The Canadian exchange rate may be related to the TSX indices of performance of various sectors of the Canadian economy. The data file used in Exercise 25 contains monthly TSX indices for various sectors of the Canadian economy together with the exchange rate between Canadian and U.S. dollars for the period 2010–2015. Perform a stepwise regression as follows:

a) Step 1. Conduct three simple (single-variable) regressions of the exchange rate against the indices for (i) energy, (ii) gold, and (iii) metals and mining (M&M). Without checking the conditions and assumptions, give the equation for each regression and the corresponding value of R². Which index explains most of the variability in exchange rate?

b) Step 2. Now perform two more regressions. On the basis of the index you chose with the highest R² in (a), add each of the other two indices one at a time. Give the equation for each regression and the corresponding value of the adjusted R². Just on the basis of the analysis you have done (Exercise 36 will address other factors), do you recommend adding a second index to combine with the one you chose in Step 1 in order to explain the variability in the exchange rate? If so, which index?