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, and Lot= 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:
- Calculate the least squares estimate of and What's the first row, second column entry of ? (Round to the nearest fourth decimal)
- Regarding the previous question, what is the estimated value of ? (Round to the nearest fourth decimal)
- Estimate , the standard deviation the error term in the model. (Round to the nearest fourth decimal)
- 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)
- Regarding the previous question, would we reject the null hypothesis
- Test the null hypothesis that . Use .
- Test the null hypothesis that . Use ?
- What is the value of ? (Round to the nearest fourth decimal)
- What is the value of the adjusted ? (Round to the nearest fourth decimal)
- 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)
- Estimate the average sale price for a home with a floor size of 2,000 sq. ft. with a lot size of 3, using a 95% prediction interval. What is upper limit for the interval? (Round to the nearest fourth decimal)