STATQUESTION Complete Solution 3

Question: #1567

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)

Solution: #1551

STATQUESTION Complete Solution 3

We know that the least square estimate of β ̂=〖(X^T X)〗^(-1) X^T Y. Now here, X=(■(1&1.9&2@1&1.7&5@1&1.7&4@1&1.2&4@1&2&3@1&2.2&3)) and Y=(■(25@26@26@27@27@28.5)) Which gives, 6 10.7 21 X'X = 10.7 19.67 36.5 21 36.5 79 Thus, 15.83429 -5.62857 -1.60857 (X^' X)^(-1) =...