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 = 1,550 and SSE = 530.

(a) At α = 0.05, test whether x1  is significant.State the null and alternative hypotheses.

H0: β1 ≠ 0
Ha: β1 = 0

H0: β0 ≠ 0
Ha: β0 = 0

H0: β0 = 0
Ha: β0 ≠ 0

H0: 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?

Do not reject H0. We conclude that x1 is significant

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

Reject H0. We conclude that x1 is significant.

Reject H0. We conclude that x1 is not 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 = 1,550 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: β1 ≠ 0
Ha: β1 = 0

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

H0: β1 = 0
Ha: β1 ≠ 0

H0: 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?

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

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

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

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

 Source SS df MS F regression 1020.00 1 1020.000 48.113 error 530.00 25 21.200 total 1550.00 26

a)

H0: β1 = 0
Ha: β1 ≠ 0

value of the test statistic =48.11

p-value.=0.000

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.

 Partial F=((SSEr-SSEc)/(c-r))/(SSEc/(n-c-1)) = 49.45

p-value =0.000

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