Question

13. Given the following data on the Dollar/Pound exchange rate (y) and the U.S. CPI (x), determine the linear regression equation, and include the Summary Output from Excel. • Based on the Summary Output is the coefficient b2 significant using the t-table (one-tail) at the 5% level with n-2 df? Prove your answer using data from the t-table. • Does the relationship given by the regression equation seem to be a reasonable economic model-- is it reasonable to assume that in this model y = f(x)? Explain why or why not. y x Period Exchange rate $ / £ CPI US 1985 1.2974 107.6 1986 1.4677 109.6 1987 1.6398 113.6 1988 1.7813 118.3 1989 1.6382 124 1990 1.7841 130.7 1991 1.7674 136.2 1992 1.7663 140.3 1993 1.5016 144.5 1994 1.5319 148.2 1995 1.5785 152.4 1996 1.5607 156.9 1997 1.6376 160.5 1998 1.6573 163 1999 1.6172 166.6 2000 1.5156 172.2 2001 1.4396 177.1 2002 1.5025 179.9 2003 1.6347 184 2004 1.833 188.9 2005 1.8204 195.3 2006 1.8434 201.6 2007 2.002 207.342

Answer 1

Part A

Here is the summery output of the regression results,

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.423154
R Square	0.179059
Adjusted R Square	0.139967
Standard Error	0.150327
Observations	23
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.103509	0.103509	4.580411	0.044235
Residual	21	0.474564	0.022598
Total	22	0.578073
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.288571	0.16913	7.618827	1.79E-07	0.936846	1.640295	0.936846	1.640295
X Variable 1	0.002286	0.001068	2.14019	0.044235	6.47E-05	0.004507	6.47E-05	0.004507

Part B

From the summary output, the P value is not statistically significant. Here the coeffcients is 0.002287 which is less than 0.05.

Part C

Yes. when 1 percent change in exchange rate gives 0.2286 percent change in CPI. It means that both inflation rate and exchange rate are positively related. The inflation can influence the exchange rate.