With reference to Fox and Hartnagel’s regression of Canadian women’s conviction rates on several explanatory variables:

(a) Use regression diagnostics, as described in Part III of the text, to explore the adequacy of the preliminary OLS regression fit to these data (Equation 16.18 on page 490). If you detect any problems, try to correct them, and then repeat the subsequent analysis of the data.

(b) Show that the estimated parameters of the AR(2) process fit to the errors, φb1 ¼ 1:068 and φb2 ¼ &0:5507 (see Equation 16.19 on page 493), correspond to a stationary timeseries process. (Hint: Use the quadratic formula to solve the equation 1 & 1:068β þ 0:5507β2 ¼ 0, and verify that both roots have modulus greater than 1.)

(c) Reestimate Fox and Hartnagel’s regression with AR(2) errors by EGLS, comparing your results with those produced by the method of maximum likelihood (in Equation 16.19). Obtain estimates of the error autoregression parameters φ1 and φ2 by solving the Yule-Walker equations (see Equations 16.7 on page 485)

r1 ¼ φb þ φb2r1 r2 ¼ φb1r1 þ φb2 where r1 and r2 are the lag-1 and lag-2 sample autocorrelations of the OLS residuals