Question

You are interested in testing whether stock volatility, controlling for size and overall market returns, has an impact on returns. You conduct a regression on 89 observations, using monthly returns, specified as follows: Ri = b0 + b1 Volatilityi + b2 Sizei + b3 Rmarket + error Where Volatility is measured as standard deviation of returns in the previous month, Size is the natural log of total assets, in millions, and Rmarket is the contemporaneous market index return.

Your regression results are as follows:

	Coefficient	Standard error
Incercept	0.23	0.13
Volatility	0.77	0.19
Size	0.57	0.28
R market	0.19	0.19

The regression sum of squares is 0.12 and the residual sum of squares is 1.92.

What is the F statistic for testing whether the three independent variables are jointly statistically related to returns?

(Bonus question: is the regression statistically significant at the 5% level? Use the FDIST function to find the p-value.)

The answer should be 1.77 and the hint professor gave was "Review how to calculate the F statistic for a multiple regression." Please do the problem on excel and show all the steps. Thank you.

Answer 1

The problem is solved in excel and the formula along with explanation of the formula is given

Formulas to be used

correct answer

Formulas used in excel.

(Bonus question: is the regression statistically significant at the 5% level? Use the FDIST function to find the p-value.)

The hypothesis for this is

Ho : All the beta coefficient are equal to zero.

H1: At least one beta coefficient is not equal to zero.

Since pvalue is greater than 0.05, we fail to reject the null hypothesis and conclude that the regression is not statistically significant at the 5% level.