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# 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 − .288x1 + .248x2 + .45x3 − .543x4 + .005x5 with a couple of outliers.
15.7 a. The estimate is

b. First we solve the following

which gives d1 = −66.41 and d2 = 205.27. Then the confidence interval is

15.9 The normal-theory confidence interval for β2 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 x0. Bootstrap this m times and store all of these mean responses. Finally, find the standard deviation of these responses. ...

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