Question

In a multiple regression analysis, k = 5 and n = 21, the MSE value is 3.58, and SS total is 498.46. At the 0.05 significance level, can we conclude that any of the regression coefficients are not equal to 0? (Round your answers to 2 decimal places.)

H₀: β₁ = β₂ = β₃ = β₄ = β₅ = 0

H₁: Not all β's equal zero.

Complete the following ANOVA table.

Answer 1

We know,

Using these, the ANOVA table is given by:

	SS	df	MSS	F
Regressors	498.46-57.28 = 441.18	k-1=5-1=4	441.18/4=110.295	110.295/3.58=30.81
Error	(3.58)(16) = 57.28	n-k=21-5=16	3.58
TOTAL	498.46	n-1=(n-k)+(k-1) = 4+16 = 20

F-tabulated value =

Since the F-calculated value 30.81 is greater than 3.007, so we have sufficient evidence to reject H0.

Thus we can conclude that not all equal zero.