Estimate a multiple linear regression relationship with the U.K. stock returns a

Question

Estimate a multiple linear regression relationship with the U.K. stock returns as the dependent variable, and U.K. T-Bill Returns, U.S. Stock Returns, and Japan Stock Returns as the independent variables using the monthly data covering the sample period 1950-2015 (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 5% level of significance. Provide the interpretation of the significant slope estimates.

Conduct a test for the overall significance of the regression equation at the 5% level of significance. (Test for the significance of the regression relationship as a whole)

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

SUMMARY OUTPUT Regression Statistics Multiple R 0.66392931 R Square 0.440802129 Adjusted R Square 0.438670498 Standard Error 4.304508798 Observations 791 ANOVA df SS MS F Significance F Regression 3 11494.76525 3831.588416 206.7910089 6.9213E-99 Residual 787 14582.16244 18.52879599 Total 790 26076.92769 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept -0.125292619 0.160245733 -0.781878033 0.434521418 -0.439852248 0.189267011 -0.539061652 0.288476414 RUK 0.871796773 0.064288839 13.56062398 8.45969E-38 0.745598883 0.997994662 0.705797153 1.037796392 RSUS 0.651924447 0.038308727 17.01764855 1.54904E-55 0.576725073 0.727123821 0.553007836 0.750841057 RSJA 0.099635519 0.027377313 3.639346142 0.00029118 0.045894322 0.153376716 0.028944811 0.170326227

Explanation / Answer

The multiple linear regression equation is

return = -0.125292619 + 0.871796773 RUK + 0.651924447 RSUS + 0.099635519 RSJA

t-test:

For intercept, P-value 0.434521418 > alpha 0.05, So we accept H0. Thus we conclude that the population intercept is zero

For RUK, P-value 8.45969E-38  < alpha 0.05, So we reject H0. Thus we conclude that the population regression coefficient is not equal to zero

For RSUS, P-value 1.54904E-55  < alpha 0.05, So we reject H0. Thus we conclude that the population regression coefficient is not equal to zero

For RSJA, P-value 0.00029118 < alpha 0.05, So we reject H0. Thus we conclude that the population regression coefficient is not equal to zero

F-test:

H0: The regression equation is not good fit to the given data

H1: The regression equation is good fit to the given data

Let the los be alpha = 5%

The p-Vlaue of regression is 6.9213E-99 <0, So we reject H0

Thus we conclude that the regression equation is good fit to the given data

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