The College Athletes data set on the text CD comes from a study of the University of Georgia female athletes. The response variable BP = maximum bench press (1RM in data set) has explanatory variables LBM = lean body mass (which is weight times 1 minus the proportion of body fat) and REP_BP = number of repetitions before fatigue with a 70-pound bench press (REPS70 in data set). Let’s look at all the steps of regression analysis for these data.
a. The first figure shows a scatterplot matrix. Which two plots in the figure describe the associations with BP as a response variable? Describe those associations.
b. The results of multiple regression analyses are shown in the next column. Write down the prediction equation, and interpret the coefficient of REP_BP.
c. Report R2, and interpret its value in the context of these variables.
d. Based on the value of R2, report, and interpret the multiple correlations.
e. Interpret the results of the F test that BP is independent of these two predictors. Show how to obtain the F statistic from the mean squares in the ANOVA table.
f. Once REP_BP is in the model, does it help to have LBM as a second predictor? Answer by showing all steps of a significance test for a regression parameter.
g. Examine the histogram shown of the residuals for the multiple regression model. What does this describe, and what does it suggest?
h. Examine the plot shown of the residuals plotted against values of REP_BP. What does this describe, and what does it suggest?
i. From the plot in part h, can you identify a subject whose BP value was considerably lower than expected based on the predictor values? Identify by indicating the approximate values of REP_BP and the standardized residual for that subject.
Regression of maximum bench press on LBM and REP_BP
Scatterplot matrix for Exercise 13.37.
Residual plot for Exercise 13.37, part g.
Residual plot for Exercise 13.37, part h.