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 :

Answer:

The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.

The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].

And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]

And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]

Step-by-step 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 [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.

The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].

And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]

And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]

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