The following data are measures of triceps skinfold thickness (X1), thigh circumference (X2), and midarm circumference (X3). These three variables are used to predict percentage of body fat (Y). You can also find the data on beachboard (titled "bodyfat").
Subject X1 X2 X3 Y
1 19.5 43.1 29.1 11.9
2 24.7 49.8 28.2 22.8
3 30.7 51.9 37.0 18.7
4 29.8 54.3 31.1 20.1
5 19.1 42.2 30.9 12.9
6 25.6 53.9 23.7 21.7
7 31.4 58.5 27.6 27.1
8 27.9 52.1 30.6 25.4
9 22.1 49.9 23.2 21.3
10 25.5 53.5 24.8 19.3
11 31.1 56.6 30.0 25.4
12 30.4 56.7 28.3 27.2
13 18.7 46.5 23.0 11.7
14 19.7 44.2 28.6 17.8
15 14.6 42.7 21.3 12.8
16 29.5 54.4 30.1 23.9
17 27.7 55.3 25.7 22.6
18 30.2 58.6 24.6 25.4
19 22.7 48.2 27.1 14.8
20 25.2 51.0 27.5 21.1
(a) Compute the regression of Y on X1.
(b) Compute the regression of Y on X2.
(c) Compute the regression of Y on X1, X2
(d) Compute the regression of Y on X1, X2, X3
In each case, report the results in a brief APA results-style paragraph. For each individual predictor remember to report bs, standard error of each b (or confidence intervals), t-test; and for each overall model report F-test,df, and R^{2}.
(e) Compute the correlation matrix of the predictors (X1-X3)
(f) Compute the tolerance (or VIF) of each predictor for the equation (d) which includes all 3 predictors.
(g) Examine the outlier statistics for the X-space, Y-space, and influence (including DFBETAS for each predictor). Identify the highly discrepant observations, if any.
(h) Comment on what you have learned about this data set, particularly with regard to the three predictors, and interpret the results.