Sta-209-04 (Spring 24) Homework #4

From the Introduction to Modern Statistics (IMS) textbook, complete the following exercises:

• Ch 7.5 Exercises: #6, #8

Also complete the additional questions given below:

Question #1: This question uses data from a large, public university facing accusations of sex-based discrimination in its graduate school admissions. The data set includes each admission decision for the 6 largest graduate departments. Each applicant was given an anonymous identifier.

adm = read.csv("https://remiller1450.github.io/data/admissions.csv")

• Part A: Create a two-way frequency table, then use conditional proportions to compare the proportion of male applicants that were admitted with the proportion of female applicants that were admitted.
• Part B: Create an appropriate type of bar chart that shows the relationship between the variables dept and sex. Briefly explain how these variables are related.
• Part C: Create an appropriate type of bar chart that shows the relationship between the variables dept and admit. Briefly explain how these variables are related.
• Part D: Is the variable dept confounding the relationship between the variables sex and admit? Briefly explain.
• Part E: Find and compare the proportion of male applicants that were admitted with the proportion of female applicants that were admitted within department “A”. Hint: use the filter() function to create a data set containing only cases that applied to department A.
• Part F: Is this an example of Simpson’s Paradox? Briefly explain.

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Question #2: This question uses team data for each of the 82 regular season games played by the Golden State Warriors during their record setting 2015-16 season.

gsw = read.csv("https://remiller1450.github.io/data/GSWarriors.csv")

• Part A: Use the mutate() function in the dplyr package to create a new variable called “pt_margin” that is the difference between the points scored by the Warriors (ie: Points) and the points scored by their opponent (ie: OppPoints). This variable should have positive values when the Warriors outscored their opponent. Hint: The mutate() function was covered in the dplyr lab.
• Part B: Create a scatter plot showing the relationship between the variables FG3A (the number of 3-point shot attempts by the Warriors) and the variable pt_margin (that you created in Part A). Briefly describe the relationship between these two variables.
• Part C: Add a “loess” smoother to the scatter plot from Part B and decide whether Pearson’s correlation or Spearman’s rank correlation is the more appropriate measure of association. Then, find and report the appropriate correlation coefficient.
• Part D: Fit a simple linear regression model that uses the response variable pt_margin and the explanatory variable FG3A. Interpret the estimated slope coefficient for the variable FG3A.
• Part E: Now fit a multivariable regression using the response variable pt_margin and the explanatory variables FG3 (the number of made 3-point shots) and FG3A. Interpret the estimated slope coefficient for the variable FG3A.
• Part F: In your own words, explain why the coefficient of FG3A is very different in the model from Part E when compared to its value in the model from Part D.
• Part G: Fit a multivariable regression model that uses the explanatory variables Location and FG3 to predict the response variable pt_margin. Interpret the estimated coefficient of the re-coded variable LocationHome.
• Part H: Now remove the explanatory variable FG3 from the model you fit Part G (ie: fit a regression model with the single predictor Location and the response variable pt_margin). Provide a brief explanation as to why the estimated coefficient of the re-coded variable LocationHome in this model is approximately the same as the estimated coefficient of this variable in the model from Part G (which also included FG3).

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Submission instructions

• Use R Markdown to create a document containing your answers and any R code used.