Question

In: Math

Consider the following data for a dependent variable y and two independent variables, x1 and x2....

Consider the following data for a dependent variable y and two independent variables, x1 and x2.

x1 x2 y
30 12 95
47 10 108
25 17 112
51 16 178
40 5 94
51 19 175
74 7 170
36 12 117
59 13 142
76 16 212

The estimated regression equation for these data is

ŷ = −18.52 + 2.01x1 + 4.75x2.

Here, SST = 15,234.1, SSR = 14,109.8, sb1 = 0.2464, and sb2 = 0.9457.

(a)Test for a significant relationship among x1, x2, and y. Use α = 0.05.

State the null and alternative hypotheses.

H0: β1 = β2 = 0
Ha: One or more of the parameters is not equal to zero.H0: β1 < β2
Ha: β1β2    H0: β1 ≠ 0 and β2 = 0
Ha: β1 = 0 and β2 ≠ 0H0: β1 > β2
Ha: β1β2H0: β1 ≠ 0 and β2 ≠ 0
Ha: One or more of the parameters is equal to zero.

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

=

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

p-value =

State your conclusion.

Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables.    Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables.Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.

(b)Is β1 significant? Use α = 0.05.

State the null and alternative hypotheses.

H0: β1 = 0
Ha: β1 ≠ 0H0: β1 < 0
Ha: β1 ≥ 0    H0: β1 = 0
Ha: β1 > 0H0: β1 > 0
Ha: β1 ≤ 0H0: β1 ≠ 0
Ha: β1 = 0

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

=

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

p-value =

State your conclusion.

Reject H0. There is sufficient evidence to conclude that β1 is significant.Reject H0. There is insufficient evidence to conclude that β1 is significant.    Do not reject H0. There is insufficient evidence to conclude that β1 is significant.Do not reject H0. There is sufficient evidence to conclude that β1 is significant.

(c)Is β2 significant? Use α = 0.05.

State the null and alternative hypotheses.

H0: β2 ≠ 0
Ha: β2 = 0H0: β2 > 0
Ha: β2 ≤ 0    H0: β2 = 0
Ha: β2 ≠ 0H0: β2 = 0
Ha: β2 > 0H0: β2 < 0
Ha: β2 ≥ 0

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

=

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

p-value =

State your conclusion.

Reject H0. There is insufficient evidence to conclude that β2 is significant.

Reject H0. There is sufficient evidence to conclude that β2 is significant.    

Do not reject H0. There is insufficient evidence to conclude that β2 is significant.

Do not reject H0. There is sufficient evidence to conclude that β2 is significant.

Solutions

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