F-Test Probability: Calculate & Test Hypothesis | 1977 Observations

[iiownz]

Hello guys!

I've been trying to solve this exercise for a long time. I know that is not that dificult.

However i can't remember how to do it.Thanks in advance.

View attachment 9510

Question
Calculate the F-test statistic for this equation and use it to perform a test for the null hypothesis that the slope coefficient is equal to zero
Ho = 0
H1 not equal to 0

1977 observations.

I found this relation between the R-squared and the F-test. Where does it come from? I have never heard about it. Also, how many degrees of freedom should i use for that test?

F= (R^2/(p-1))/((1-R^2)/(n-p)) -- Is this right? because it seems that some authors have been using F (p, n-p-1) as degrees of freedom. I am not sure which one is right.

Thanks!

 

[Valkarie]

The F-test statistic for this equation is calculated by taking the ratio of the explained variance (R-squared) to the unexplained variance (1 - R-squared). The numerator of this ratio is the explained variance, and the denominator is the unexplained variance. The degrees of freedom to use for the F-test are p, the number of explanatory variables in the model, and n-p-1, the number of observations minus the number of explanatory variables. Therefore, in this case, the F-test statistic is equal to F(p, n-p-1).