Author:
Christine Farr

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.

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