The data file freddiel contains a monthly housing price index for the price of houses in Beckley, West Virginia (BEKLY), and the monthly value of Australian exports to China (XCHINA), from 1988M1 to \(2015 \mathrm{M} 12\).

a. Estimate the regression equation XCHINA \(_{t}=\beta_{1}+\beta_{2} B E K L Y_{t}+e_{t}\) and comment on the results.

b. Plot the series BEKLY, XCHINA, and \(\ln (X C H I N A)\) and describe the graphs. Do they provide any insights into the results from part (a)?

c. Estimate the equation \(\ln \left(X C H I N A_{t}\right)=\beta_{1}+\delta t+\beta_{2} B E K L Y_{t}+e_{t}\) and comment on the results. Suggest a reason why \(\ln (X C H I N A)\) rather than XCHINA was chosen as the left-hand-side variable.

d. Do unit root tests suggest \(\ln (X C H I N A)\) and \(B E K L Y\) are stationary or trend stationary? Do the test results provide any insights into the results in part (c)?