At the beginning of this chapter, we repeated data from Chapter 4 on shoe size and height for a sample of students at Arizona State University. In Chapter 4, you used those data to perform some descriptive regression and correlation analyses. Now you are to employ those same data to carry out several inferential procedures in regression and correlation. We recommend that you use statistical software or a graphing calculator to solve the following problems, but they can also be done by hand:
a. Separate the data in the table on page 551 into two tables, one for males and the other for females. Parts (b)–(j) are for the male data.
b. Determine the sample regression equation with shoe size as the predictor variable for height.
c. Perform a residual analysis to decide whether considering Assumptions 1–3 for regression inferences to be satisfied by the variables shoe size and height appears reasonable.
d. Find and interpret the standard error of the estimate.
e. Determine the P-value for a test of whether shoe size is useful for predicting height. Then refer to Table 9.8 on page 360 to assess the evidence in favor of utility.
f. Find a point estimate for the mean height of all males who wear a size 1012 shoe.
g. Obtain a 95% confidence interval for the mean height of all males who wear a size 1012 shoe. Interpret your answer.
h. Determine the predicted height of a male who wears a size 1012 shoe.
i. Find a 95% prediction interval for the height of a male who wears a size 1012 shoe. Interpret your answer.
j. At the 5% significance level, do the data provide sufficient evidence to conclude that shoe size and height are positively linearly correlated?
k. Repeat parts (b)–(j) for the unabridged data on shoe size and height for females. Do the estimation and prediction problems for a size 8 shoe.
l. Repeat part (k) for the data on shoe size and height for females with the outlier removed. Compare your results with those obtained in part (k).