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##### regression models problem

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solution

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Question;4-27.;Develop a linear regresion model to predict MPG, using;horsepower as the only independent variable,. Develop another model with weight;as the independent variable.;Which of these two models is better? Please explain.;Independent Independent Horsepower;MPG HORSEPOWER WEIGHT MPG SUMMARY OUTPUT;44 67 1,844 44;44 50 1,998 44 Regression Statistics;40 62 1,752 40 Multiple R 0.877607;37 69 1,980 37 R Square 0.770194;37 66 1,797 37 Adjusted R Square 0.757427;34 63 2,199 34 Standard Error 4.481278;35 90 2,404 35 Observations 20;32 99 2,611 32;30 63 3,236 30 ANOVA;28 91 2,606 28 df SS MS F Significance;F;26 94 2,580 26 Regression 1 1211.477 1211.477 60.32692 3.72E-07;26 88 2,507 26 Residual 18 361.4734 20.08186;25 124 2,922 25 Total 19 1572.95;22 97 2,434 22;20 114 3,248 20 Coefficients Standard Error t Stat P-value Lower 95% Upper;95% Lower 95.0% Upper 95.0%;21 102 2,812 21 Intercept 53.87238 3.42306 15.73808 5.76E-12 46.68079 61.06396 46.68079 61.06396;18 114 3,382 18 HORSEPOWER -0.26945 0.034691 -7.76704 3.72E-07 -0.34233 -0.19656 -0.34233 -0.19656;18 142 3,197 18;16 153 4,380 16;16 139 4,036 16;Weight;SUMMARY OUTPUT;Regression Statistics;Multiple R 0.855923;R Square 0.732604;Adjusted R Square 0.717749;Standard Error 4.833909;Observations 20;ANOVA;df SS MS F Significance;F;Regression 1 1152.35 1152.35 49.31596 1.49E-06;Residual 18 420.6001 23.36667;Total 19 1572.95;Coefficients Standard Error t Stat P-value Lower 95% Upper;95% Lower 95.0% Upper 95.0%;Intercept 57.53293 4.280105 13.44194 7.96E-11 48.54076 66.52509 48.54076 66.52509;WEIGHT -0.01079 0.001536 -7.02253 1.49E-06 -0.01401 -0.00756 -0.01401 -0.00756;4-28.;Use the data in problem 4-27 to develop a multiple linear;regression model. How does this compare with each of the models in prolem 4-27?;SUMMARY OUTPUT;Regression Statistics;Multiple R 0.903472;R Square 0.816262;Adjusted R Square 0.794646;Standard Error 4.123182;Observations 20;ANOVA;df SS MS F Significance;F;Regression 2 1283.939 641.9697 37.76153 5.57E-07;Residual 17 289.0106 17.00063;Total 19 1572.95;Coefficients Standard Error t Stat P-value Lower 95% Upper;95% Lower 95.0% Upper 95.0%;Intercept 57.68586 3.651218 15.79907 1.36E-11 49.98247 65.38926 49.98247 65.38926;HORSEPOWER -0.16567 0.059546 -2.78213 0.012777 -0.2913 -0.04003 -0.2913 -0.04003;WEIGHT -0.00505 0.002444 -2.06455 0.054568 -0.0102 0.000111 -0.0102 0.000111

Paper#52870 | Written in 18-Jul-2015

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