I am given the information in the table below and need to answer the questions a

Question

I am given the information in the table below and need to answer the questions after the chart.

A realtor used the regression model, y = beta0 + beta1x1 +beta2x2 + epsilon, to predict selling prices of homes (in thousands of $) in a Columbus suburb. The variable x1 represents the home size (square feet), and x2 represents the number of bedrooms. The following Excel partial output is available.

1. Which of the two independent variables seems to have a stronger impact on the selling price?

2. What is the estimated variance of the error term epsilon?

3. What is the predicted selling price of a home with 1700 square feet and 3 bedrooms?         

4. If you conduct the t test for the significance of Bedrooms, the p-value of the test is?

5. If for a fixed square footage, a house has one extra bedroom, the predicted selling price?

6. If you conduct a test for the overall significance of the model at a 1% significance level, the critical value for this test is?

7. If you conduct a test for the overall significance of the model, then the p-value of the test is?

8. What is the percentage of variation in the selling price explained by the regression equation?

9. How many homes are included in the sample?

10. What is the 99% confidence interval for the coefficient beta1 ?

ANOVA df SS MS F Regression 2 5800.44 2900.22 92.66 Residual 10 312.99 31.30 Total 12 6113.43 Coefficients Standard Error t Stat Intercept 27.13 22.80 1.19 Size 0.16 0.03 5.33 Bedrooms 20.22 6.42 3.15

Explanation / Answer

Result:

1. Which of the two independent variables seems to have a stronger impact on the selling price?

Size ( t vale for size is larger).

2. What is the estimated variance of the error term epsilon?

variance of the error term=312.99

3. What is the predicted selling price of a home with 1700 square feet and 3 bedrooms?         

Predicted selling price = 27.13+0.16*1700+20.22*3

=359.79

4. If you conduct the t test for the significance of Bedrooms, the p-value of the test is?

P=0.0104

5. If for a fixed square footage, a house has one extra bedroom, the predicted selling price?

predicted selling price increase by 20.22

6. If you conduct a test for the overall significance of the model at a 1% significance level, the critical value for this test is?

Critical F(2,10)=7.56

7. If you conduct a test for the overall significance of the model, then the p-value of the test is?

P=0.0000

8. What is the percentage of variation in the selling price explained by the regression equation?

R square = 5800.44/6113.43 =0.9488

Percentage of variation in the selling price explained = 94.88%

9. How many homes are included in the sample?

13

10. What is the 99% confidence interval for the coefficient beta1 ?

Critical t value for 99% at 10 Df, t=3.17

Lower limit = 0.16-3.17*0.03 = 0.0649

upper limit = 0.16+3.17*0.03 = 0.2551

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