Statistics 108
Homework Assignments
Note, all problems listed here are to be written up and handed in on the due date provided. Homework is posted concurrently with the class material. Sections may be assigned at different times but have the same due date as previously assigned problems.
Chapter 4 problems have a due date of Oct 25
(P1) For the data set manager.xslx obtain the Anova table and F-test from the Anova table for the regression of salary on rating from a computer program such as R directly by requesting the output with the statement anova(model) where model is the regression model you fit to the data. State your conclusions in context and compare the F-test to the t-test for non-zero slope.
(P2) For the data set manager.xlsx fit the regression of salary on ratings and obtain the results through the summary(model) statement. Use the output obtained from the summary statement to construct the Anova table. Carry out necessary calculations by hand and show your work. Did you arrive at the same results as in problem 1?
(P3) For the data set manager.xlsx fit a regression of salary on ratings. Obtain the residual plot, plotting the residuals against the fitted values and also against ratings. Label both plots with a title and label the x-axis in both plots. Compare the plots and comment on similarities and differences in appearance. Make a list of model violations and aspects of model fit that can be addressed with a residual analysis. Assess each aspect with respect to both plots. Do the plots show the same or are there differences such that one plot would lead you to conclude that the model assumptions are violated but the other plot would not?
(P4) For the regression model fit in problems 1-3, assess the assumption of normality of the errors. Identify an appropriate plot to use, obtain that plot and comment on the appearance.
(P5) For the data set FEV.csv fit a regression model with lung function FEV (Y) as the response and age as the predictor. Carry out a residual analysis and assess which model assumptions are violated. State all conclusions clearly and in context.
(P6) Using the data set FEV.csv carry out a lack of fit test. State the steps needed to take and provide the R code you used. State your conclusions in context.
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(P7) Carry out a comprehensive data analysis of the association between tips and price of a meal for the restauranttips.xlsx data set. Clearly state all the steps you should take, fit the model, check assumptions and state conclusions in context. Answer the question: do tips increase linearly, on average, with increasing price of a meal? Justify your answer with the analysis you carried out.
(P8) Show b1 is normally distributed in the simple linear regression, using model assump- tions made that are needed to justify the normal distribution and identify the terms involved. Using the data set manager.xlsx calculate the ki explicitly for the first 20 observations.
(P9) Show the residuals are normally distributed and show Pni=1 ei = 0.
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