8.15 Suppose the production of certain model automobile is summarized by the data below.

Fit a regression line to the data by ordinary least squares, adopting the model yt = a + bt + et, t = 1, ... , 4, where yt = production at time t, and t = (year—1970). This should be done without mechanical aids. Assume et = ρet—1 + ut, |ρ| < 1, where the ut’s are mutually uncorrelated with mean zero and constant variance. Give an estimate of ρ. Use a computer program such as BMD01R (UCLA Biomed) to carry out Part

(a) and compare results. Plot the residuals. Would you expect to have the sign found in Part

(b) based upon your plot of the residuals? Why?