You may need to use the appropriate technology to answer this question. In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = XXXXXXXXXX8x 1...


You may need to use the appropriate technology to answer this question.

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.


ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4


For this estimated regression equation, SST = 1,825 and SSR = 1,780.


(a)


At ? = 0.05, test the significance of the relationship among the variables.

State the null and alternative hypotheses.




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

H
a: ?1 = ?2 = ?3 = ?4 = 0H
0: One or more of the parameters is not equal to zero.

H
a: ?0 = ?1 = ?2 = ?3 = ?4 = 0H
0: ?0 = ?1 = ?2 = ?3 = ?4 = 0

H
a: One or more of the parameters is not equal to zero.H
0: ?1 = ?2 = ?3 = ?4 = 0

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



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


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


p-value =

State your conclusion.



Do not rejectH
0. We conclude that the overall relationship is not significant.RejectH
0. We conclude that the overall relationship is not significant.    RejectH
0. We conclude that the overall relationship is significant.Do not rejectH
0. We conclude that the overall relationship is significant.



Suppose variables
x1 and x4

are dropped from the model and the following estimated regression equation is obtained.


ŷ = 11.1 − 3.6x2 + 8.1x3


For this model, SST = 1,825 and SSR = 1,725.




(b)


Compute
SSE(x1, x2, x3, x4).



SSE(x1, x2, x3, x4)

=




(c)


Compute
SSE(x2, x3).



SSE(x2, x3)

=




(d)


Use anF test and a 0.05 level of significance to determine whether
x1 and x4

contribute significantly to the model.

State the null and alternative hypotheses.




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

H
a: ?1 = ?4 = 0H
0: One or more of the parameters is not equal to zero.

H
a: ?2 = ?3 = 0H
0: ?2 = ?3 = 0

H
a: One or more of the parameters is not equal to zero.H
0: ?1 = ?4 = 0

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



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


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


p-value =


Jun 09, 2022
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