Question

To test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

Answer 1

The degrees of freedom for the numerator on this case is given by
`df_(num)=df_(within)=k=3` where k =3 represent the number of independent variables.

The degrees of freedom for the denominator on this case is given by
`df_(den)=df_(between)=N-p-1=47-3-1 =43`.

And the total degrees of freedom would be
`df=N-1=47 -1 =46`

And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value
`F_(3,43)`

Explanation:

We need to take in count that we are conducting a regression model with just one dependent variable and 3 independent variables

The degrees of freedom for the numerator on this case is given by
`df_(num)=df_(within)=k=3` where k =3 represent the number of independent variables.

The degrees of freedom for the denominator on this case is given by
`df_(den)=df_(between)=N-p-1=47-3-1 =43`.

And the total degrees of freedom would be
`df=N-1=47 -1 =46`

And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value
`F_(3,43)`