Weight and height. The weights and heights of twenty male 'Students in a freshman class are recorded in order to see how well weight (Y, in pounds) can be predicted from height (X, in inches). The data are given below. Assume that first-order regression (I. 1) is appropriate.
a. Fit a simple linear regression model using ordinary least square and plot the data together
with the hued regression function. Also, obtain an Index plot of Cook s distance (10.33 What do these plots suggest'?
b. Obtain the scaled residuals in (11.47) and use the Huber weight function (11.44) to ohm' case weights for a first iteration of IRLS robust regression. Which cases receive the smallest Huber weights? Why'!
c. Using the weights calculated in part (b), obtain the weighted least squares estimates of the regression coefficients. How do these estimates compare to those found in part (a) using ordinary least squires'?
d. Continue the IRLS procedure for two more iterations. Which cases receive the smallest weights in the final iteration'? How do the linal IRLS robust regression estimates compare to the ordinary least squares estimates obtained in part (a)?