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STAT QUESTION | Complete Solution
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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)
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STAT QUESTION | Complete Solution 3
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- Submitted On 31 Mar, 2015 10:14:26
Solution posted by
- ExpertT
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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) =...
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