Question

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.72707618
R Square	0.52863977
Adjusted R Square	0.52550434
Standard Error	3.57320675
Observations	455
ANOVA
	df	SS	MS	F	Significance F
Regression	3	6458.02511	2152.67504	168.601791	2.7119E-73
Residual	451	5758.28072	12.7678065
Total	454	12216.3058
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	-0.2501489	0.35921136	-0.6963835	0.48654745	-0.9560846	0.45578693	-1.1793476	0.67904987
RUK	0.02507938	0.0238127	1.05319345	0.29281626	-0.0217182	0.07187699	-0.0365187	0.08667745
RSUS	0.71372752	0.04232832	16.8617037	8.0578E-50	0.6305423	0.79691273	0.60423372	0.82322131
RSJA	0.22210429	0.02999629	7.40439254	6.5208E-13	0.16315445	0.28105414	0.14451066	0.29969792

Estimate a multiple linear regression relationship with the U.K. stock returns as the dependent variable, and U.K. Corporate Bond yield (Proxy for Interest rate), U.S. Stock Returns, and Japan Stock Returns as the independent variables using the monthly data covering the sample period 1980-2017

1. Show estimated regression relationship

2. Conduct a t-test for statistical significance of the individual slope coefficients at the 1%

   level of significance. Provide the interpretation of the significant slope estimates.

3. Conduct a test for the overall significance of the regression equation at the 1% level of

   significance

4. R2?

Answer 1

A) Let U.K. stock return be denoted by UK . The regression equation is given by :-

UK = 0.02507938 RUK + 0.22210429 RSJA + 0.71372752 RSUS - 0.2501489.

B) The t Statistic is given above and it is defined by

t_stat = coefficient/ standard error and by the t table we can compute the p-value. Here the p-value< 0.01(level of significance) . This is satisfied by only RSUS and RSJA. Therefore, RSUS and RSJA are significant. This means that RSUS and RSJA does effecr the return. But the other two does not show significant effect on return . The positive magnitude of coefficients show that as one of them increase return increases positively.

C) The overall significance will be shown by F statistic . As calculated F (168.601791) > tabulated F. Therefore we can conclude that overall model is significant and the US stock return is dependent on these variables.

D) The is given by 0.52863977 which explains the variation explained by the model.