# 1.a. Conduct a two-sample t-test to find out if there is a significant difference between U.S. stock returns and U.S. corporate bond returns using the monthly data covering the sample period 1980-2017…

1.a. Conduct a two-sample t-test to find out if there is a
significant difference between U.S. stock returns and U.S.
corporate bond returns using the monthly data covering the sample
period 1980-2017. 1.b. Conduct a two-sample t-test to find out if
there is a greater returns for U.S. stock as compared to U.K. stock
returns using the monthly data covering the sample period
1980-2017. 2. Estimate a multiple linear regression relationship
with the U.K. stock returns as the dependent variable, and U.K.
Bonds Returns, 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).
a. Show the estimated regression relationship b. Conduct a t-test
for statistical significance of the individual slope coefficients.
Provide the interpretation of the significant slope estimates. c.
Conduct a test for the overall significance of the regression
equation. (Test for the significance of the regression relationship
as a whole) d. Present the R-Square (Coefficient of Determination)
and its interpretation.

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.735992889 0.541685532 0.538636877 3.523412257 455 ANOVA Significance F MS Regression Residual Total 3 6617.396126 2205.798709 177.6801681 4.89572E-76 451 5598.90970512.41443393 454 12216.30583 Coefficients Standard Error t Stat 0.115186435 0.17010687 0.730332455 0.041983928 17.39552475 3.10678E-52 0.647824048 0.812840861 0.621729509 0.8389354 0.209729348 0.029769306 7.045154189 6.96789E-12 0.15122558 0.268233116 0.132722873 0.286735823 0.113600031 0.030384391 3.738762846 0.000208723 0.053887475 0.173312588 0.030500247 0.192197593 P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept RSUS RSJA RUK 0.677141581 0.498663306-0.219114035 0.449486905 -0.324841646 0.555214515

## Solutions

##### Expert Solution

Based on the output obtained,

The fitted regression equation

Estimated UK Stock Returns

To test the significance of each of these estimated regression
coefficients:

To test:
Vs

The columns 't stat' and 'p-value' gives the result for the t
test for significance for each regression coefficient:

Since, the p-values for the t test of significance of each of
the 3 predictors were significant, we do not have sufficient
evidence to support the null hypothesis. We may reject
H0 at 5% level.We may conclude that:

The individual predictors of the model were examined and the
result indicated that RSUS (t = 17.395, p = .000), RSJA (t = 7.045,
p = .000) and RUK (t =3.738, p = .0002) were significant predictors
in the model.

To test the overall significance of the model:

To test: H0: The fitted model is similar to the
intercept only model. Ha: The fitted model is more
efficient than the intercept model.

Since, the p-value of the F test for overall significance 0.000
< 0.05, we do not have sufficient evidence to support the null
hypothesis. We may reject H0 at 5% level.We may conclude
that:

Results of the multiple linear regression indicated that there
was a overall significant effect of RSUS, RSJA and RUK on UK Stock
returns, (F(3,451) = 177.6801681, p = 4.89572E-76).

d. The goodness of fit measure R2 explains the amount
of variation in the dependent variable that is explained by the
predictors in the model.

We find that the coefficient of determination, R2 =
0.5417; i.e. the predictors of the model together explains about
54.17% of the variation in UK Stock returns. The model may be
concluded to be a moderate fit to the data.It can be improved by
increasing the number of potential predictors.