A multiple regression was performed on a sample of 16 observations.The estimated equation is $\hat { y }$ = 23.5 - 14.28x₁ + 6.72x₂ + 15.68x₃.The standard errors for the coefficients are sb₁ = 4.2, sb₂ = 5.6, and sb₃ = 2.8.For this model, SST = 3809.6 and SSR = 3285.4.

a.
Compute the appropriate t ratios.
b.
Test for the significance of β₁, β₂, and β₃at the 5% level of significance.
c.
Do you think any of the variables should be dropped from the model? Explain.
d.
Compute R² and $R _ { \mathrm { a } } ^ { 2 }$ . Interpret R².
e.
Test the significance of the relationship among the variables at the 5% level of significance.

Question

A multiple regression was performed on a sample of 16 observations.The estimated equation is

\hat { y }

= 23.5 - 14.28x₁ + 6.72x₂ + 15.68x₃.The standard errors for the coefficients are sb₁ = 4.2, sb₂ = 5.6, and sb₃ = 2.8.For this model, SST = 3809.6 and SSR = 3285.4.

a.
Compute the appropriate t ratios.
b.
Test for the significance of β₁, β₂, and β₃at the 5% level of significance.
c.
Do you think any of the variables should be dropped from the model? Explain.
d.
Compute R² and

R _ { \mathrm { a } } ^ { 2 }

. Interpret R².
e.
Test the significance of the relationship among the variables at the 5% level of significance.

Quizplus · Accepted Answer

The Answer of A multiple regression was performed on a sample of 16 observations.The estimated equation is $\hat { y }$ = 23.5 - 14.28x₁ + 6.72x₂ + 15.68x₃.The standard errors for the coefficients are sb₁ = 4.2, sb₂ = 5.6, and sb₃ = 2.8.For this model, SST = 3809.6 and SSR = 3285.4. a. Compute the appropriate t ratios. b. Test for the significance of β₁, β₂, and β₃at the 5% level of significance. c. Do you think any of the variables should be dropped from the model? Explain. d. Compute R² and $R _ { \mathrm { a } } ^ { 2 }$ . Interpret R². e. Test the significance of the relationship among the variables at the 5% level of significance.

A Multiple Regression Was Performed on a Sample of 16 y^\hat { y }y^​

A Multiple Regression Was Performed on a Sample of 16 $\hat { y }$