For the Johnson & Johnson data, say yt, shown in Figure 1.1, let xt = log(yt). (a) Fit the regression model xt = t +

For the Johnson & Johnson data, say yt, shown in Figure 1.1, let xt =

log(yt).

(a) Fit the regression model xt = βt + α1Q1(t) + α2Q2(t) + α3Q3(t) + α4Q4(t) + wt where Qi(t) = 1 if time t corresponds to quarter i = 1, 2, 3, 4, and zero otherwise. The Qi(t)’s are called indicator variables. We will assume for now that wt is a Gaussian white noise sequence. What is the interpretation of the parameters β, α1, α2, α3, and α4? (Detailed code is given in Appendix R on page 574.)

(b)What happens if you include an intercept term in the model in (a)?

(c) Graph the data, xt, and superimpose the fitted values, say xbt, on the graph. Examine the residuals, xt − xbt, and state your conclusions. Does it appear that the model fits the data well (do the residuals look white)?