Sta-209 (Fall 2026) Homework #5

Directions:

• Submit your final answers and all supporting work on Canvas (under the “Assignments” tab)
• You must submit HTML output generated using R Markdown for this assignment.
• Homework is intended to be individual work. While you may discuss the assignment with your peers, you should submit answers that are uniquely your own.
• Any assistance you receive from resources/materials not on our course website (such as other websites, course mentors, peer students, AI, etc.) should be clearly acknowledged

Question #1

In a previous lab you worked with the “TSA claims” data set, which contains information on a random sample of \(n=5000\) claims made against the Transportation Security Administration by travelers.

tsa_data = read.csv("https://remiller1450.github.io/data/tsa_small.csv")

• Part A: Use the filter() function (introduced in Lab 5) to create a subset of the TSA claims dataset that only contains claims whose status is “Settled” and whose claim amount is greater than zero. These are claims where the TSA settled, meaning they agreed to pay the claimant somewhat less than they asked for.
• Part B: Using your subset from Part A, create a scatterplot with a loess smoother showing the relationship between claim_amount (how much the traveler asked for in damages) and close_amount (the settled amount that the TSA actually paid them). Describe the strength, form, and direction of the relationship you see.
• Part C: Consider a regression analysis involving these two variables and the principle that we should never use information from the future to predict the past. With this in mind, which variable, claim_amount or close_amount, should be the explanatory variable in the regression model? Which should be the response variable? Briefly explain.
• Part D: Write out the population-level simple linear regression model using the variables you provided in Part C.
• Part E: Use the lm() function to fit the model, then use the summary() function to print a summary of it. Based upon this output, write out the fitted model equation.
• Part F: Use your fitted model to predict the mean settled amount when the claim amount is $1000.
• Part G: Provide a 1-sentence conclusion summarizing the hypothesis test on the slope coefficient provided in the summary of your fitted model from Part E. Your conclusion should include:
  • The statement indicating the strength of statistical evidence.
  • An interpretation of the estimated slope coefficient in the fitted model.
• Part H: Use the plot() function to create the two diagnostic plots covered in Lab 9. Do the assumptions of the model proposed in Part D seem appropriate? Briefly explain.
• Part I: Perform a log-transformation on both the explanatory and response variables in the model you fit in Part E (you may do the transformation directly in the model formula using the log() function). Recreate the diagnostic plots you made in Part H using this model, then briefly comment upon whether the model using log-transformed data seems more appropriate for statistical inference, based on the residual diagnostics.

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Question #2

The data below were collected by The College Scorecard on all primarily undergraduate colleges in the US in the year 2024. Recall that you worked with these data on our previous homework assignment.

colleges2024 = read.csv("https://remiller1450.github.io/data/Colleges_2024_Complete.csv")

• Part A: Create side-by-side boxplots showing the distribution of Avg_Fac_Salary by Region. Briefly describe whether there appears to be substantial variability in Avg_Fac_Salary across regions. Hint: You made this type of graph in Lab 5
• Part B: Fit a regression model using Avg_Fac_Salary as the outcome and Region as a categorical predictor. Print a summary of the fitted model.
• Part C: Use the table() function to produce a frequency table showing how many colleges are located in each region. Comparing this table to the output from Part B, which region did the model use as its reference category?
• Part D: Interpret the intercept of the fitted model. What quantity does it estimate?
• Part E: Interpret the coefficient of the dummy variable RegionPacific. Is there statistically significant evidence that the mean Avg_Fac_Salary for colleges in this region differs from the reference category?
• Part F: Suppose we wanted to use a regression model with Region as a categorical predictor to compare the mean values of Avg_Fac_Salary for the New England and Pacific regions. Briefly explain how we’d need to modify our initial model so that this comparison is provided in the output produced by the summary() function.