Let's carry out regression between rates of return of index x and that of stock y. In Excel, go to Data tab->Data Analysis->Regression, and choose returns on index x as X-column and returns of stock y as Y-column. We select 90% as the confidence level for the regression. We get the following regression output:
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.664741084 | |||||||
R Square | 0.441880708 | |||||||
Adjusted R Square | 0.379867454 | |||||||
Standard Error | 3.22363256 | |||||||
Observations | 11 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 74.04770173 | 74.04770173 | 7.125584856 | 0.025648537 | |||
Residual | 9 | 93.52626191 | 10.39180688 | |||||
Total | 10 | 167.5739636 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 90.0% | Upper 90.0% | |
Intercept | 1.248840147 | 0.984653872 | 1.268303699 | 0.236513141 | -0.978601661 | 3.476281956 | -0.556141599 | 3.053821893 |
x | 0.76992373 | 0.288428019 | 2.669379114 | 0.025648537 | 0.117454221 | 1.42239324 | 0.241202598 | 1.298644862 |
a) Looking at the coefficients in the output, we get:
= 1.2488
= 0.7699
b) The p-value of the coefficient of stock return x is 0.0256 < 0.1
=> x is a significant predictor of y. Hence, there is a significant linear relationship between x and y at the 0.1 level of significance.
Null and alternative hypotheses are:
H0: = 0
Ha: 0
Hence, C is the correct option.
As seen above from the table, p-value = 0.026
i Rate of Return Month Rates of return of the Rates of return of the index,...
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