### 1A Conduct A Two Sample T Test To Find Out If

##### Question

# 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

H_{0} 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: H_{0}: The fitted model is similar to the

intercept only model. H_{a}: 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 H_{0} 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 R^{2} 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, R^{2} =

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.