# Chapter 15

# Other Topics in the Use of Regression Analysis

**15.1** It is possible, especially in small data sets, that a few outliers that follow the pattern of the “good” points can throw the fit off.

**15.3** They are both oscillating functions that have similar shapes with Tukey’s bi-weight being a faster wave. However, Tukey’s bi-weight can exceed 1 while Andrew’s wave function cannot.

**15.5** The fitted model is

= 2.34 − .288

*x*_{1} + .248

*x*_{2} + .45

*x*_{3} − .543

*x*_{4} + .005

*x*_{5} with a couple of outliers.

**15.7** **a.** The estimate is

**b.** First we solve the following

which gives *d*_{1} = −66.41 and *d*_{2} = 205.27. Then the confidence interval is

**15.9** The normal-theory confidence interval for β_{2} is .014385±1.717(.003613) = (.0082, .0206). The bootstrap confidence interval is (.0073, .0240) which is similar to the normal-theory interval.

**15.11** First, fit the model. Then, estimate the mean response at *x*_{0}. Bootstrap this *m* times and store all of these mean responses. Finally, find the standard deviation of these responses. ...