Question

# In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ =...

In a regression analysis involving 27 observations, the following estimated regression equation was developed.

ŷ = 25.2 + 5.5x1

For this estimated regression equation SST = 1,600 and SSE = 550.

(a) At α = 0.05, test whether x1 is significant.

State the null and alternative hypotheses.

H0: β0 = 0
Ha: β0 ≠ 0H0: β0 ≠ 0
Ha: β0 = 0    H0: β1 ≠ 0
Ha: β1 = 0H0: β1 = 0
Ha: β1 ≠ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

F =

p-value =

Is x1 significant?

A)Reject H0. We conclude that x1 is significant.

B)Do not reject H0. We conclude that x1 is not significant.

C)Reject H0. We conclude that x1 is not significant.

D)Do not reject H0. We conclude that x1 is significant.

Suppose that variables x2 and x3 are added to the model and the following regression equation is obtained.

ŷ = 16.3 + 2.3x1 + 12.1x2 − 5.8x3

For this estimated regression equation SST = 1,600 and SSE = 100.

(b) Use an F test and a 0.05 level of significance to determine whether x2 and x3 contribute significantly to the model.

State the null and alternative hypotheses.

H0: One or more of the parameters is not equal to zero.
Ha: β2 = β3 = 0H0: β1 ≠ 0
Ha: β1 = 0    H0: β1 = 0
Ha: β1 ≠ 0H0: β2 = β3 = 0
Ha: One or more of the parameters is not equal to zero.

Find the value of the test statistic.

=

p-value =

Is the addition of x2 and x3 significant?

A)Reject H0. We conclude that the addition of variables x2 and x3 is not significant.

B)Do not reject H0. We conclude that the addition of variables x2 and x3 is significant.

C)Do not reject H0. We conclude that the addition of variables x2 and x3 is not significant.

D)Reject H0. We conclude that the addition of variables x2 and x3 is significant.

a)

H0: β1 = 0
Ha: β1 ≠ 0

 SS DF MS F p value regression 1050 1 1050 47.73 0.0000 error 550 25 22 total 1600 26

F = 47.73

p value=0.000

A)Reject H0. We conclude that x1 is significant.

===================

b)

H0: β2 = β3 = 0
Ha: One or more of the parameters is not equal to zero.

 SS DF MS F p value regression 1500 3 500 115.00 0.00000 error 100 23 4.347826 total 1600 26

test stat=115

p vaue = 0.000

D)Reject H0. We conclude that the addition of variables x2 and x3 is significant.