Based on the output obtained,
The fitted regression equation
Estimated UK Stock Returns
To test the significance of each of these estimated regression
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
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.
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0.1 1 51 86435+0.730332455( RSUS)-0.209729348 (RSJA)一0.11 3600031( RUK)
На : 3, 0.1 = 1.2,3
Coefficients Standard Errort Stat 0.1151864350.17010687 0.677141581 0.498663306 -0.219114035 0.449486905 0.730332455 0.041983928 17.39552475 3.10678E-52 0.647824048 0.812840861 0.209729348 0.029769306 7.045154189 6.96789E-12 0.15122558 0.268233116 0.113600031 0.030384391 3.738762846 0.000208723 0.053887475 0.173312588 P-value Lower 95% |Upper 95% Intercept RSUS RSJA RUK
ANOVA Significance F 3 6617.3961262205.798709 177.68016814.89572E-76 df 3 Regression Residual Total 515598.909705 12.41443393 5412216.30583
Regression Statistics Multiple R R Square Adjusted R Square 0.538636877 Standard Error Observations 0.735992889 0.541685532 3.523412257