Question

In: Statistics and Probability

The following estimated regression equation based on 10 observations was presented. ŷ = 21.1370 + 0.5903x1...

The following estimated regression equation based on 10 observations was presented.

ŷ = 21.1370 + 0.5903x1 + 0.4920x2

Here, SST = 6,736.125, SSR = 6,228.375,

sb1 = 0.0819,

and

sb2 = 0.0563.

(a)

Compute MSR and MSE. (Round your answers to three decimal places.)

MSR=MSE=

(b)

Compute F and perform the appropriate F test. Use α = 0.05.

State the null and alternative hypotheses.

H0: β1 < β2
Ha: β1 ≥ β2
H0: β1 > β2
Ha: β1 ≤ β2

    

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

State your conclusion.

Reject H0. There is sufficient evidence to conclude that the overall model is significant.Do not reject H0. There is sufficient evidence to conclude that the overall model is significant.    Reject H0. There is insufficient evidence to conclude that the overall model is significant.Do not reject H0. There is insufficient evidence to conclude that the overall model is significant.

(c)

Perform a t test for the significance of

β1.

Use α = 0.05.

State the null and alternative hypotheses.

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

    

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

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

t =

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

p-value =

State your conclusion.

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

(d)

Perform a t test for the significance of

β2.

Use α = 0.05.

State the null and alternative hypotheses.

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

    

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

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

t =

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

p-value =

State your conclusion.

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

There is insufficient evidence to conclude that β2 is significant.   

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

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

Solutions

Expert Solution

orchestra answered 1 year ago
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