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a) State the null and alternative hypothesis in this global test for linear model utility. b) Give the p-value and your conclusion. c) Conduct t-tests on each of the beta parameters. What is your conclusion in each case?

a) State the null and alternative hypothesis in this global test for linear model utility. b) Give the p-value and your conclusion. c) Conduct t-tests on each of the beta parameters. What is your conclusion in each case?

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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Square Feet Sum of Bedrooms and Bathrooms Age of the Home Sales Price Square Feet Residual Plot Square Feet Line Fit Plot 1,610 5 70 227,900 800,000 2,146 6 59 284,900 700,000 816 4 70 149,900 FO000 600,000 2,183 6.5 48 309,900 40000 1,046 5.5 64 134,900 500.000 20000 5,183 10.5 21 440,000 400,000 • 2 000 1,150 4 62 150,000 1,000 4,000 5.000 6,000 2000 0 300,000 1,068 70 154,900 4000 0 5,570 7 50 700,000 200,000 6000 0 2,449 6. 53 257,000 100,000 BO00 0 1,950 59 239,900 1000 00 2,630 7.5 73 349,900 Square Feet 1,000 2,000 3,000 4,000 5,000 6,000 Square Feet 2,732 7.5 20 339,900 1,908 5 46 289,000 3,666 6.5 17 399,900 Sum of Bedrooms and Bathrooms Residual Plot Sum of Bedrooms and Bathrooms Line Fit Plot 80000 1,878 7 19 290,000 800,000 2,172 62 278,000 60000 700,000 40000 600,000 SUMMARY OUTPUT 20000 500,000 400,000 Regression Statistics 12 2000 0 Multiple R 0.949366054 300,000 R Square 0.901295904 4000 0 200,000 Adjusted R Square 0.878518035 6000 0 100,000 Standard Error 47571.46177 8000 0 Observations 17 2 12 1000 00 Sum of Bedrooms and Bathrooms Sum of Bedrooms and Bathrooms ANOVA df SS MS F Significance F Age of the Home Residual Plot Age of the Home Line Fit Plot Regression 3 2.68639E+11 8.9546E+10 39.5689 8,44E-07 80000 800,000 Residual 13 29419571670 2263043975 60000 700,000 Total 16 2.98058E+11 40000 20000 500,000 t Stat 1.588278630.13624 -49422.95889 323846 Coefficients Standard Error P-value Lower 95% Upper 95%ɔwer 95.0spper 95.0 -49423 323846 400,000 Intercept 137211.6729 86390,17753 10 20 60 80 Square Feet 13.62585831 2000 0 112.2753036 8.23987018 1.62E-06 82.83842641 141.712 82.8384 141.712 300,000 of Bedrooms and Bathro -18138.453 12012.77866 -1.50992984 0.15498 -44090.48349 7813.58 -44090 7813,58 4000 0 200,000 Age of the Home 110.7493211 750.4232224 0.14758248 0.88494 -1510.441488 1731.94 -1510.4 1731.94 100,000 8000 0 80 1000 00 Age of the Home Age of the Home RESIDUAL OUTPUT PROBABILITY OUTPUT Normal Probability Plot Observation Predicted Sales Price Residuals indard Residuals Percentile Sales Price 800000 235035.0992 -7135.099201 -0.1663956 2,941176471 134900 700000 275857.9664 9042.033582 0.21086667 8.823529412 149900 3 164026.9611 -14126.96112 -0.3294508 14.70588235 150000 4 269724.6836 40175.31638 0.93691701 20.58823529 154900 So000 5 161978.1055 -27078.10553 -0.63148072 26.47058824 227900 531006.5509 -91006.55085 -2.12233763 32.35294118 239900 * 400000 7 200640.918 -50640.91796 -1.1809823 38.23529412 257000 300000 8 174181.8846 -19281.88463 -0.44966729 44.11764706 278000 200000 641153.4092 58846.59085 1.37234444 50 284900 10 309212.8875 -52212.88749 -1.21764175 55.88235294 289000 100000 11 235713.5539 4186.446089 0.09763091 61.76470588 290000 12 304542.0244 45357.97562 1.05778032 67.64705882 309900 20 40 60 80 100 120 Sample Percentile 13 310124.3913 29775.60867 0.69438842 73.52941176 339900 14 265835.156 23164.84402 0.54022067 79.41176471 349900 15 432795.7299 -32895.72995 -0.76715187 85.29411765 399900 16 223199.7592 66800.24079 1.55782922 91.17647059 440000 17 260970.9193 17029.08072 0.3971303 97.05882353 700000
Transcribed Image Text:Square Feet Sum of Bedrooms and Bathrooms Age of the Home Sales Price Square Feet Residual Plot Square Feet Line Fit Plot 1,610 5 70 227,900 800,000 2,146 6 59 284,900 700,000 816 4 70 149,900 FO000 600,000 2,183 6.5 48 309,900 40000 1,046 5.5 64 134,900 500.000 20000 5,183 10.5 21 440,000 400,000 • 2 000 1,150 4 62 150,000 1,000 4,000 5.000 6,000 2000 0 300,000 1,068 70 154,900 4000 0 5,570 7 50 700,000 200,000 6000 0 2,449 6. 53 257,000 100,000 BO00 0 1,950 59 239,900 1000 00 2,630 7.5 73 349,900 Square Feet 1,000 2,000 3,000 4,000 5,000 6,000 Square Feet 2,732 7.5 20 339,900 1,908 5 46 289,000 3,666 6.5 17 399,900 Sum of Bedrooms and Bathrooms Residual Plot Sum of Bedrooms and Bathrooms Line Fit Plot 80000 1,878 7 19 290,000 800,000 2,172 62 278,000 60000 700,000 40000 600,000 SUMMARY OUTPUT 20000 500,000 400,000 Regression Statistics 12 2000 0 Multiple R 0.949366054 300,000 R Square 0.901295904 4000 0 200,000 Adjusted R Square 0.878518035 6000 0 100,000 Standard Error 47571.46177 8000 0 Observations 17 2 12 1000 00 Sum of Bedrooms and Bathrooms Sum of Bedrooms and Bathrooms ANOVA df SS MS F Significance F Age of the Home Residual Plot Age of the Home Line Fit Plot Regression 3 2.68639E+11 8.9546E+10 39.5689 8,44E-07 80000 800,000 Residual 13 29419571670 2263043975 60000 700,000 Total 16 2.98058E+11 40000 20000 500,000 t Stat 1.588278630.13624 -49422.95889 323846 Coefficients Standard Error P-value Lower 95% Upper 95%ɔwer 95.0spper 95.0 -49423 323846 400,000 Intercept 137211.6729 86390,17753 10 20 60 80 Square Feet 13.62585831 2000 0 112.2753036 8.23987018 1.62E-06 82.83842641 141.712 82.8384 141.712 300,000 of Bedrooms and Bathro -18138.453 12012.77866 -1.50992984 0.15498 -44090.48349 7813.58 -44090 7813,58 4000 0 200,000 Age of the Home 110.7493211 750.4232224 0.14758248 0.88494 -1510.441488 1731.94 -1510.4 1731.94 100,000 8000 0 80 1000 00 Age of the Home Age of the Home RESIDUAL OUTPUT PROBABILITY OUTPUT Normal Probability Plot Observation Predicted Sales Price Residuals indard Residuals Percentile Sales Price 800000 235035.0992 -7135.099201 -0.1663956 2,941176471 134900 700000 275857.9664 9042.033582 0.21086667 8.823529412 149900 3 164026.9611 -14126.96112 -0.3294508 14.70588235 150000 4 269724.6836 40175.31638 0.93691701 20.58823529 154900 So000 5 161978.1055 -27078.10553 -0.63148072 26.47058824 227900 531006.5509 -91006.55085 -2.12233763 32.35294118 239900 * 400000 7 200640.918 -50640.91796 -1.1809823 38.23529412 257000 300000 8 174181.8846 -19281.88463 -0.44966729 44.11764706 278000 200000 641153.4092 58846.59085 1.37234444 50 284900 10 309212.8875 -52212.88749 -1.21764175 55.88235294 289000 100000 11 235713.5539 4186.446089 0.09763091 61.76470588 290000 12 304542.0244 45357.97562 1.05778032 67.64705882 309900 20 40 60 80 100 120 Sample Percentile 13 310124.3913 29775.60867 0.69438842 73.52941176 339900 14 265835.156 23164.84402 0.54022067 79.41176471 349900 15 432795.7299 -32895.72995 -0.76715187 85.29411765 399900 16 223199.7592 66800.24079 1.55782922 91.17647059 440000 17 260970.9193 17029.08072 0.3971303 97.05882353 700000
a) State the null and alternative hypothesis in this global test for linear model utility. b) Give the p-value and your conclusion. c) Conduct t-tests on each of the beta parameters. What is your conclusion in each case? d) What percentage of the variation in the price is explained by these independent variables? Based on this, is a multiple linear regression model a good model for these data? Explain. e) Give the point estimate for the price of a 44 year old single family home in Beavercreek, OH with 1704 square feet of living space, 3 bedrooms, and 2.5 bathrooms.
Transcribed Image Text:a) State the null and alternative hypothesis in this global test for linear model utility. b) Give the p-value and your conclusion. c) Conduct t-tests on each of the beta parameters. What is your conclusion in each case? d) What percentage of the variation in the price is explained by these independent variables? Based on this, is a multiple linear regression model a good model for these data? Explain. e) Give the point estimate for the price of a 44 year old single family home in Beavercreek, OH with 1704 square feet of living space, 3 bedrooms, and 2.5 bathrooms.
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