In Exercise 25, we regressed the Canadian exchange rate against TSX indices for metals and mining (M&M), gold, and energy, since these are sectors in which the Canadian economy is strong, and they could therefore inf luence the exchange rate. Investigate the effectiveness of these indices at predicting the exchange rate as follows:

a) Perform a simple (single-variable) regression of exchange rate as the dependent variable against the metals and mining index. Give the results of the regression, including the R², the standard errors, and the P-values for each coefficient.

b) Now add the gold index to the regression you did in (a). Give the results of the regression, including the R², the standard errors, and the P-values for each coefficient.

c) By what percentage has the coefficient of the M&M index increased between (a) and (b)?

d) In order to see how much additional information the gold index is bringing to our regression over and above what we already had from the M&M index, we now regress the gold index as the dependent variable against the M&M index as the explanatory variable. Give the results of the regression, including the R², the standard errors, and the P-values for each coefficient.

e) What is the variance inf lation factor (VIF) for the gold index?

f) Using the results of (a) to (e) above, give reasons for including the gold index in the exchange rate regression in addition to the M&M index.

g) Using the results of (a) to (e) above, give reasons against including the gold index in the exchange rate regression in addition to the M&M index.