Question

Refer to the ANOVA table for this regression.

Source	SS	d.f.	MS
Regression	1,035,678	15	69,045
Residual	1,415,013	35	40,429
Total	2,450,691	50

(a)	State the degrees of freedom for the F test for overall significance.

The degrees of freedom for regression are ________ and for error ______ .

(b)	Use Appendix F to look up the critical value of F for α = .05. (Round your answer to 2 decimal places.)

F.05

(c-1)

Calculate the F statistic. (Round your answer to 4 decimal places.)

F statistic

(c-2)	The overall regression is significant.
	No Yes

(c-3)	The hypotheses is

a.	H0: All the coefficients are zero (β1 = β2 = β3 = 0) vs. H1: At least one coefficient is not zero.
b.	H0: At least one coefficient is non-zero vs. H1: All the coefficients are zero (β1 = β2 = β3 = 0)

a b

(d)	Calculate R2 and R2adj. (Round your answers to 4 decimal places.)

   

R2
R2adj

Answer 1

Solution:

We are given following ANOVA table:

Source	SS	d.f.	MS
Regression	1,035,678	15	69,045
Residual	1,415,013	35	40,429
Total	2,450,691	50

Part a) State the degrees of freedom for the F test for overall significance.

The degrees of freedom for regression are 15 and for error are 35.

Part b) Use Appendix F to look up the critical value of F for α = .05.

Look in F table for DF_Numerator = DF_N = 15 and DF_Denominator = DF_D = 35

at α =0.05 and find F critical value.

F critical value = 1.96

Part c-1) Calculate the F statistic.

Part c-2) The overall regression is significant.

Since F test statistic value = 1.7078 < F critical value = 1.96, we fail to reject H0: All the coefficients are zero and hence we conclude that: The overall regression is not significant.

Thus answer is: No.

Part c-3) The hypotheses is :

a) H₀: All the coefficients are zero (β₁ = β₂ = β₃ = 0) vs. H₁: At least one coefficient is not zero.

Part d) Calculate R² and R²_adj.

and

n = Sample size

k = number of independent variables = 15

We know Total DF = n - 1 , then

n = Total DF + 1 = 50 + 1 = 51

Thus