The following data consists of 6 homes with variables Price = sale price in tens of thousands of dollars,
Floor = floor size in thousands of square feet, andLot = lot size.
|
Floor
|
Lot
|
Price
|
|
1.9
|
2
|
25
|
|
1.7
|
5
|
26
|
|
1.7
|
4
|
26
|
|
1.2
|
4
|
27
|
|
2
|
3
|
27
|
|
2.2
|
3
|
28.5
|
Consider the first order multiple regression model:
Where Price, Floor, and Lot. Perform the following calculations, by hand using matrices:
1. Calculate the least squares estimate of and What's the first row, second column entry of ? (Round to the nearest fourth decimal)
2. Regarding the previous question, what is the estimated value of ? (Round to the nearest fourth decimal)
3. Estimate , the standard deviation the error term in the model. (Round to the nearest fourth decimal)
4. Calculate the ANOVA table and conduct the global F-test for the model usefulness at significance level. What is the value of the F-statistic? (Round to the nearest second decimal)
5. Regarding the previous question, would we reject the null hypothesis
6. Test the null hypothesis that . Use
7. Test the null hypothesis that . Use
8. What is the value of ? (Round to the nearest fourth decimal)
9. What is the value of the adjusted ? (Round to the nearest fourth decimal)
10. Estimate the average sale price for all homes with a floor size of 2,000 sq. ft. with a lot size of 3, using a 95% confidence interval. What is upper limit for the interval? (Round to the nearest fourth decimal)