Question

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

Show the estimated regression relationship

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.

Conduct a test for the overall significance of the regression equation at the 1% level of significance. (Test for the significance of the regression relationship as a whole)

Present the R-Square (Coefficient of Determination) and its interpretation.

Solution:

First, we need to obtain the Excel print out using the data in Table GFD Final Monthly Returns.

1% level of significance in both t tests and the F test.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.735992889
R Square	0.541685532
Adjusted R Square	0.538636877
Standard Error	3.523412257
Observations	455
ANOVA
	df	SS	MS	F	Significance F
Regression	3	6617.396126	2205.798709	177.6801681	4.89572E-76
Residual	451	5598.909705	12.41443393
Total	454	12216.30583

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	0.115186435	0.17010687	0.677141581	0.498663306	-0.219114035	0.449486905	-0.324841646	0.555214515
RSUS	0.730332455	0.041983928	17.39552475	3.10678E-52	0.647824048	0.812840861	0.621729509	0.8389354
RSJA	0.209729348	0.029769306	7.045154189	6.96789E-12	0.15122558	0.268233116	0.132722873	0.286735823
RUK	0.113600031	0.030384391	3.738762846	0.000208723	0.053887475	0.173312588	0.03500247	0.192197593

Answer 1

The regression equation:

Regression equation dependent variables are linearly relationship with an output variables.

For every additonal RSUS, the Uk stock value increases by 0.730332455 units

Fore very additonal unit of RSJA value, the UK stock value increases by 0.209729348 units

For every additonal unit of RUK value, tha UK stock value increases by 0.113600031 units.

b) T-test for statistical significane for slope:

and

the degree of freedom: DFresidual= 451

The test statistic:

RSUS test statistic: 17.39552475 and P-value: 0.0000

The test statistic is significant and rejects H0. There is sufficient evidence to support that there is a significant relationship with output variable.

RSJA test statistic: 7.045154189 and P-value: 0.0000

The test statistic is significant and rejects H0. There is sufficient evidence to support that there is a significant relationship with output variable.

RUK test statistic: 3.738762846 and P-value: 0.0002

The test statistic is significant and rejects H0. There is sufficient evidence to support that there is a significant relationship with output variable.

c) Overall significane test:

Atleast one is not equal

df1= DFRegression=3

df2= DFresidual=451

The test statistic:

P-value: 0.000

The test statistic is significant and rejects H0. There is sufficient evidence to support that there is significant relationship between input and output variables.

R-squared value:

The proporiton of variation explained by regression equation is 0.541685532.