Question

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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 = 590.

(a)

At α = 0.05, test whether

x1

is significant.

State the null and alternative hypotheses.

H0: β0 ≠ 0

Ha: β0 = 0

H0: β1 = 0

Ha: β1 ≠ 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 =

Find the p-value. (Round your answer to three decimal places.)

p-value =

Is x1 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.

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 = 1,550 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: One or more of the parameters is not equal to zero.

Ha: β2 = β3 = 0

H0: β1 ≠ 0

Ha: β1 = 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.

Find the p-value. (Round your answer to three decimal places.)

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.

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.

Answer 1

anova table
	SS	df	MS	F	p-value
Between:	960.0	1	960.0	40.68	0.000
Within:	590.0	25	23.6
Total:	1550.0	26

F stat = 40.68

p value = 0.000

Reject H0. We conclude that x1 is significant.   

...................

H0: β2 = β3 = 0

Ha: One or more of the parameters is not equal to zero.

anova table
	SS	df	MS	F	p-value
Between:	1450.0	3	483.3	111.17	0.000
Within:	100.0	23	4.3
Total:	1550.0	26

F stat = 111.17

p value = 0.00

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

.......

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