1. From monthly observations from 1985 to 2015, the following regression results were obtained,
where Y = exchange rate of the Canadian dollar to the U.S. dollar (CAD=USD) and X =
ratio of the U.S. consumer price index to the Canadian consumer price index; that is, X
represents the relative prices in the two countries:
Y hat i =-0.902 + 2.430Xi;
R^2 = 0.440
a) Interpret the estimated intercept and slope coecient. How would you interpret R^2?
b) Does the positive value of the estimated slope coecient make economic sense? What is
the underlying economic theory?
c) Suppose we were to redefine X as the ratio of the Canadian CPI to the U.S. CPI. Would
that change the sign of the coecient of X? Why?
Now Consider the model Yi = 0 + B1Xi + ui
where X and Y are defined as in the previous model. Suppose you are told that the standard error of
B1 is 0.096. Based on this and the estimates presented in question 1:
d) What is the p-value of a test of the hypothesis H0 : B1 = 2 against H1 : B1 > 2?
e) What is the p-value of a test of the hypothesis H0 : B1 = 2 against H1 : B1 not equal to 2?
f) Are your answers to d) and f) dierent? Explain.
g) Construct a 95% condence interval for B1.