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Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?

Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Table 14.17

The Least Squares Point Estimates for Exercise 14.51

Bo = 10.3676 (.3710)

B1 = .0500 (<.001)

B2 = 6.3218 (.0152)

B3 = -11.1032 (.0635)

B4 = -.4319 (.0002)

Questions

  1. Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?
  2. Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01?
  3. Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model?
  4. Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval.
  5. Calculate the 99 percent confidence interval for βj.  
13.10 Measurements Taken on 63 Single-Family Residences (for Exercise 13.57) OxHome Sales Price, y Residence (x $1,000) x, Square Feet, Sales Price, y Residence (x $1,000) x, Rooms, Bedrooms, Age. Square Feet, Rooms, Bedrooms, Age. X2 1 53.5 1,008 2. 2 35 33 63.0 1,053 49.0 1,290 6 3 24 36 34 60.0 1,728 3 50.5 860 8 25 2 36 35 34.0 416 4 49.9 912 42 41 36 52.0 1,040 5 52.0 1,204 6 40 37 75.0 1,496 3. 6 55.0 1,204 30 3. 10 38 93.0 1,936 8 4 7. 80.5 1,764 8 39 4 39 60.0 1,904 1,080 64 32 86.0 1,600 7 3. 19 40 73.0 5 24 69.0 1,255 3. 16 41 71.0 1,768 8 4 74 10 200. 149.0 3,600 10 42 83.0 1,503 1,736 17 6 14 11 46.0 864 37 90.0 43 16 12 38.0 720 83.0 4 41 44 1,695 6. 12 13 49.5 1,008 6. 3. 35 45 115.0 2,186 8 12 14 105.0 1,950 8 52 46 50.0 888 2 34 15 152.5 2,086 12 47 55.2 1,120 3. 29 16 85.0 2,011 4 76 48 61.0 1,400 33 17 60.0 1,465 6. 3 102 49 147.0 2,165 18 58.5 1,232 5 2 69 50 210.0 2,353 8. 15 19 101.0 1,736 3 67 51 60.0 1,536 35 20 79.4 1,296 6. 11 52 100.0 1,972 37 21 125.0 1,996 3. 9. 53 44.5 1,120 27 22 87.9 1,874 2 14 54 55.0 1,664 7. 3 79 23 80.0 1,580 5 11 55 53.4 925 20 24 94.0 1,920 3 14 56 65.0 1,288 5. 25 74.0 1,430 9 3 16 57 73.0 1,400 2 1,486 3 27 58 40.0 1,376 103 26 69.0 6. 1,008 2. 35 59 141.0 2,038 12 62 27 63.0 67.5 1,282 3 20 60 68.0 1,572 29 28 29 35.0 1,134 74 61 139.0 1,545 62 140.0 1,993 1,130 30 142.5 2,400 9. 4 15 6. 21 3 15 63 55.0 2. 92.2 1,701 31 3. 16 56.0 1,020 32
Transcribed Image Text:13.10 Measurements Taken on 63 Single-Family Residences (for Exercise 13.57) OxHome Sales Price, y Residence (x $1,000) x, Square Feet, Sales Price, y Residence (x $1,000) x, Rooms, Bedrooms, Age. Square Feet, Rooms, Bedrooms, Age. X2 1 53.5 1,008 2. 2 35 33 63.0 1,053 49.0 1,290 6 3 24 36 34 60.0 1,728 3 50.5 860 8 25 2 36 35 34.0 416 4 49.9 912 42 41 36 52.0 1,040 5 52.0 1,204 6 40 37 75.0 1,496 3. 6 55.0 1,204 30 3. 10 38 93.0 1,936 8 4 7. 80.5 1,764 8 39 4 39 60.0 1,904 1,080 64 32 86.0 1,600 7 3. 19 40 73.0 5 24 69.0 1,255 3. 16 41 71.0 1,768 8 4 74 10 200. 149.0 3,600 10 42 83.0 1,503 1,736 17 6 14 11 46.0 864 37 90.0 43 16 12 38.0 720 83.0 4 41 44 1,695 6. 12 13 49.5 1,008 6. 3. 35 45 115.0 2,186 8 12 14 105.0 1,950 8 52 46 50.0 888 2 34 15 152.5 2,086 12 47 55.2 1,120 3. 29 16 85.0 2,011 4 76 48 61.0 1,400 33 17 60.0 1,465 6. 3 102 49 147.0 2,165 18 58.5 1,232 5 2 69 50 210.0 2,353 8. 15 19 101.0 1,736 3 67 51 60.0 1,536 35 20 79.4 1,296 6. 11 52 100.0 1,972 37 21 125.0 1,996 3. 9. 53 44.5 1,120 27 22 87.9 1,874 2 14 54 55.0 1,664 7. 3 79 23 80.0 1,580 5 11 55 53.4 925 20 24 94.0 1,920 3 14 56 65.0 1,288 5. 25 74.0 1,430 9 3 16 57 73.0 1,400 2 1,486 3 27 58 40.0 1,376 103 26 69.0 6. 1,008 2. 35 59 141.0 2,038 12 62 27 63.0 67.5 1,282 3 20 60 68.0 1,572 29 28 29 35.0 1,134 74 61 139.0 1,545 62 140.0 1,993 1,130 30 142.5 2,400 9. 4 15 6. 21 3 15 63 55.0 2. 92.2 1,701 31 3. 16 56.0 1,020 32
Supplementary Exercises The trend in home building in recent years has been to emphasize open spaces and great roome 14.51 community of Oxford, Ohio, had been building such homes, but his homes had been taking ge months to sell and selling for substantially less than the asking price. In order to determine wube types of homes would attract residents of the community, the builder contacted a statistician at a local college. The statistician went to a local real estate agency and obtained the data in Table 13.10 on page 518. This table presents the sales price y, square footage x, number of rooms x, number of bedrooms x3, and age x4 for each of 63 single-family residences recently sold in the community. When we perform a regression analysis of these data using the model y= B, + Bjx, + Bx2 + Bzx3 + BX4 + ɛ we find that the least squares point estimates of the model parameters and their associated p-values (given in parentheses) are as shown in Table 14.17. Discuss why the estimates b. - 6.3218 and ba specified square footage (1) to include both a (smaller) living room and family room rather than a (larger) great room and (2) to not increase the number of bedrooms (at the cost of another type of room) that would normally be included in a house of the specified square footage. Note: Based on the statistical results, the builder realized that there are many families with children in a col- lege town and that the parents in such families would rather have one living area for the children (the family room) and a separate living area for themselves (the living room). The builder started modifying his open-space homes accordingly and greatly increased his profits. = -11.1032 suggest that it might be more profitable when building a house of a OS OxHome
Transcribed Image Text:Supplementary Exercises The trend in home building in recent years has been to emphasize open spaces and great roome 14.51 community of Oxford, Ohio, had been building such homes, but his homes had been taking ge months to sell and selling for substantially less than the asking price. In order to determine wube types of homes would attract residents of the community, the builder contacted a statistician at a local college. The statistician went to a local real estate agency and obtained the data in Table 13.10 on page 518. This table presents the sales price y, square footage x, number of rooms x, number of bedrooms x3, and age x4 for each of 63 single-family residences recently sold in the community. When we perform a regression analysis of these data using the model y= B, + Bjx, + Bx2 + Bzx3 + BX4 + ɛ we find that the least squares point estimates of the model parameters and their associated p-values (given in parentheses) are as shown in Table 14.17. Discuss why the estimates b. - 6.3218 and ba specified square footage (1) to include both a (smaller) living room and family room rather than a (larger) great room and (2) to not increase the number of bedrooms (at the cost of another type of room) that would normally be included in a house of the specified square footage. Note: Based on the statistical results, the builder realized that there are many families with children in a col- lege town and that the parents in such families would rather have one living area for the children (the family room) and a separate living area for themselves (the living room). The builder started modifying his open-space homes accordingly and greatly increased his profits. = -11.1032 suggest that it might be more profitable when building a house of a OS OxHome
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