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 85 observations, using monthly returns, specified as follows:

R_i = b₀ + b₁ Volatility_i + b₂ Size_i + b₃ R_market + 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	0.27	0.1
Volatility	0.37	0.31
Size	0.17	0.11
R market	0.49	0.16

The regression sum of squares is 0.18 and the residual sum of squares is 1.12.

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.)

Answer 1

H0: the three independent variables are jointly statistically not related to returns

H1: the three independent variables are jointly statistically related to returns

From the given data

ANOVA Table
Source	df	Sum of Square	Mean Square	F-ratio	F-critical	P-value
Regression	3	0.18	0.06	4.3478	2.717343	0.0068
Residual	81	1.12	0.0138
Total	84	1.3

Since F - Ratio > F -Critical value so we reject H0

Or

Since P-value < alpha 0.05 so we reject H0.

Thus we conclude that  the three independent variables are jointly statistically related to returns

i) F-Critical value can be obtained from Excel:

Syntax: =FINV(0.05,3,81)

ii) P-value can be obtained from Excel

Syntax: =FDIST(4.3478,3,81)