Question

ANOVA
	DF	SS	MS
Regression	1	0.0994	0.0985
Residual	62	0.1413	0.0025
Total	61	0.2407
	Coefficients	Standard Error
Intercept	-0.013	0.0053
S&P 500 Returns	1,2139	0.1878

Looking both at the specification of the model and at the estimated coefficient, how can you interpret the coefficient of S&P 500 Returns

Answer 1

Here' the answer to the question. Please let me know in case you've problems understanding.

Interpretation of model specification:

R-square is calculated as SSregression/SStotal = .0994/.2407 = .4129 or 41.29%

This is a low R-Square, hence the variable S & P 500 Returns doesn't do a good job of explaining variance in the dependent variable.

Lets also calclualate the p-value of the regression by converting F-statistic to a probability value using the formula:

= 1 - F.DIST(F, df1, df2, TRUE)

F is MS regression/MS residual = .0985/.0025 = 39.4

df 1 = df of regression = 1

df 2 = df of residual = 61

Inputting: 1- F.DIST(39.4, 1, 61, TRUE) = 0.00 < .05, which means that the regression is statistically significant

p-value = 0 < .05 ( generally assumed threhold when alpha is not given in the question)

i.e. Regression is statistically significant ( there exists atleast 1 variable which has a statistically significant linear relation with dependent variable.

Interpretation of estimated coefficient

The model says that the coefficient for S & P 500 Returns is 1.2139 , which means that for 1 unit increase in the S & P 500 returns the dependent variable increases by 1.2139 units.