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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:

  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)
  11. 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
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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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