7.9.1. To see the effect on fits that "good" and "bad" points of high leverage can have, consider the following dataset:

The point x = 20 is a point of high leverage. The data for y (rounded) are realizations from the model y = 4x + e, where e has a N (0, 9) distribution. Hence, the the value of y follows the model and is a "good" point of high leverage. Notice that y2 is the same as y, except the last component of y2 has been changed to 20 and, thus, is a "bad" point of high leverage.

1. (a)Obtain the scatterplot for x and y, the Wilcoxon and HBR fits, and overlay these fits on the scatterplot.
2. (b)Obtain the scatterplot for x and y2, the Wilcoxon and HBR fits, and overlay these fits on the scatterplot.
3. (c)Comment on the differences among the fits and plots.