396.36
## - Wealth 1 26168 787345 396.72
## - U1 1 29468 790645 396.88
## <none> 761177 397.47
## - Pop 1 93750 854927 399.77
## - Prob 1 119576 880753 400.87
## - U2 1 125588 886765 401.12
## - Po2 1 128366 889543 401.24
## - M 1 178119 939296 403.25
## - Ed 1 241862 1003039 405.68
## - Po1 1 267087 1028264 406.60
## - Ineq 1 377456 1138633 410.37
##
## Step: AIC=395.51
## .outcome ~ M + Ed + Po1 + Po2 + M.F + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 4599 766471 393.73
## - NW 1 7270 769142 393.86
## - Time 1 17915 779788 394.37
## - Wealth 1 27161 789034 394.80
## - U1 1 28905 790778 394.88
## <none> 761872 395.51
## - Pop 1 99712 861585 398.06
## - Prob 1 124620 886492 399.11
## - U2 1 127945 889818 399.25
## - Po2 1 130035 891907 399.34
## - M 1 190423 952295 401.76
## - Ed 1 244014 1005886 403.79
## - Po1 1 269605 1031477 404.72
## - Ineq 1 387019 1148891 408.71
##
## Step: AIC=393.73
## .outcome ~ M + Ed + Po1 + Po2 + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 5958 772429 392.02
## - Time 1 14255 780726 392.41
## - Wealth 1 24347 790819 392.89
## - U1 1 35162 801633 393.39
## <none> 766471 393.73
## - Pop 1 99467 865938 396.24
## - Prob 1 120745 887216 397.14
## - U2 1 126948 893419 397.40
## - Po2 1 131605 898077 397.59
## - M 1 186991 953463 399.81
## - Ed 1 287819 1054290 403.53
## - Po1 1 293639 1060111 403.73
## - Ineq 1 439130 1205601 408.49
##
## Step: AIC=392.02
## .outcome ~ M + Ed + Po1 + Po2 + Pop + U1 + U2 + Wealth + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 9643 782073 390.48
## - Wealth 1 23320 795749 391.12
## - U1 1 37829 810258 391.79
## <none> 772429 392.02
## - Pop 1 96706 869135 394.38
## - Prob 1 123557 895987 395.51
## - Po2 1 125770 898199 395.60
## - U2 1 128819 901248 395.72
## - M 1 231860 1004289 399.73
## - Ed 1 282995 1055424 401.57
## - Po1 1 287965 1060394 401.74
## - Ineq 1 494118 1266547 408.31
##
## Step: AIC=390.48
## .outcome ~ M + Ed + Po1 + Po2 + Pop + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 25640 807713 389.67
## - U1 1 38556 820629 390.26
## <none> 782073 390.48
## - Po2 1 116593 898666 393.62
## - U2 1 124593 906665 393.94
## - Prob 1 131935 914008 394.24
## - Pop 1 143423 925496 394.71
## - M 1 228724 1010797 397.97
## - Po1 1 278489 1060562 399.75
## - Ed 1 312536 1094609 400.91
## - Ineq 1 524689 1306761 407.47
##
## Step: AIC=389.67
## .outcome ~ M + Ed + Po1 + Po2 + Pop + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 807713 389.67
## - U1 1 49738 857451 389.88
## - Po2 1 123306 931018 392.93
## - Pop 1 155853 963565 394.20
## - U2 1 156090 963803 394.21
## - Prob 1 171735 979448 394.80
## - M 1 205228 1012941 396.05
## - Po1 1 316190 1123903 399.89
## - Ed 1 392739 1200452 402.33
## - Ineq 1 568235 1375948 407.38
## Start: AIC=402.48
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po1 1 374 826030 400.50
## - So 1 4792 830447 400.70
## - Wealth 1 5701 831357 400.74
## - Pop 1 6844 832499 400.79
## - LF 1 7280 832935 400.81
## - Po2 1 20012 845668 401.37
## - M.F 1 22179 847834 401.46
## - NW 1 23679 849334 401.53
## <none> 825655 402.48
## - Time 1 56163 881818 402.92
## - U1 1 62010 887665 403.16
## - Ineq 1 150284 975939 406.67
## - M 1 257856 1083512 410.54
## - Prob 1 283609 1109265 411.41
## - U2 1 289574 1115230 411.61
## - Ed 1 307919 1133574 412.21
##
## Step: AIC=400.5
## .outcome ~ M + So + Ed + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 5079 831108 398.73
## - Wealth 1 5380 831410 398.74
## - LF 1 7213 833243 398.82
## - Pop 1 7925 833954 398.85
## - M.F 1 22995 849024 399.51
## - NW 1 24308 850338 399.57
## <none> 826030 400.50
## - Time 1 55904 881934 400.92
## - U1 1 63587 889616 401.24
## - Ineq 1 156451 982480 404.92
## - M 1 278829 1104858 409.26
## - U2 1 292171 1118201 409.70
## - Po2 1 296295 1122325 409.84
## - Prob 1 296711 1122740 409.85
## - Ed 1 327661 1153690 410.86
##
## Step: AIC=398.73
## .outcome ~ M + Ed + Po2 + LF + M.F + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 5261 836369 396.96
## - Pop 1 9908 841016 397.16
## - NW 1 19340 850448 397.58
## - LF 1 21832 852940 397.68
## - M.F 1 32819 863927 398.16
## <none> 831108 398.73
## - Time 1 53176 884284 399.02
## - U1 1 61391 892499 399.36
## - Ineq 1 153321 984429 402.99
## - M 1 283185 1114293 407.57
## - U2 1 288633 1119741 407.75
## - Prob 1 292671 1123779 407.89
## - Ed 1 337422 1168530 409.33
## - Po2 1 346031 1177139 409.60
##
## Step: AIC=396.96
## .outcome ~ M + Ed + Po2 + LF + M.F + Pop + NW + U1 + U2 + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 13413 849782 395.55
## - NW 1 16609 852977 395.69
## - LF 1 19557 855926 395.81
## - M.F 1 34278 870647 396.44
## <none> 836369 396.96
## - Time 1 49171 885539 397.07
## - U1 1 56178 892546 397.36
## - M 1 287511 1123880 405.89
## - U2 1 295232 1131601 406.14
## - Prob 1 305682 1142050 406.48
## - Ineq 1 315356 1151724 406.80
## - Ed 1 336468 1172837 407.47
## - Po2 1 340955 1177323 407.61
##
## Step: AIC=395.55
## .outcome ~ M + Ed + Po2 + LF + M.F + NW + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - LF 1 15402 865184 394.21
## - NW 1 20665 870447 394.44
## - M.F 1 26907 876689 394.70
## <none> 849782 395.55
## - U1 1 68226 918008 396.40
## - Time 1 78770 928552 396.83
## - U2 1 289165 1138947 404.38
## - Ineq 1 305253 1155035 404.90
## - M 1 308837 1158619 405.02
## - Ed 1 340148 1189930 406.00
## - Prob 1 345349 1195131 406.17
## - Po2 1 416579 1266361 408.31
##
## Step: AIC=394.21
## .outcome ~ M + Ed + Po2 + M.F + NW + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - NW 1 12740 877924 392.75
## - M.F 1 13799 878983 392.80
## <none> 865184 394.21
## - Time 1 64545 929729 394.87
## - U1 1 97542 962726 396.16
## - U2 1 286537 1151721 402.80
## - Prob 1 334517 1199701 404.31
## - M 1 348499 1213682 404.74
## - Po2 1 401688 1266872 406.32
## - Ineq 1 445591 1310775 407.58
## - Ed 1 581613 1446797 411.24
##
## Step: AIC=392.75
## .outcome ~ M + Ed + Po2 + M.F + U1 + U2 + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 20310 898234 391.60
## <none> 877924 392.75
## - Time 1 61440 939364 393.26
## - U1 1 96390 974315 394.61
## - U2 1 316606 1194530 402.15
## - Prob 1 321849 1199774 402.31
## - M 1 375713 1253637 403.93
## - Po2 1 557234 1435158 408.94
## - Ed 1 571715 1449639 409.31
## - Ineq 1 740450 1618374 413.38
##
## Step: AIC=391.6
## .outcome ~ M + Ed + Po2 + U1 + U2 + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 41926 940160 391.29
## <none> 898234 391.60
## - U1 1 154430 1052664 395.47
## - Prob 1 324808 1223042 401.02
## - U2 1 347221 1245456 401.69
## - M 1 357274 1255509 401.99
## - Ed 1 599379 1497614 408.51
## - Po2 1 677103 1575338 410.39
## - Ineq 1 722320 1620555 411.43
##
## Step: AIC=391.29
## .outcome ~ M + Ed + Po2 + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 940160 391.29
## - U1 1 114389 1054549 393.54
## - U2 1 305351 1245511 399.69
## - M 1 331776 1271936 400.47
## - Prob 1 332415 1272575 400.49
## - Ed 1 675118 1615278 409.31
## - Ineq 1 750047 1690207 410.99
## - Po2 1 769443 1709602 411.41
## Start: AIC=428.72
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 4189 1024717 426.88
## - Time 1 9324 1029852 427.07
## - NW 1 17196 1037724 427.37
## - LF 1 18650 1039178 427.42
## - So 1 19694 1040222 427.46
## - Po2 1 27209 1047737 427.74
## - Wealth 1 36449 1056977 428.09
## - M.F 1 43848 1064376 428.36
## - U1 1 44566 1065094 428.39
## <none> 1020528 428.72
## - U2 1 72533 1093061 429.40
## - Prob 1 95324 1115852 430.20
## - M 1 102008 1122536 430.43
## - Po1 1 123032 1143560 431.16
## - Ed 1 294362 1314890 436.60
## - Ineq 1 444584 1465111 440.82
##
## Step: AIC=426.88
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 7242 1031959 425.15
## - NW 1 17118 1041835 425.52
## - LF 1 17841 1042559 425.55
## - So 1 19595 1044312 425.62
## - Po2 1 30672 1055389 426.03
## - Wealth 1 38935 1063652 426.33
## - M.F 1 39686 1064403 426.36
## - U1 1 45191 1069908 426.56
## <none> 1024717 426.88
## - U2 1 80498 1105215 427.83
## - Prob 1 101999 1126716 428.58
## - M 1 104642 1129359 428.67
## - Po1 1 137393 1162110 429.79
## - Ed 1 295927 1320644 434.77
## - Ineq 1 458084 1482801 439.29
##
## Step: AIC=425.15
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 10490 1042449 423.55
## - LF 1 15453 1047413 423.73
## - So 1 21261 1053221 423.95
## - Po2 1 23828 1055788 424.04
## - Wealth 1 31703 1063663 424.33
## - U1 1 40782 1072741 424.66
## - M.F 1 45786 1077746 424.85
## <none> 1031959 425.15
## - U2 1 76480 1108439 425.94
## - M 1 112809 1144768 427.20
## - Prob 1 121236 1153196 427.48
## - Po1 1 130160 1162120 427.79
## - Ed 1 288698 1320657 432.77
## - Ineq 1 451117 1483077 437.30
##
## Step: AIC=423.55
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 8816 1051265 421.88
## - So 1 16279 1058729 422.15
## - Po2 1 17579 1060028 422.20
## - Wealth 1 23231 1065680 422.41
## - M.F 1 36533 1078982 422.89
## - U1 1 39870 1082319 423.01
## <none> 1042449 423.55
## - U2 1 90422 1132871 424.79
## - Prob 1 110751 1153201 425.49
## - Po1 1 124046 1166496 425.93
## - M 1 210420 1252870 428.72
## - Ed 1 280654 1323104 430.85
## - Ineq 1 464549 1506998 435.92
##
## Step: AIC=421.88
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - So 1 10209 1061474 420.25
## - Po2 1 12099 1063364 420.32
## - Wealth 1 21103 1072369 420.65
## - M.F 1 27766 1079031 420.89
## - U1 1 31085 1082350 421.01
## <none> 1051265 421.88
## - U2 1 83620 1134885 422.86
## - Prob 1 107360 1158625 423.67
## - Po1 1 115240 1166505 423.93
## - M 1 208563 1259828 426.93
## - Ed 1 273569 1324834 428.90
## - Ineq 1 457283 1508548 433.96
##
## Step: AIC=420.25
## .outcome ~ M + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 12878 1074352 418.72
## - Wealth 1 23498 1084971 419.11
## - U1 1 26397 1087871 419.21
## - M.F 1 35557 1097031 419.54
## <none> 1061474 420.25
## - U2 1 75057 1136531 420.92
## - Po1 1 112642 1174115 422.19
## - Prob 1 176939 1238413 424.27
## - M 1 210735 1272209 425.32
## - Ed 1 310525 1371999 428.26
## - Ineq 1 449968 1511441 432.04
##
## Step: AIC=418.72
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - U1 1 26271 1100623 417.67
## - Wealth 1 28338 1102690 417.74
## - M.F 1 43677 1118029 418.28
## <none> 1074352 418.72
## - U2 1 73193 1147545 419.29
## - Prob 1 171818 1246169 422.51
## - M 1 199668 1274019 423.37
## - Ed 1 303888 1378239 426.44
## - Ineq 1 538158 1612510 432.56
## - Po1 1 1017920 2092271 442.72
##
## Step: AIC=417.67
## .outcome ~ M + Ed + Po1 + M.F + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - M.F 1 20455 1121077 416.38
## - Wealth 1 31982 1132605 416.78
## <none> 1100623 417.67
## - U2 1 67227 1167850 417.98
## - Prob 1 164606 1265229 421.10
## - M 1 204871 1305494 422.32
## - Ed 1 289478 1390100 424.77
## - Ineq 1 596141 1696764 432.55
## - Po1 1 1458298 2558921 448.57
##
## Step: AIC=416.38
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 34984 1156062 415.58
## <none> 1121077 416.38
## - U2 1 93943 1215020 417.52
## - Prob 1 158911 1279988 419.55
## - M 1 248039 1369116 422.18
## - Ed 1 496113 1617191 428.67
## - Ineq 1 632159 1753237 431.82
## - Po1 1 1439471 2560548 446.59
##
## Step: AIC=415.58
## .outcome ~ M + Ed + Po1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1156062 415.58
## - U2 1 103128 1259189 416.91
## - Prob 1 206601 1362663 419.99
## - M 1 225856 1381918 420.54
## - Ed 1 537090 1693152 428.46
## - Ineq 1 846195 2002257 435.00
## - Po1 1 2988982 4145044 463.38
## Start: AIC=426.45
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 1022 963835 424.49
## - Time 1 8543 971356 424.79
## - NW 1 21194 984007 425.30
## - Wealth 1 29288 992101 425.62
## - LF 1 35661 998474 425.87
## - So 1 45704 1008517 426.26
## - Po2 1 47257 1010070 426.32
## <none> 962813 426.45
## - U1 1 87033 1049845 427.82
## - U2 1 112528 1075341 428.76
## - Po1 1 146820 1109633 429.98
## - M.F 1 165107 1127919 430.62
## - M 1 176691 1139504 431.02
## - Prob 1 185990 1148803 431.34
## - Ineq 1 205858 1168671 432.00
## - Ed 1 464449 1427262 439.80
##
## Step: AIC=424.49
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 10324 974159 422.90
## - NW 1 20832 984667 423.32
## - Wealth 1 29965 993801 423.68
## - LF 1 34644 998479 423.87
## - So 1 44688 1008524 424.26
## - Po2 1 46641 1010476 424.33
## <none> 963835 424.49
## - U1 1 86993 1050829 425.86
## - U2 1 111683 1075518 426.77
## - Po1 1 145988 1109823 427.99
## - M 1 175974 1139809 429.03
## - Prob 1 185404 1149239 429.35
## - M.F 1 187196 1151031 429.41
## - Ineq 1 240978 1204813 431.19
## - Ed 1 464756 1428591 437.84
##
## Step: AIC=422.9
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 31861 1006020 422.16
## - Wealth 1 35518 1009677 422.30
## - So 1 36040 1010199 422.32
## - LF 1 36946 1011104 422.36
## <none> 974159 422.90
## - Po2 1 68932 1043090 423.57
## - U1 1 95863 1070022 424.57
## - U2 1 122538 1096696 425.53
## - M.F 1 179251 1153410 427.49
## - Po1 1 186317 1160476 427.73
## - M 1 187673 1161831 427.78
## - Ineq 1 260396 1234555 430.14
## - Prob 1 307262 1281421 431.60
## - Ed 1 456868 1431027 435.90
##
## Step: AIC=422.16
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 20638 1026658 420.95
## - Wealth 1 22846 1028865 421.04
## <none> 1006020 422.16
## - Po2 1 53167 1059187 422.17
## - So 1 76648 1082667 423.02
## - U1 1 77573 1083593 423.06
## - U2 1 119690 1125709 424.54
## - M.F 1 149913 1155933 425.58
## - Po1 1 173539 1179558 426.37
## - M 1 272808 1278828 429.52
## - Ineq 1 273563 1279582 429.54
## - Prob 1 282569 1288589 429.81
## - Ed 1 432805 1438825 434.12
##
## Step: AIC=420.95
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 18804 1045461 419.66
## - Po2 1 44892 1071550 420.62
## <none> 1026658 420.95
## - U1 1 57478 1084136 421.08
## - U2 1 114821 1141479 423.09
## - So 1 129537 1156194 423.59
## - M.F 1 134343 1161000 423.75
## - Po1 1 161688 1188345 424.66
## - Ineq 1 253159 1279817 427.55
## - M 1 271802 1298460 428.11
## - Prob 1 285920 1312578 428.53
## - Ed 1 415901 1442559 432.22
##
## Step: AIC=419.66
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 46152 1091613 419.34
## <none> 1045461 419.66
## - U1 1 64484 1109945 419.99
## - U2 1 128715 1174177 422.19
## - So 1 147152 1192613 422.80
## - M.F 1 156917 1202378 423.11
## - Po1 1 176454 1221915 423.74
## - M 1 253240 1298702 426.12
## - Ineq 1 280437 1325899 426.93
## - Prob 1 332920 1378381 428.44
## - Ed 1 482234 1527695 432.45
##
## Step: AIC=419.34
## .outcome ~ M + So + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1091613 419.34
## - U1 1 70835 1162448 419.80
## - So 1 116808 1208422 421.31
## - U2 1 137298 1228912 421.97
## - M.F 1 188008 1279621 423.54
## - M 1 250957 1342570 425.41
## - Prob 1 318270 1409884 427.32
## - Ineq 1 359360 1450973 428.44
## - Ed 1 447629 1539243 430.75
## - Po1 1 1513771 2605384 451.27
## Start: AIC=402.47
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 202 1060692 400.47
## - So 1 474 1060964 400.48
## - Pop 1 4198 1064689 400.61
## - NW 1 21486 1081976 401.19
## - M.F 1 23416 1083907 401.25
## - Po2 1 24126 1084617 401.28
## - Time 1 33953 1094444 401.60
## - Wealth 1 47158 1107648 402.03
## - M 1 55726 1116217 402.31
## - U1 1 58533 1119023 402.40
## - U2 1 58609 1119099 402.40
## <none> 1060491 402.47
## - Po1 1 67678 1128168 402.69
## - Ed 1 90889 1151380 403.43
## - Prob 1 167458 1227948 405.74
## - Ineq 1 221882 1282373 407.31
##
## Step: AIC=400.47
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 294 1060987 398.48
## - Pop 1 4046 1064739 398.61
## - NW 1 26148 1086841 399.35
## - Po2 1 28125 1088818 399.42
## - M.F 1 28394 1089086 399.42
## - Time 1 35931 1096623 399.67
## - Wealth 1 49040 1109732 400.10
## - M 1 55567 1116259 400.31
## - U2 1 58408 1119100 400.40
## <none> 1060692 400.47
## - U1 1 69197 1129890 400.75
## - Po1 1 74981 1135674 400.93
## - Ed 1 96545 1157238 401.61
## - Prob 1 177269 1237961 404.04
## - Ineq 1 231083 1291776 405.57
##
## Step: AIC=398.48
## .outcome ~ M + Ed + Po1 + Po2 + M.F + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 4213 1065199 396.63
## - Po2 1 27941 1088927 397.42
## - M.F 1 28211 1089198 397.43
## - NW 1 32072 1093059 397.55
## - Time 1 37349 1098336 397.73
## - Wealth 1 52311 1113298 398.22
## - M 1 58326 1119313 398.41
## <none> 1060987 398.48
## - U2 1 64218 1125205 398.60
## - Po1 1 74697 1135683 398.93
## - U1 1 77001 1137988 399.01
## - Ed 1 96251 1157238 399.61
## - Prob 1 181038 1242025 402.15
## - Ineq 1 257413 1318400 404.30
##
## Step: AIC=396.63
## .outcome ~ M + Ed + Po1 + Po2 + M.F + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 27853 1093052 395.55
## - NW 1 33781 1098981 395.75
## - Time 1 42493 1107693 396.03
## - M.F 1 43557 1108757 396.07
## - Wealth 1 48423 1113622 396.23
## - M 1 60848 1126047 396.63
## <none> 1065199 396.63
## - Po1 1 72277 1137477 396.99
## - U2 1 76599 1141799 397.13
## - U1 1 93655 1158854 397.66
## - Ed 1 95520 1160720 397.72
## - Prob 1 179399 1244598 400.23
## - Ineq 1 279026 1344226 403.00
##
## Step: AIC=395.55
## .outcome ~ M + Ed + Po1 + M.F + NW + U1 + U2 + Wealth + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 18241 1111294 394.15
## - NW 1 23107 1116160 394.31
## - Wealth 1 46217 1139270 395.05
## <none> 1093052 395.55
## - M 1 73662 1166715 395.90
## - U1 1 114276 1207328 397.13
## - Ed 1 119846 1212898 397.30
## - U2 1 119885 1212937 397.30
## - M.F 1 124571 1217623 397.44
## - Prob 1 151997 1245049 398.24
## - Ineq 1 306618 1399670 402.46
## - Po1 1 531358 1624410 407.82
##
## Step: AIC=394.15
## .outcome ~ M + Ed + Po1 + M.F + NW + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 16743 1128037 392.69
## - Wealth 1 38406 1149700 393.37
## <none> 1111294 394.15
## - M 1 66532 1177826 394.24
## - U1 1 109356 1220650 395.53
## - U2 1 123256 1234550 395.94
## - Prob 1 146636 1257930 396.61
## - Ed 1 156925 1268219 396.91
## - M.F 1 160060 1271354 396.99
## - Ineq 1 304470 1415764 400.87
## - Po1 1 533244 1644538 406.26
##
## Step: AIC=392.69
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 33936 1161972 391.76
## <none> 1128037 392.69
## - M 1 104698 1232735 393.88
## - U1 1 106814 1234851 393.95
## - U2 1 117737 1245774 394.26
## - Prob 1 129974 1258010 394.61
## - M.F 1 144764 1272801 395.04
## - Ed 1 149383 1277420 395.17
## - Ineq 1 406379 1534415 401.77
## - Po1 1 826364 1954400 410.47
##
## Step: AIC=391.76
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1161972 391.76
## - M 1 89845 1251817 392.44
## - U1 1 152806 1314778 394.20
## - Prob 1 166058 1328030 394.56
## - U2 1 171817 1333789 394.72
## - M.F 1 175485 1337457 394.82
## - Ed 1 198911 1360883 395.44
## - Ineq 1 434165 1596137 401.18
## - Po1 1 1139048 2301020 414.35
## Start: AIC=422.3
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 4186 869847 420.49
## - So 1 5011 870672 420.52
## - Po2 1 9211 874872 420.71
## - Pop 1 19686 885347 421.18
## - NW 1 24780 890441 421.40
## - Time 1 27974 893635 421.54
## - M.F 1 36267 901928 421.90
## <none> 865661 422.30
## - LF 1 49764 915426 422.48
## - Po1 1 61977 927638 423.00
## - M 1 150455 1016116 426.55
## - U1 1 212924 1078585 428.88
## - Prob 1 247048 1112709 430.09
## - U2 1 288622 1154283 431.52
## - Ineq 1 325356 1191017 432.74
## - Ed 1 407440 1273101 435.34
##
## Step: AIC=420.49
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 4415 874263 418.69
## - Po2 1 7857 877704 418.84
## - Pop 1 19697 889544 419.36
## - NW 1 22021 891869 419.46
## - Time 1 29266 899114 419.78
## - M.F 1 34742 904590 420.02
## <none> 869847 420.49
## - LF 1 47068 916915 420.54
## - Po1 1 60483 930330 421.11
## - M 1 146707 1016554 424.57
## - U1 1 222336 1092183 427.36
## - Prob 1 297282 1167129 429.95
## - U2 1 330114 1199962 431.04
## - Ineq 1 395130 1264977 433.09
## - Ed 1 451151 1320999 434.78
##
## Step: AIC=418.69
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 6662 880924 416.98
## - NW 1 17618 891880 417.46
## - Pop 1 21380 895643 417.63
## - Time 1 25193 899456 417.79
## - M.F 1 31329 905592 418.06
## - LF 1 45716 919979 418.67
## <none> 874263 418.69
## - Po1 1 58798 933061 419.22
## - M 1 142552 1016815 422.58
## - U1 1 255463 1129725 426.68
## - Prob 1 298747 1173009 428.15
## - U2 1 358936 1233199 430.10
## - Ineq 1 445679 1319941 432.75
## - Ed 1 466824 1341086 433.37
##
## Step: AIC=416.98
## .outcome ~ M + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 12718 893643 415.54
## - Time 1 19881 900805 415.85
## - Pop 1 23027 903951 415.99
## - M.F 1 29440 910364 416.26
## - LF 1 39674 920598 416.70
## <none> 880924 416.98
## - M 1 151513 1032437 421.17
## - U1 1 249385 1130310 424.70
## - Prob 1 293708 1174632 426.20
## - U2 1 359232 1240156 428.32
## - Ineq 1 460154 1341078 431.37
## - Ed 1 463705 1344629 431.47
## - Po1 1 568167 1449091 434.39
##
## Step: AIC=415.54
## .outcome ~ M + Ed + Po1 + LF + M.F + Pop + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - Time 1 15436 909079 414.21
## - M.F 1 22614 916257 414.52
## - Pop 1 24128 917771 414.58
## - LF 1 34790 928433 415.03
## <none> 893643 415.54
## - M 1 223619 1117262 422.25
## - U1 1 240694 1134337 422.84
## - Prob 1 290335 1183978 424.51
## - U2 1 363893 1257536 426.86
## - Ed 1 452873 1346516 429.53
## - Ineq 1 563663 1457305 432.61
## - Po1 1 798178 1691821 438.43
##
## Step: AIC=414.21
## .outcome ~ M + Ed + Po1 + LF + M.F + Pop + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 35548 944626 413.70
## - M.F 1 37865 946944 413.80
## - LF 1 40779 949858 413.92
## <none> 909079 414.21
## - M 1 208789 1117868 420.27
## - U1 1 233176 1142254 421.11
## - Prob 1 321955 1231033 424.03
## - U2 1 348481 1257559 424.86
## - Ed 1 447166 1356245 427.81
## - Ineq 1 550837 1459916 430.68
## - Po1 1 836695 1745773 437.66
##
## Step: AIC=413.7
## .outcome ~ M + Ed + Po1 + LF + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 944626 413.70
## - LF 1 67911 1012538 414.41
## - M.F 1 119799 1064426 416.36
## - M 1 248552 1193178 420.81
## - U1 1 273532 1218158 421.62
## - Prob 1 302232 1246858 422.53
## - U2 1 348140 1292766 423.94
## - Ed 1 490080 1434706 428.00
## - Ineq 1 522932 1467558 428.89
## - Po1 1 865856 1810483 437.08
## Start: AIC=404.21
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 440 1113494 402.22
## - M.F 1 1068 1114122 402.24
## - Wealth 1 2694 1115748 402.29
## - NW 1 3230 1116284 402.31
## - Pop 1 9905 1122959 402.53
## - Po2 1 13845 1126899 402.65
## - U1 1 17250 1130304 402.76
## - LF 1 26031 1139085 403.04
## - So 1 40865 1153919 403.51
## <none> 1113054 404.21
## - Po1 1 83912 1196966 404.82
## - Ineq 1 90359 1203413 405.02
## - Prob 1 122070 1235124 405.95
## - U2 1 148041 1261095 406.70
## - M 1 197308 1310362 408.08
## - Ed 1 204864 1317918 408.29
##
## Step: AIC=402.22
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - M.F 1 915 1114409 400.25
## - Wealth 1 2943 1116437 400.32
## - NW 1 4380 1117874 400.36
## - Pop 1 9479 1122973 400.53
## - Po2 1 16195 1129689 400.74
## - U1 1 17419 1130913 400.78
## - LF 1 26289 1139783 401.06
## - So 1 40435 1153929 401.51
## <none> 1113494 402.22
## - Ineq 1 90060 1203554 403.02
## - Po1 1 91172 1204666 403.05
## - U2 1 148184 1261678 404.72
## - M 1 211605 1325099 406.49
## - Ed 1 211809 1325303 406.49
## - Prob 1 236275 1349769 407.15
##
## Step: AIC=400.25
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 3467 1117876 398.36
## - NW 1 3865 1118274 398.38
## - Pop 1 15815 1130225 398.76
## - Po2 1 15902 1130311 398.76
## - U1 1 17257 1131666 398.80
## - So 1 48098 1162507 399.77
## - LF 1 51797 1166206 399.89
## <none> 1114409 400.25
## - Po1 1 91755 1206164 401.10
## - Ineq 1 91849 1206258 401.10
## - U2 1 150328 1264737 402.81
## - Ed 1 218900 1333309 404.71
## - Prob 1 235832 1350241 405.16
## - M 1 297322 1411731 406.77
##
## Step: AIC=398.36
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + Pop + NW + U1 + U2 +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 2364 1120240 396.44
## - Pop 1 13370 1131245 396.79
## - Po2 1 15172 1133048 396.85
## - U1 1 16340 1134216 396.89
## <none> 1117876 398.36
## - LF 1 70481 1188356 398.56
## - So 1 73901 1191777 398.67
## - Po1 1 92745 1210621 399.23
## - Ineq 1 122376 1240252 400.10
## - U2 1 158278 1276154 401.13
## - Ed 1 218754 1336629 402.80
## - Prob 1 265025 1382901 404.02
## - M 1 295727 1413602 404.81
##
## Step: AIC=396.44
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + Pop + U1 + U2 + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 11866 1132105 394.82
## - Po2 1 13976 1134216 394.89
## - U1 1 15138 1135378 394.92
## <none> 1120240 396.44
## - LF 1 72982 1193221 396.71
## - So 1 88694 1208933 397.18
## - Po1 1 91235 1211475 397.26
## - Ineq 1 134229 1254469 398.51
## - U2 1 156101 1276341 399.14
## - Ed 1 217594 1337834 400.83
## - Prob 1 264357 1384597 402.07
## - M 1 321104 1441344 403.51
##
## Step: AIC=394.82
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - U1 1 12031 1144136 393.20
## - Po2 1 14923 1147029 393.29
## <none> 1132105 394.82
## - Po1 1 88261 1220367 395.52
## - LF 1 91253 1223358 395.61
## - So 1 121465 1253570 396.49
## - Ineq 1 122649 1254754 396.52
## - U2 1 151088 1283194 397.33
## - Ed 1 225868 1357973 399.37
## - Prob 1 254709 1386814 400.12
## - M 1 374013 1506118 403.09
##
## Step: AIC=393.2
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 10246 1154381 391.52
## <none> 1144136 393.20
## - Po1 1 80520 1224656 393.65
## - Ineq 1 112446 1256581 394.57
## - LF 1 125042 1269178 394.93
## - So 1 157388 1301523 395.84
## - Ed 1 230346 1374481 397.80
## - U2 1 271100 1415236 398.85
## - Prob 1 291697 1435833 399.37
## - M 1 386817 1530953 401.68
##
## Step: AIC=391.52
## .outcome ~ M + So + Ed + Po1 + LF + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1154381 391.52
## - Ineq 1 107831 1262212 392.73
## - So 1 151573 1305954 393.96
## - LF 1 185640 1340021 394.89
## - Ed 1 226937 1381318 395.98
## - Prob 1 287121 1441503 397.52
## - U2 1 336364 1490746 398.73
## - M 1 443648 1598030 401.23
## - Po1 1 1801302 2955683 423.37
## Start: AIC=423.58
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 4710 1140001 421.74
## - Time 1 23310 1158601 422.36
## - LF 1 25335 1160627 422.42
## - So 1 25439 1160730 422.43
## - NW 1 25789 1161080 422.44
## - M.F 1 34881 1170172 422.73
## - Wealth 1 54395 1189686 423.36
## <none> 1135291 423.58
## - Po2 1 82247 1217539 424.24
## - U1 1 105590 1240881 424.96
## - Prob 1 146609 1281900 426.20
## - Po1 1 177808 1313099 427.11
## - M 1 194629 1329920 427.60
## - U2 1 221197 1356489 428.35
## - Ineq 1 307316 1442608 430.69
## - Ed 1 370620 1505911 432.32
##
## Step: AIC=421.74
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 23732 1163733 420.52
## - So 1 26189 1166190 420.60
## - Time 1 27485 1167486 420.65
## - LF 1 27519 1167520 420.65
## - M.F 1 43303 1183304 421.16
## - Wealth 1 51251 1191252 421.41
## <none> 1140001 421.74
## - Po2 1 79880 1219881 422.31
## - U1 1 113246 1253247 423.34
## - Prob 1 144373 1284374 424.27
## - Po1 1 173100 1313101 425.11
## - M 1 207963 1347964 426.11
## - U2 1 222800 1362801 426.52
## - Ineq 1 306273 1446274 428.78
## - Ed 1 369954 1509955 430.42
##
## Step: AIC=420.52
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 12293 1176026 418.92
## - Time 1 12772 1176506 418.94
## - So 1 15153 1178886 419.01
## - Wealth 1 37791 1201525 419.74
## - M.F 1 39786 1203519 419.80
## - Po2 1 56879 1220612 420.34
## <none> 1163733 420.52
## - U1 1 113934 1277667 422.07
## - Prob 1 121972 1285705 422.31
## - Po1 1 149511 1313244 423.12
## - U2 1 240520 1404253 425.66
## - Ed 1 346225 1509958 428.42
## - M 1 352219 1515953 428.57
## - Ineq 1 368270 1532003 428.97
##
## Step: AIC=418.92
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 8709 1184736 417.20
## - Time 1 12647 1188673 417.33
## - M.F 1 28408 1204434 417.83
## - Wealth 1 32288 1208315 417.95
## - Po2 1 49462 1225489 418.49
## <none> 1176026 418.92
## - U1 1 102788 1278814 420.11
## - Prob 1 121245 1297272 420.65
## - Po1 1 140866 1316892 421.22
## - U2 1 230857 1406884 423.73
## - Ed 1 340243 1516270 426.58
## - Ineq 1 359907 1535933 427.07
## - M 1 360307 1536334 427.08
##
## Step: AIC=417.2
## .outcome ~ M + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 13913 1198649 415.65
## - M.F 1 29247 1213983 416.13
## - Wealth 1 30738 1215473 416.18
## - Po2 1 55010 1239746 416.93
## <none> 1184736 417.20
## - U1 1 94463 1279199 418.12
## - Po1 1 146533 1331269 419.63
## - Prob 1 194552 1379288 420.98
## - U2 1 222741 1407476 421.75
## - Ed 1 360453 1545189 425.30
## - Ineq 1 371926 1556662 425.58
## - M 1 375393 1560129 425.66
##
## Step: AIC=415.65
## .outcome ~ M + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 24461 1223110 414.41
## - Po2 1 46068 1244716 415.08
## - M.F 1 48922 1247571 415.17
## <none> 1198649 415.65
## - U1 1 86779 1285428 416.30
## - Po1 1 135351 1334000 417.71
## - Prob 1 209191 1407839 419.76
## - U2 1 210407 1409056 419.79
## - Ineq 1 358134 1556782 423.58
## - M 1 363406 1562055 423.71
## - Ed 1 368198 1566846 423.83
##
## Step: AIC=414.41
## .outcome ~ M + Ed + Po1 + Po2 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 57151 1280261 414.15
## <none> 1223110 414.41
## - M.F 1 66586 1289695 414.43
## - U1 1 104503 1327613 415.53
## - Po1 1 173148 1396258 417.45
## - U2 1 244725 1467835 419.35
## - Prob 1 251300 1474409 419.51
## - M 1 338945 1562055 421.71
## - Ed 1 391188 1614297 422.96
## - Ineq 1 431703 1654813 423.90
##
## Step: AIC=414.15
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - M.F 1 61385 1341646 413.93
## <none> 1280261 414.15
## - U1 1 100945 1381206 415.03
## - U2 1 237841 1518102 418.62
## - Prob 1 260984 1541245 419.20
## - M 1 323557 1603818 420.71
## - Ed 1 389243 1669504 422.24
## - Ineq 1 565838 1846099 426.06
## - Po1 1 1212223 2492484 437.47
##
## Step: AIC=413.93
## .outcome ~ M + Ed + Po1 + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - U1 1 45534 1387180 413.20
## <none> 1341646 413.93
## - U2 1 182215 1523862 416.77
## - Prob 1 285189 1626835 419.25
## - M 1 396252 1737899 421.76
## - Ed 1 590022 1931668 425.78
## - Ineq 1 670211 2011857 427.33
## - Po1 1 1204682 2546329 436.28
##
## Step: AIC=413.2
## .outcome ~ M + Ed + Po1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1387180 413.20
## - U2 1 198705 1585885 416.28
## - Prob 1 299094 1686274 418.62
## - M 1 391060 1778240 420.63
## - Ed 1 566914 1954094 424.22
## - Ineq 1 684525 2071705 426.44
## - Po1 1 2077965 3465146 445.99
## Start: AIC=408.76
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 171 978509 406.77
## - Time 1 2385 980724 406.85
## - Pop 1 12129 990467 407.22
## - Prob 1 15606 993945 407.35
## - Po1 1 22824 1001163 407.61
## - Wealth 1 24744 1003082 407.68
## - M 1 31316 1009655 407.93
## - LF 1 32544 1010883 407.97
## - U1 1 39396 1017735 408.22
## - So 1 43118 1021457 408.36
## <none> 978339 408.76
## - U2 1 62959 1041297 409.07
## - M.F 1 73382 1051721 409.44
## - NW 1 83633 1061972 409.79
## - Ed 1 315756 1294094 417.11
## - Ineq 1 436202 1414540 420.40
##
## Step: AIC=406.77
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 3118 981627 404.88
## - Pop 1 12169 990679 405.22
## - Prob 1 16033 994542 405.37
## - Wealth 1 24706 1003215 405.69
## - M 1 31146 1009655 405.93
## - LF 1 32811 1011321 405.99
## - U1 1 39437 1017947 406.23
## - So 1 42976 1021485 406.36
## <none> 978509 406.77
## - U2 1 62840 1041349 407.07
## - M.F 1 75294 1053803 407.51
## - NW 1 86366 1064876 407.90
## - Po1 1 261873 1240382 413.54
## - Ed 1 322798 1301308 415.31
## - Ineq 1 464485 1442994 419.14
##
## Step: AIC=404.88
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 18541 1000168 403.58
## - Prob 1 28748 1010375 403.95
## - LF 1 30111 1011738 404.00
## - M 1 33136 1014763 404.11
## - Wealth 1 33605 1015232 404.13
## - U1 1 39791 1021418 404.35
## - So 1 42386 1024013 404.45
## <none> 981627 404.88
## - U2 1 64530 1046158 405.24
## - M.F 1 72178 1053805 405.51
## - NW 1 90601 1072228 406.15
## - Po1 1 269012 1250639 411.85
## - Ed 1 321794 1303421 413.37
## - Ineq 1 491343 1472970 417.90
##
## Step: AIC=403.58
## .outcome ~ M + So + Ed + Po1 + LF + M.F + NW + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 22504 1022671 402.40
## - U1 1 31893 1032060 402.74
## - Wealth 1 35035 1035203 402.85
## - So 1 38096 1038264 402.96
## - M 1 39934 1040101 403.02
## - Prob 1 49205 1049373 403.35
## - M.F 1 53696 1053864 403.51
## <none> 1000168 403.58
## - U2 1 64855 1065023 403.90
## - NW 1 80867 1081035 404.45
## - Ed 1 321656 1321824 411.89
## - Po1 1 383172 1383340 413.58
## - Ineq 1 554148 1554316 417.89
##
## Step: AIC=402.4
## .outcome ~ M + So + Ed + Po1 + M.F + NW + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - U1 1 16975 1039647 401.01
## - So 1 19737 1042408 401.11
## - M.F 1 31704 1054375 401.53
## - Wealth 1 35443 1058114 401.66
## - Prob 1 42923 1065594 401.92
## - M 1 47919 1070590 402.09
## <none> 1022671 402.40
## - U2 1 59990 1082662 402.51
## - NW 1 60898 1083570 402.54
## - Ed 1 299280 1321951 409.90
## - Po1 1 409583 1432254 412.86
## - Ineq 1 532565 1555236 415.91
##
## Step: AIC=401.01
## .outcome ~ M + So + Ed + Po1 + M.F + NW + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - So 1 14206 1053853 399.51
## - M.F 1 16189 1055836 399.58
## - Prob 1 44303 1083950 400.55
## - Wealth 1 45772 1085418 400.60
## - M 1 53125 1092771 400.85
## - NW 1 56032 1095679 400.95
## <none> 1039647 401.01
## - U2 1 74477 1114124 401.57
## - Ed 1 291588 1331234 408.16
## - Po1 1 532968 1572615 414.32
## - Ineq 1 632505 1672151 416.59
##
## Step: AIC=399.51
## .outcome ~ M + Ed + Po1 + M.F + NW + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - M.F 1 22782 1076635 398.30
## - Wealth 1 34150 1088003 398.69
## - NW 1 42942 1096794 398.99
## - M 1 45850 1099703 399.09
## <none> 1053853 399.51
## - U2 1 70743 1124596 399.91
## - Prob 1 89224 1143077 400.52
## - Ed 1 319417 1373269 407.31
## - Po1 1 582431 1636284 413.79
## - Ineq 1 666045 1719898 415.63
##
## Step: AIC=398.3
## .outcome ~ M + Ed + Po1 + NW + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 30307 1106942 397.33
## - Wealth 1 30808 1107443 397.35
## <none> 1076635 398.30
## - M 1 65945 1142580 398.50
## - Prob 1 81896 1158531 399.01
## - U2 1 93940 1170575 399.40
## - Ed 1 492219 1568854 410.23
## - Po1 1 619389 1696024 413.12
## - Ineq 1 733406 1810041 415.52
##
## Step: AIC=397.33
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 28252 1135193 396.26
## <none> 1106942 397.33
## - Prob 1 67953 1174894 397.53
## - U2 1 93154 1200096 398.32
## - M 1 126457 1233398 399.33
## - Ed 1 475089 1582031 408.54
## - Ineq 1 808517 1915458 415.62
## - Po1 1 888069 1995011 417.12
##
## Step: AIC=396.26
## .outcome ~ M + Ed + Po1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1135193 396.26
## - U2 1 90640 1225834 397.10
## - Prob 1 95042 1230235 397.24
## - M 1 104251 1239445 397.51
## - Ed 1 548639 1683832 408.85
## - Ineq 1 926704 2061898 416.34
## - Po1 1 2592798 3727991 438.26
## Start: AIC=408.13
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 30 755905 406.13
## - NW 1 524 756398 406.15
## - M.F 1 1399 757273 406.20
## - U1 1 5401 761275 406.40
## - So 1 22706 778580 407.25
## - Wealth 1 31314 787188 407.67
## - U2 1 39911 795785 408.08
## <none> 755874 408.13
## - Pop 1 45421 801295 408.34
## - Time 1 46084 801958 408.37
## - Po2 1 86440 842314 410.24
## - M 1 130418 886292 412.17
## - Ed 1 175728 931602 414.07
## - Po1 1 221359 977233 415.89
## - Prob 1 275331 1031205 417.93
## - Ineq 1 329962 1085836 419.89
##
## Step: AIC=406.13
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 498 756402 404.15
## - M.F 1 1467 757371 404.20
## - U1 1 6123 762028 404.43
## - So 1 30919 786824 405.65
## - Wealth 1 31347 787252 405.67
## - U2 1 39909 795813 406.08
## <none> 755905 406.13
## - Time 1 47082 802986 406.42
## - Pop 1 47343 803247 406.44
## - Po2 1 95591 851496 408.65
## - M 1 130769 886674 410.19
## - Ed 1 188441 944346 412.59
## - Po1 1 237590 993495 414.51
## - Prob 1 277302 1033206 416.00
## - Ineq 1 333249 1089154 418.01
##
## Step: AIC=404.15
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + Pop + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 1237 757639 402.21
## - U1 1 5660 762063 402.44
## - Wealth 1 30912 787314 403.67
## - U2 1 39828 796230 404.10
## <none> 756402 404.15
## - So 1 41488 797890 404.18
## - Pop 1 48970 805373 404.54
## - Time 1 50243 806645 404.60
## - Po2 1 95497 851899 406.67
## - M 1 144849 901252 408.81
## - Ed 1 190958 947360 410.71
## - Po1 1 237130 993532 412.51
## - Prob 1 306294 1062696 415.07
## - Ineq 1 371446 1127848 417.33
##
## Step: AIC=402.21
## .outcome ~ M + So + Ed + Po1 + Po2 + Pop + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - U1 1 4437 762077 400.44
## - Wealth 1 34498 792137 401.91
## - U2 1 38599 796238 402.10
## - So 1 40544 798183 402.20
## <none> 757639 402.21
## - Time 1 61933 819572 403.20
## - Pop 1 62665 820304 403.23
## - Po2 1 122752 880391 405.92
## - M 1 171519 929158 407.97
## - Ed 1 213077 970717 409.63
## - Po1 1 301482 1059121 412.94
## - Prob 1 318736 1076375 413.56
## - Ineq 1 413297 1170937 416.76
##
## Step: AIC=400.44
## .outcome ~ M + So + Ed + Po1 + Po2 + Pop + U2 + Wealth + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 39368 801445 400.35
## <none> 762077 400.44
## - U2 1 52884 814960 400.99
## - Time 1 57559 819636 401.20
## - So 1 63209 825285 401.46
## - Pop 1 67876 829953 401.68
## - Po2 1 123410 885486 404.14
## - M 1 168935 931011 406.04
## - Ed 1 209043 971120 407.65
## - Po1 1 307210 1069287 411.31
## - Prob 1 327929 1090006 412.04
## - Ineq 1 431801 1193878 415.49
##
## Step: AIC=400.35
## .outcome ~ M + So + Ed + Po1 + Po2 + Pop + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## <none> 801445 400.35
## - Pop 1 54209 855654 400.84
## - Time 1 70858 872303 401.57
## - U2 1 71210 872655 401.58
## - So 1 79839 881283 401.96
## - Po2 1 136177 937621 404.31
## - M 1 178084 979529 405.98
## - Ed 1 341707 1143152 411.85
## - Po1 1 354604 1156048 412.27
## - Prob 1 376963 1178408 413.00
## - Ineq 1 475964 1277408 416.06
## Start: AIC=410.61
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 58 1028507 408.61
## - Pop 1 1055 1029503 408.65
## - NW 1 2931 1031380 408.71
## - So 1 6800 1035249 408.85
## - Po2 1 17570 1046019 409.23
## - M.F 1 30895 1059344 409.70
## - U1 1 40931 1069379 410.05
## - Po1 1 51546 1079995 410.42
## - LF 1 53194 1081643 410.47
## <none> 1028448 410.61
## - Prob 1 67317 1095765 410.95
## - U2 1 94723 1123171 411.87
## - Wealth 1 179061 1207510 414.55
## - Ed 1 232595 1261043 416.15
## - M 1 244197 1272645 416.49
## - Ineq 1 592713 1621161 425.45
##
## Step: AIC=408.61
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 997 1029504 406.65
## - NW 1 4173 1032680 406.76
## - So 1 7079 1035586 406.86
## - Po2 1 21278 1049785 407.37
## - M.F 1 30926 1059433 407.71
## - U1 1 46151 1074658 408.23
## - LF 1 54759 1083265 408.53
## <none> 1028507 408.61
## - Po1 1 57596 1086103 408.63
## - U2 1 100212 1128719 410.05
## - Prob 1 107887 1136394 410.30
## - Wealth 1 179039 1207546 412.55
## - Ed 1 237729 1266236 414.30
## - M 1 245183 1273689 414.52
## - Ineq 1 604024 1632531 423.70
##
## Step: AIC=406.65
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 4012 1033516 404.79
## - So 1 8262 1037765 404.94
## - Po2 1 20331 1049835 405.37
## - M.F 1 36823 1066327 405.95
## - U1 1 47684 1077188 406.32
## <none> 1029504 406.65
## - LF 1 57346 1086850 406.65
## - Po1 1 57650 1087154 406.66
## - U2 1 99215 1128719 408.05
## - Prob 1 109221 1138725 408.38
## - Wealth 1 178474 1207978 410.56
## - Ed 1 236763 1266267 412.30
## - M 1 257328 1286832 412.90
## - Ineq 1 610394 1639898 421.87
##
## Step: AIC=404.79
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - So 1 5699 1039215 402.99
## - Po2 1 17063 1050578 403.40
## - M.F 1 33698 1067214 403.98
## - U1 1 44122 1077638 404.34
## - Po1 1 54349 1087865 404.69
## - LF 1 54896 1088412 404.70
## <none> 1033516 404.79
## - U2 1 95746 1129262 406.07
## - Prob 1 105240 1138756 406.38
## - Wealth 1 176265 1209781 408.62
## - Ed 1 240315 1273831 410.52
## - M 1 338564 1372079 413.27
## - Ineq 1 654201 1687717 420.93
##
## Step: AIC=402.99
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 20256 1059471 401.71
## - M.F 1 34666 1073881 402.21
## - U1 1 39844 1079059 402.39
## - LF 1 51179 1090394 402.77
## <none> 1039215 402.99
## - Po1 1 59116 1098331 403.04
## - U2 1 91843 1131058 404.13
## - Wealth 1 171627 1210842 406.65
## - Prob 1 183033 1222248 407.00
## - Ed 1 255427 1294642 409.12
## - M 1 346220 1385435 411.63
## - Ineq 1 760400 1799616 421.31
##
## Step: AIC=401.71
## .outcome ~ M + Ed + Po1 + LF + M.F + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - M.F 1 26484 1085955 400.62
## - U1 1 31076 1090547 400.78
## - LF 1 40550 1100020 401.10
## <none> 1059471 401.71
## - U2 1 86171 1145641 402.60
## - Wealth 1 181746 1241216 405.57
## - Prob 1 189459 1248930 405.79
## - Po1 1 209318 1268789 406.38
## - Ed 1 239157 1298627 407.24
## - M 1 359572 1419043 410.52
## - Ineq 1 794567 1854038 420.41
##
## Step: AIC=400.62
## .outcome ~ M + Ed + Po1 + LF + U1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - U1 1 8821 1094776 398.92
## - LF 1 20487 1106442 399.31
## <none> 1085955 400.62
## - U2 1 65748 1151703 400.80
## - Prob 1 175744 1261699 404.17
## - Po1 1 196662 1282618 404.78
## - Wealth 1 227917 1313872 405.67
## - Ed 1 242445 1328401 406.08
## - M 1 486072 1572027 412.31
## - Ineq 1 861339 1947294 420.23
##
## Step: AIC=398.92
## .outcome ~ M + Ed + Po1 + LF + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 19664 1114440 397.58
## <none> 1094776 398.92
## - U2 1 86972 1181748 399.75
## - Prob 1 179237 1274013 402.53
## - Po1 1 225741 1320517 403.86
## - Wealth 1 262295 1357071 404.87
## - Ed 1 273718 1368495 405.18
## - M 1 501613 1596389 410.88
## - Ineq 1 898429 1993205 419.09
##
## Step: AIC=397.58
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1114440 397.58
## - U2 1 130874 1245314 399.69
## - Prob 1 160774 1275214 400.57
## - Wealth 1 245135 1359574 402.94
## - Ed 1 259224 1373664 403.32
## - Po1 1 327448 1441888 405.11
## - M 1 491761 1606201 409.10
## - Ineq 1 958865 2073305 418.55
## Start: AIC=384.73
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 26 511053 382.73
## - Po2 1 3221 514247 382.96
## - NW 1 8061 519088 383.31
## - Po1 1 10228 521255 383.46
## - U1 1 15552 526578 383.84
## - M.F 1 25186 536212 384.51
## <none> 511027 384.73
## - So 1 37483 548510 385.35
## - LF 1 69394 580421 387.44
## - Time 1 91100 602127 388.80
## - Pop 1 94907 605934 389.03
## - Ineq 1 133595 644621 391.32
## - Ed 1 141916 652943 391.80
## - U2 1 217422 728448 395.85
## - M 1 310142 821168 400.28
## - Prob 1 386797 897823 403.58
##
## Step: AIC=382.73
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 3199 514252 380.96
## - NW 1 9452 520505 381.41
## - Po1 1 10214 521267 381.46
## - U1 1 15526 526579 381.84
## - M.F 1 25170 536223 382.51
## <none> 511053 382.73
## - So 1 37915 548968 383.38
## - LF 1 69692 580745 385.46
## - Time 1 91195 602248 386.81
## - Pop 1 96341 607394 387.12
## - Ed 1 147597 658650 390.12
## - Ineq 1 212299 723352 393.59
## - U2 1 231955 743008 394.58
## - M 1 315474 826527 398.52
## - Prob 1 387079 898132 401.59
##
## Step: AIC=380.96
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + NW + U1 + U2 +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 13381 527633 379.91
## - U1 1 18083 532336 380.24
## - M.F 1 26063 540316 380.79
## <none> 514252 380.96
## - So 1 34716 548969 381.38
## - LF 1 76700 590953 384.11
## - Pop 1 93496 607748 385.14
## - Time 1 114969 629222 386.43
## - Ineq 1 211609 725861 391.72
## - Ed 1 216409 730661 391.96
## - U2 1 229464 743716 392.61
## - M 1 312723 826975 396.54
## - Prob 1 387507 901760 399.74
## - Po1 1 1116813 1631065 421.67
##
## Step: AIC=379.91
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + U1 + U2 + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - U1 1 13613 541246 378.86
## <none> 527633 379.91
## - M.F 1 37443 565076 380.45
## - So 1 49488 577121 381.23
## - LF 1 80337 607970 383.16
## - Pop 1 95278 622911 384.06
## - Time 1 108095 635728 384.81
## - Ed 1 223278 750911 390.97
## - U2 1 226727 754360 391.14
## - Ineq 1 259360 786993 392.71
## - Prob 1 385040 912673 398.19
## - M 1 387547 915180 398.29
## - Po1 1 1382426 1910059 425.51
##
## Step: AIC=378.86
## .outcome ~ M + So + Ed + Po1 + LF + M.F + Pop + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## <none> 541246 378.86
## - M.F 1 68671 609917 381.28
## - So 1 91033 632279 382.61
## - Time 1 106897 648143 383.53
## - Pop 1 110328 651574 383.72
## - LF 1 145596 686841 385.67
## - Ed 1 209747 750993 388.97
## - Ineq 1 246789 788035 390.76
## - U2 1 335769 877015 394.71
## - M 1 420998 962244 398.15
## - Prob 1 427916 969162 398.41
## - Po1 1 1791483 2332729 430.91
## Start: AIC=413.37
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 220 1108300 411.37
## - So 1 4150 1112230 411.51
## - NW 1 15990 1124070 411.90
## - LF 1 17617 1125697 411.95
## - M.F 1 26314 1134395 412.24
## - Po2 1 55637 1163717 413.18
## - Time 1 60293 1168374 413.33
## <none> 1108080 413.37
## - U1 1 62036 1170116 413.38
## - Wealth 1 117717 1225797 415.10
## - U2 1 140469 1248549 415.78
## - Po1 1 149936 1258016 416.06
## - M 1 187152 1295233 417.14
## - Prob 1 190069 1298150 417.22
## - Ed 1 507432 1615512 425.32
## - Ineq 1 534719 1642799 425.94
##
## Step: AIC=411.37
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 4560 1112860 409.53
## - NW 1 15771 1124071 409.90
## - LF 1 17565 1125865 409.96
## - M.F 1 27798 1136099 410.29
## - Po2 1 55424 1163724 411.18
## <none> 1108300 411.37
## - U1 1 61918 1170219 411.39
## - Time 1 71165 1179465 411.68
## - Wealth 1 117509 1225809 413.10
## - U2 1 140455 1248756 413.79
## - Po1 1 151073 1259373 414.10
## - M 1 189025 1297326 415.20
## - Prob 1 190049 1298350 415.23
## - Ed 1 513297 1621597 423.46
## - Ineq 1 540156 1648456 424.06
##
## Step: AIC=409.53
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 11506 1124366 407.91
## - LF 1 13006 1125866 407.96
## - M.F 1 25102 1137962 408.35
## - Po2 1 53264 1166124 409.26
## - U1 1 57469 1170329 409.39
## <none> 1112860 409.53
## - Time 1 67239 1180099 409.70
## - Wealth 1 114737 1227597 411.16
## - U2 1 135952 1248812 411.79
## - Po1 1 149580 1262440 412.19
## - M 1 184565 1297425 413.20
## - Prob 1 202847 1315708 413.72
## - Ed 1 508738 1621598 421.46
## - Ineq 1 584019 1696879 423.14
##
## Step: AIC=407.91
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 11812 1136178 406.29
## - M.F 1 25785 1150151 406.75
## - Po2 1 44971 1169337 407.36
## - Time 1 57635 1182001 407.76
## <none> 1124366 407.91
## - U1 1 71335 1195701 408.18
## - Wealth 1 105251 1229617 409.22
## - Po1 1 141454 1265820 410.29
## - U2 1 173106 1297472 411.21
## - Prob 1 194528 1318894 411.81
## - M 1 291854 1416220 414.45
## - Ed 1 497493 1621859 419.46
## - Ineq 1 641139 1765505 422.60
##
## Step: AIC=406.29
## .outcome ~ M + Ed + Po1 + Po2 + M.F + U1 + U2 + Wealth + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 15136 1151314 404.78
## - Po2 1 37137 1173315 405.48
## - Time 1 59293 1195471 406.18
## - U1 1 60854 1197032 406.22
## <none> 1136178 406.29
## - Wealth 1 108322 1244500 407.66
## - Po1 1 130609 1266788 408.32
## - U2 1 178933 1315111 409.71
## - Prob 1 182896 1319074 409.82
## - M 1 306043 1442221 413.12
## - Ed 1 500154 1636332 417.79
## - Ineq 1 634913 1771092 420.72
##
## Step: AIC=404.78
## .outcome ~ M + Ed + Po1 + Po2 + U1 + U2 + Wealth + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - U1 1 45922 1197236 404.23
## - Po2 1 56308 1207622 404.55
## <none> 1151314 404.78
## - Time 1 98244 1249558 405.81
## - Wealth 1 139676 1290990 407.02
## - U2 1 164074 1315389 407.71
## - Po1 1 171568 1322882 407.92
## - Prob 1 205665 1356980 408.86
## - M 1 398277 1549591 413.78
## - Ed 1 665308 1816622 419.66
## - Ineq 1 772851 1924165 421.79
##
## Step: AIC=404.23
## .outcome ~ M + Ed + Po1 + Po2 + U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 41122 1238358 403.48
## <none> 1197236 404.23
## - Time 1 70469 1267705 404.35
## - Po1 1 154926 1352162 406.73
## - Wealth 1 177064 1374300 407.33
## - Prob 1 179211 1376447 407.39
## - U2 1 190252 1387488 407.69
## - M 1 379195 1576431 412.41
## - Ed 1 619562 1816798 417.66
## - Ineq 1 928228 2125464 423.47
##
## Step: AIC=403.48
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 58883 1297241 403.20
## <none> 1238358 403.48
## - Prob 1 158201 1396559 405.93
## - Wealth 1 171288 1409646 406.27
## - U2 1 190926 1429284 406.79
## - M 1 363787 1602145 411.01
## - Ed 1 622698 1861056 416.55
## - Ineq 1 962413 2200771 422.76
## - Po1 1 1128295 2366653 425.44
##
## Step: AIC=403.2
## .outcome ~ M + Ed + Po1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1297241 403.20
## - Prob 1 103648 1400889 404.04
## - Wealth 1 154899 1452140 405.37
## - U2 1 190143 1487384 406.26
## - M 1 331370 1628611 409.62
## - Ed 1 748756 2045997 418.06
## - Ineq 1 905511 2202752 420.79
## - Po1 1 1077082 2374323 423.56
## Start: AIC=419.13
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Pop 1 152 1009847 417.13
## - NW 1 432 1010128 417.14
## - Wealth 1 826 1010522 417.16
## - LF 1 1539 1011235 417.19
## - So 1 13451 1023147 417.63
## - Po2 1 17082 1026777 417.77
## - U1 1 19588 1029284 417.86
## - Time 1 21202 1030897 417.92
## - Prob 1 36308 1046004 418.47
## - M.F 1 41242 1050938 418.65
## <none> 1009696 419.13
## - U2 1 75769 1085465 419.88
## - M 1 87017 1096712 420.27
## - Po1 1 96709 1106405 420.60
## - Ineq 1 154405 1164101 422.54
## - Ed 1 386290 1395986 429.44
##
## Step: AIC=417.13
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - NW 1 447 1010294 415.15
## - Wealth 1 702 1010550 415.16
## - LF 1 1409 1011256 415.19
## - So 1 13456 1023303 415.64
## - Po2 1 17237 1027085 415.78
## - U1 1 19892 1029740 415.87
## - Time 1 22088 1031935 415.96
## - Prob 1 36194 1046041 416.47
## - M.F 1 45192 1055039 416.80
## <none> 1009847 417.13
## - U2 1 77698 1087545 417.95
## - M 1 88909 1098756 418.34
## - Po1 1 97577 1107424 418.64
## - Ineq 1 167834 1177681 420.98
## - Ed 1 388780 1398628 427.51
##
## Step: AIC=415.15
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Wealth +
## Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Wealth 1 858 1011152 413.18
## - LF 1 1010 1011304 413.19
## - Po2 1 17495 1027789 413.80
## - So 1 19946 1030240 413.89
## - U1 1 20009 1030303 413.90
## - Time 1 30517 1040811 414.28
## - Prob 1 40954 1051248 414.66
## - M.F 1 45033 1055327 414.81
## <none> 1010294 415.15
## - U2 1 78240 1088534 415.98
## - M 1 97455 1107750 416.65
## - Po1 1 99986 1110280 416.74
## - Ineq 1 170017 1180311 419.06
## - Ed 1 396168 1406463 425.72
##
## Step: AIC=413.18
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + U1 + U2 + Ineq +
## Prob + Time
##
## Df Sum of Sq RSS AIC
## - LF 1 1114 1012266 411.22
## - Po2 1 16833 1027985 411.81
## - So 1 19215 1030367 411.90
## - U1 1 19319 1030471 411.90
## - Time 1 30341 1041493 412.31
## - Prob 1 41763 1052916 412.72
## - M.F 1 44395 1055547 412.82
## <none> 1011152 413.18
## - U2 1 77890 1089042 414.00
## - Po1 1 99766 1110918 414.76
## - M 1 109491 1120643 415.09
## - Ineq 1 268160 1279312 420.12
## - Ed 1 406768 1417920 424.03
##
## Step: AIC=411.22
## .outcome ~ M + So + Ed + Po1 + Po2 + M.F + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - Po2 1 15797 1028064 409.81
## - U1 1 18873 1031140 409.93
## - So 1 28258 1040525 410.27
## - Time 1 30890 1043156 410.37
## - Prob 1 40680 1052947 410.72
## - M.F 1 46015 1058282 410.91
## <none> 1012266 411.22
## - U2 1 76807 1089074 412.00
## - Po1 1 99206 1111472 412.78
## - M 1 111423 1123690 413.19
## - Ineq 1 288220 1300486 418.75
## - Ed 1 426887 1439153 422.60
##
## Step: AIC=409.81
## .outcome ~ M + So + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob +
## Time
##
## Df Sum of Sq RSS AIC
## - U1 1 17019 1045082 408.44
## - So 1 22931 1050995 408.65
## - Prob 1 31675 1059739 408.97
## <none> 1028064 409.81
## - Time 1 56563 1084627 409.85
## - M.F 1 69119 1097183 410.29
## - U2 1 75330 1103393 410.50
## - M 1 113072 1141136 411.78
## - Ineq 1 324091 1352155 418.23
## - Ed 1 429863 1457927 421.09
## - Po1 1 971994 2000058 433.10
##
## Step: AIC=408.44
## .outcome ~ M + So + Ed + Po1 + M.F + U2 + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Prob 1 26784 1071866 407.40
## - So 1 37120 1082202 407.76
## - M.F 1 54036 1099119 408.35
## <none> 1045082 408.44
## - Time 1 74208 1119290 409.04
## - U2 1 90818 1135900 409.60
## - M 1 109159 1154242 410.21
## - Ineq 1 320083 1365165 416.59
## - Ed 1 418630 1463712 419.24
## - Po1 1 1505887 2550969 440.35
##
## Step: AIC=407.4
## .outcome ~ M + So + Ed + Po1 + M.F + U2 + Ineq + Time
##
## Df Sum of Sq RSS AIC
## - So 1 37464 1109330 406.70
## <none> 1071866 407.40
## - U2 1 80185 1152051 408.14
## - M.F 1 84838 1156705 408.29
## - M 1 94264 1166130 408.60
## - Time 1 233054 1304920 412.87
## - Ineq 1 293446 1365312 414.59
## - Ed 1 418871 1490737 417.93
## - Po1 1 1856869 2928735 443.59
##
## Step: AIC=406.7
## .outcome ~ M + Ed + Po1 + M.F + U2 + Ineq + Time
##
## Df Sum of Sq RSS AIC
## - M.F 1 54956 1164286 406.54
## <none> 1109330 406.70
## - U2 1 87984 1197313 407.60
## - M 1 125893 1235223 408.79
## - Time 1 206795 1316125 411.20
## - Ed 1 396920 1506250 416.33
## - Ineq 1 632978 1742308 421.86
## - Po1 1 2181178 3290508 446.02
##
## Step: AIC=406.54
## .outcome ~ M + Ed + Po1 + U2 + Ineq + Time
##
## Df Sum of Sq RSS AIC
## <none> 1164286 406.54
## - U2 1 135069 1299355 408.71
## - Time 1 163092 1327378 409.52
## - M 1 167407 1331693 409.65
## - Ed 1 615263 1779549 420.66
## - Ineq 1 719523 1883809 422.83
## - Po1 1 2223866 3388152 445.13
## Start: AIC=431.29
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 2935 1093042 429.40
## - Pop 1 7081 1097188 429.54
## - So 1 12103 1102210 429.72
## - Wealth 1 25104 1115211 430.18
## - LF 1 25532 1115639 430.19
## - Po2 1 43576 1133684 430.82
## - M.F 1 50341 1140448 431.05
## - NW 1 52537 1142644 431.13
## <none> 1090107 431.29
## - M 1 72415 1162522 431.80
## - U1 1 82621 1172728 432.14
## - Prob 1 107298 1197405 432.95
## - U2 1 115517 1205624 433.22
## - Po1 1 133433 1223540 433.79
## - Ed 1 192487 1282594 435.63
## - Ineq 1 302582 1392689 438.84
##
## Step: AIC=429.4
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 9548 1102590 427.73
## - So 1 13339 1106381 427.87
## - Wealth 1 22483 1115525 428.19
## - LF 1 28777 1121819 428.41
## - Po2 1 41812 1134854 428.86
## - NW 1 54247 1147289 429.28
## <none> 1093042 429.40
## - M.F 1 59847 1152890 429.47
## - M 1 69480 1162523 429.80
## - U1 1 82754 1175796 430.24
## - U2 1 118335 1211378 431.40
## - Po1 1 139143 1232186 432.07
## - Prob 1 145337 1238380 432.26
## - Ed 1 225814 1318856 434.72
## - Ineq 1 305268 1398311 437.00
##
## Step: AIC=427.73
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - So 1 11207 1113797 426.13
## - Wealth 1 19206 1121796 426.41
## - LF 1 31741 1134331 426.84
## - Po2 1 38580 1141170 427.08
## - NW 1 47879 1150469 427.39
## <none> 1102590 427.73
## - M 1 74668 1177258 428.29
## - U1 1 115069 1217659 429.61
## - M.F 1 126782 1229372 429.98
## - Po1 1 130069 1232659 430.08
## - U2 1 130806 1233396 430.11
## - Prob 1 136126 1238716 430.27
## - Ed 1 216956 1319546 432.74
## - Ineq 1 314578 1417168 435.52
##
## Step: AIC=426.13
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 15839 1129636 424.68
## - LF 1 20584 1134380 424.84
## - Po2 1 35072 1148868 425.34
## - NW 1 37895 1151691 425.43
## <none> 1113797 426.13
## - M 1 74174 1187971 426.64
## - U1 1 104667 1218464 427.63
## - M.F 1 115627 1229424 427.98
## - U2 1 119754 1233551 428.11
## - Po1 1 127875 1241672 428.37
## - Prob 1 170379 1284176 429.68
## - Ed 1 206078 1319874 430.75
## - Ineq 1 318871 1432667 433.95
##
## Step: AIC=424.68
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + NW + U1 + U2 + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 21498 1151134 423.42
## - Po2 1 36227 1165863 423.91
## - NW 1 41714 1171350 424.09
## <none> 1129636 424.68
## - M 1 64817 1194453 424.86
## - U1 1 117717 1247353 426.55
## - M.F 1 127251 1256886 426.84
## - Po1 1 139337 1268973 427.22
## - U2 1 142781 1272417 427.32
## - Prob 1 203262 1332898 429.13
## - Ed 1 244352 1373988 430.32
## - Ineq 1 356843 1486479 433.39
##
## Step: AIC=423.42
## .outcome ~ M + Ed + Po1 + Po2 + M.F + NW + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 23155 1174289 422.19
## - NW 1 28490 1179624 422.37
## <none> 1151134 423.42
## - M 1 87436 1238569 424.27
## - U1 1 100918 1252052 424.69
## - M.F 1 106184 1257318 424.86
## - Po1 1 120531 1271665 425.30
## - U2 1 147823 1298957 426.13
## - Prob 1 182216 1333350 427.15
## - Ed 1 224618 1375752 428.37
## - Ineq 1 352165 1503299 431.82
##
## Step: AIC=422.19
## .outcome ~ M + Ed + Po1 + M.F + NW + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 23179 1197467 420.95
## <none> 1174289 422.19
## - M 1 91064 1265353 423.10
## - U1 1 108818 1283107 423.65
## - M.F 1 120388 1294677 424.00
## - U2 1 166416 1340705 425.36
## - Prob 1 182036 1356325 425.81
## - Ed 1 212888 1387177 426.69
## - Ineq 1 389816 1564105 431.37
## - Po1 1 956089 2130378 443.42
##
## Step: AIC=420.95
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1197467 420.95
## - M.F 1 115466 1312934 422.54
## - U1 1 132261 1329728 423.04
## - M 1 153904 1351372 423.67
## - Prob 1 160456 1357923 423.86
## - U2 1 177196 1374663 424.34
## - Ed 1 191740 1389207 424.75
## - Ineq 1 478895 1676363 432.07
## - Po1 1 1350069 2547537 448.40
## Start: AIC=514.65
## .outcome ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 29 1354974 512.65
## - LF 1 8917 1363862 512.96
## - Time 1 10304 1365250 513.00
## - Pop 1 14122 1369068 513.14
## - NW 1 18395 1373341 513.28
## - M.F 1 31967 1386913 513.74
## - Wealth 1 37613 1392558 513.94
## - Po2 1 37919 1392865 513.95
## <none> 1354946 514.65
## - U1 1 83722 1438668 515.47
## - Po1 1 144306 1499252 517.41
## - U2 1 181536 1536482 518.56
## - M 1 193770 1548716 518.93
## - Prob 1 199538 1554484 519.11
## - Ed 1 402117 1757063 524.86
## - Ineq 1 423031 1777977 525.42
##
## Step: AIC=512.65
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 10341 1365315 511.01
## - LF 1 10878 1365852 511.03
## - Pop 1 14127 1369101 511.14
## - NW 1 21626 1376600 511.39
## - M.F 1 32449 1387423 511.76
## - Po2 1 37954 1392929 511.95
## - Wealth 1 39223 1394197 511.99
## <none> 1354974 512.65
## - U1 1 96420 1451395 513.88
## - Po1 1 144302 1499277 515.41
## - U2 1 189859 1544834 516.81
## - M 1 195084 1550059 516.97
## - Prob 1 204463 1559437 517.26
## - Ed 1 403140 1758114 522.89
## - Ineq 1 488834 1843808 525.13
##
## Step: AIC=511.01
## .outcome ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - LF 1 10533 1375848 509.37
## - NW 1 15482 1380797 509.54
## - Pop 1 21846 1387161 509.75
## - Po2 1 28932 1394247 509.99
## - Wealth 1 36070 1401385 510.23
## - M.F 1 41784 1407099 510.42
## <none> 1365315 511.01
## - U1 1 91420 1456735 512.05
## - Po1 1 134137 1499452 513.41
## - U2 1 184143 1549458 514.95
## - M 1 186110 1551425 515.01
## - Prob 1 237493 1602808 516.54
## - Ed 1 409448 1774763 521.33
## - Ineq 1 502909 1868224 523.75
##
## Step: AIC=509.37
## .outcome ~ M + Ed + Po1 + Po2 + M.F + Pop + NW + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - NW 1 11675 1387523 507.77
## - Po2 1 21418 1397266 508.09
## - Pop 1 27803 1403651 508.31
## - M.F 1 31252 1407100 508.42
## - Wealth 1 35035 1410883 508.55
## <none> 1375848 509.37
## - U1 1 80954 1456802 510.06
## - Po1 1 123896 1499744 511.42
## - U2 1 190746 1566594 513.47
## - M 1 217716 1593564 514.27
## - Prob 1 226971 1602819 514.54
## - Ed 1 413254 1789103 519.71
## - Ineq 1 500944 1876792 521.96
##
## Step: AIC=507.77
## .outcome ~ M + Ed + Po1 + Po2 + M.F + Pop + U1 + U2 + Wealth +
## Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Po2 1 16706 1404229 506.33
## - Pop 1 25793 1413315 506.63
## - M.F 1 26785 1414308 506.66
## - Wealth 1 31551 1419073 506.82
## <none> 1387523 507.77
## - U1 1 83881 1471404 508.52
## - Po1 1 118348 1505871 509.61
## - U2 1 201453 1588976 512.14
## - Prob 1 216760 1604282 512.59
## - M 1 309214 1696737 515.22
## - Ed 1 402754 1790276 517.74
## - Ineq 1 589736 1977259 522.41
##
## Step: AIC=506.33
## .outcome ~ M + Ed + Po1 + M.F + Pop + U1 + U2 + Wealth + Ineq +
## Prob
##
## Df Sum of Sq RSS AIC
## - Pop 1 22345 1426575 505.07
## - Wealth 1 32142 1436371 505.39
## - M.F 1 36808 1441037 505.54
## <none> 1404229 506.33
## - U1 1 86373 1490602 507.13
## - U2 1 205814 1610043 510.76
## - Prob 1 218607 1622836 511.13
## - M 1 307001 1711230 513.62
## - Ed 1 389502 1793731 515.83
## - Ineq 1 608627 2012856 521.25
## - Po1 1 1050202 2454432 530.57
##
## Step: AIC=505.07
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Wealth + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## - Wealth 1 26493 1453068 503.93
## <none> 1426575 505.07
## - M.F 1 84491 1511065 505.77
## - U1 1 99463 1526037 506.24
## - Prob 1 198571 1625145 509.20
## - U2 1 208880 1635455 509.49
## - M 1 320926 1747501 512.61
## - Ed 1 386773 1813348 514.35
## - Ineq 1 594779 2021354 519.45
## - Po1 1 1127277 2553852 530.44
##
## Step: AIC=503.93
## .outcome ~ M + Ed + Po1 + M.F + U1 + U2 + Ineq + Prob
##
## Df Sum of Sq RSS AIC
## <none> 1453068 503.93
## - M.F 1 103159 1556227 505.16
## - U1 1 127044 1580112 505.87
## - Prob 1 247978 1701046 509.34
## - U2 1 255443 1708511 509.55
## - M 1 296790 1749858 510.67
## - Ed 1 445788 1898855 514.51
## - Ineq 1 738244 2191312 521.24
## - Po1 1 1672038 3125105 537.93Now we’re going to create a regression model based on the results of the Stepwise regression output to only include the features based on the highest AIC score. We’ll first run the lm with the original dataset, followed by the reduced feature set produced from the stepwise output.
##
## Call:
## lm(formula = Crime ~ M.F + U1 + Prob + U2 + M + Ed + Ineq + Po1,
## data = uscrime_data.norm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -444.70 -111.07 3.03 122.15 483.30
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 905.09 28.52 31.731 < 2e-16 ***
## M.F 65.83 40.08 1.642 0.10874
## U1 -109.73 60.20 -1.823 0.07622 .
## Prob -86.31 33.89 -2.547 0.01505 *
## U2 158.22 61.22 2.585 0.01371 *
## M 117.28 42.10 2.786 0.00828 **
## Ed 201.50 59.02 3.414 0.00153 **
## Ineq 244.70 55.69 4.394 8.63e-05 ***
## Po1 305.07 46.14 6.613 8.26e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 195.5 on 38 degrees of freedom
## Multiple R-squared: 0.7888, Adjusted R-squared: 0.7444
## F-statistic: 17.74 on 8 and 38 DF, p-value: 1.159e-10## [1] "Seperation between output for model1 and model2"##
## Call:
## lm(formula = Crime ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop +
## NW + U1 + U2 + Wealth + Ineq + Prob + Time, data = uscrime_data.norm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -395.74 -98.09 -6.69 112.99 512.67
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 906.380 59.113 15.333 5.08e-16 ***
## M 110.382 52.424 2.106 0.04344 *
## So -3.803 148.755 -0.026 0.97977
## Ed 210.678 69.458 3.033 0.00486 **
## Po1 572.995 315.347 1.817 0.07889 .
## Po2 -305.958 328.483 -0.931 0.35883
## LF -26.826 59.394 -0.452 0.65465
## M.F 51.293 59.977 0.855 0.39900
## Pop -27.906 49.095 -0.568 0.57385
## NW 43.234 66.642 0.649 0.52128
## U1 -105.056 75.906 -1.384 0.17624
## U2 141.714 69.536 2.038 0.05016 .
## Wealth 92.792 100.028 0.928 0.36075
## Ineq 281.954 90.630 3.111 0.00398 **
## Prob -110.394 51.667 -2.137 0.04063 *
## Time -24.655 50.780 -0.486 0.63071
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 209.1 on 31 degrees of freedom
## Multiple R-squared: 0.8031, Adjusted R-squared: 0.7078
## F-statistic: 8.429 on 15 and 31 DF, p-value: 3.539e-07As you can see the increase in score for the adjusted R2 taking into account the number of features, I would say that model1 with the features defined by stepwise is the better perfmorming model compared to model2.
coef(lasso,s = lasso$lambda.min)## 16 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) 888.760971
## M 82.888559
## So 47.952148
## Ed 116.058564
## Po1 310.189409
## Po2 .
## LF 2.228622
## M.F 49.818594
## Pop .
## NW 3.623195
## U1 -13.837819
## U2 46.698552
## Wealth .
## Ineq 175.547425
## Prob -80.415268
## Time .lasso_lm <- lm(Crime ~ M + So + Ed + Po1 + M.F + Pop + NW + U1 + U2 + Wealth + Ineq + Prob, data = uscrime_data.norm)
summary(lasso_lm)##
## Call:
## lm(formula = Crime ~ M + So + Ed + Po1 + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob, data = uscrime_data.norm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -434.18 -107.01 18.55 115.88 470.32
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 897.29 51.91 17.286 < 2e-16 ***
## M 112.71 49.35 2.284 0.02876 *
## So 22.89 125.35 0.183 0.85621
## Ed 195.70 62.94 3.109 0.00378 **
## Po1 293.18 64.99 4.511 7.32e-05 ***
## M.F 48.92 48.12 1.017 0.31656
## Pop -33.25 45.63 -0.729 0.47113
## NW 19.16 57.71 0.332 0.74195
## U1 -89.76 65.68 -1.367 0.18069
## U2 140.78 66.77 2.108 0.04245 *
## Wealth 83.30 95.53 0.872 0.38932
## Ineq 285.77 85.19 3.355 0.00196 **
## Prob -92.75 41.12 -2.255 0.03065 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 202.6 on 34 degrees of freedom
## Multiple R-squared: 0.7971, Adjusted R-squared: 0.7255
## F-statistic: 11.13 on 12 and 34 DF, p-value: 1.52e-083- Elastic
Elastic net can be configured to either use Ridge Regression or Lasso based on the alpha value. In our case we will specify an alpha of 0.5 to remain in the between the 0-1 range.
elastic_net=cv.glmnet(x=matrix_x,y=matrix_y,alpha=0.5,
nfolds = 5,type.measure="mse",family="gaussian")
#Output the coefficients of the variables selected by Elastic Net
coef(elastic_net, s=elastic_net$lambda.min)## 16 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) 886.927584
## M 86.292289
## So 53.337721
## Ed 127.635972
## Po1 231.389510
## Po2 57.601279
## LF 5.083741
## M.F 60.187490
## Pop .
## NW 14.671228
## U1 -41.489261
## U2 76.953380
## Wealth 16.598189
## Ineq 178.902468
## Prob -85.594752
## Time .elastic_lm <- lm(Crime ~ M + So + Ed + Po1 + Po2+ LF + M.F + NW + U1 + U2 + Wealth + Ineq + Prob, data = uscrime_data.norm)
summary(elastic_lm)##
## Call:
## lm(formula = Crime ~ M + So + Ed + Po1 + Po2 + LF + M.F + NW +
## U1 + U2 + Wealth + Ineq + Prob, data = uscrime_data.norm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -362.46 -111.81 -11.25 110.56 470.07
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 902.116 57.581 15.667 < 2e-16 ***
## M 108.054 50.708 2.131 0.04064 *
## So 8.722 144.545 0.060 0.95225
## Ed 212.991 68.053 3.130 0.00365 **
## Po1 497.845 292.064 1.705 0.09767 .
## Po2 -239.636 301.133 -0.796 0.43185
## LF -30.057 57.578 -0.522 0.60514
## M.F 75.048 51.770 1.450 0.15659
## NW 31.952 62.388 0.512 0.61196
## U1 -108.086 72.904 -1.483 0.14767
## U2 138.808 67.811 2.047 0.04869 *
## Wealth 78.913 96.758 0.816 0.42059
## Ineq 266.813 85.986 3.103 0.00391 **
## Prob -91.216 41.227 -2.213 0.03396 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 205 on 33 degrees of freedom
## Multiple R-squared: 0.7984, Adjusted R-squared: 0.719
## F-statistic: 10.05 on 13 and 33 DF, p-value: 4.781e-08