13.38 College athletes The College Athletes data set on the book’s website comes from a study of University of Georgia female athletes. Using the column names from the data set, the response variable 1RM = maximum bench press has explanatory variables LBM = lean body mass (which is weight times 1 minus the proportion of body fat) and REPS70 = number of repetitions before fatigue with a 70-pound bench press. Let’s look at all the steps of a regression analysis for these data.

a. The first figure shows a scatterplot matrix. Which two plots in the figure describe the associations with 1RM as a response variable? Describe those associations.

b. Results of a multiple regression analysis are shown.

Write down the prediction equation and interpret the coefficient of REPS70.

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 correlation.

e. Interpret results of the F test that 1RM is independent of these two predictors. Show how to obtain the F statistic from the mean squares in the ANOVA table.

f. Once REPS70 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 REPS70. What does this describe, and what does it suggest?
i. From the plot in part h, can you identify a subject whose 1RM value was considerably lower than expected based on the predictor values? Identify by indicating the approximate values of REPS70 and the standardized residual for that subject.

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Regression Equation 1RM 55.01 +0.1668 LBM +1.658 REPS70 Coefficients Term Constant LBM Coef 55.01 0.1668 SE Coef T-Value P-Value 7.74 7.11 0.000 REPS70 1.658 0.0752 0.109 2.22 0.030 15.21 0.000 Model Summary S 7.11957 R-sq 83.17% Analysis of Variance Source DF SS MS F-Value P-Value Regression 2 15283 7641.5 150.75 0.000 Error 61 3092 50.7 Total 63 18375 - LE Matrix Pict of LBM, REPS70, 1RM a RESID Scatterplot matrix for Exercise 13.38. 1RM 320