50 lines
2.8 KiB
Plaintext
50 lines
2.8 KiB
Plaintext
---
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title: "hw9"
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author: "Mark Pearl"
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date: "3/12/2020"
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output:
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html_document: default
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pdf_document: default
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---
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```{r setup, include=FALSE}
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library('FrF2')
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```
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## R Markdown
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# Question 12.1
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Describe a situation or problem from your job, everyday life, current events, etc., for which a design of experiments approach would be appropriate.
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If I were to trace this back to sports. A good example of an experiment would be when a company is testing the effectiveness of a new hockey stick when producing a shot. Factors such as player weight, age, strength, technique, etc. We would be able to control these factors to determine their overall effectiveness of the stick.
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# Question 12.2
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To determine the value of 10 different yes/no features to the market value of a house (large yard, solar
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roof, etc.), a real estate agent plans to survey 50 potential buyers, showing a fictitious house with
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different combinations of features. To reduce the survey size, the agent wants to show just 16 fictitious
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houses. Use R’s FrF2 function (in the FrF2 package) to find a fractional factorial design for this
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experiment: what set of features should each of the 16 fictitious houses have? Note: the output of
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FrF2 is “1” (include) or “-1” (don’t include) for each feature.
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```{r house}
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library('FrF2')
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FrF2(nruns = 16, nfactors = 10)
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```
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From the results we can see that the first combination we should only keep the following features: {A, B, D, E, H}. This same logic can be used to determine which factors to keep from rows (i.e. houses) 2-16. Since we have 10 features and 2 possible expected values, then we can have 1024 permutations or combinations of 16 factor sets.
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# Question 13.1
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For each of the following distributions, give an example of data that you would expect to follow this distribution (besides the examples already discussed in class).
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Answer
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i) Bionmial: An example of data that follows the Binomial distribution is a survey of responses to a yes-no question where the probably of responses is known or can be estimated. An example could be a team winning or losing a game.
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ii) Geometric: Number of times I take a shot with my hockey stick before my stick breaks.
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iii) Poisson: This distribution is excellent at modeling event occurances over an interval of time. Number of parking tickets issued in the City of Ottawa in the morning between 7 to 9 AM.
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iv) Exponential: This distribution can model the lengths of inter-arrival times between events modeled by the Poisson distribution. An example of this could be the time between parking tickets issued.
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v) Weibull: This distribution is used to model factors where the probability changes over time. An example of this would be the odds of winning a 50 to 50 ticket at a hockey game as the time get closer to the annoucement of the winner.
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