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Standard deviation the error term in the model

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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)

Reference no: EM13919947

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