Data Car Size Price ($) Cost/Mile Road-Test Score Predicted Reliability Value Score Toyota Corolla (base, manual) Small Sedan 16,419 0.44 70 4 1.99 Mazda3 i Touring (manual) Small Sedan 18,895 0.5 74 1.94 UI Toyota Corolla LE Small Sedan 18,404 0.47 71 1.89 Mazda3 i Touring Small Sedan 19,745 0.52 70 1.82 Hyundai Elantra GLS Small Sedan 18,445 0.53 80 1.64 Nissan Sentra 2.0 SL Small Sedan 20,150 0.57 74 4 1.51 Kia Forte Sedan EX Small Sedan 19,040 0.57 71 1.32 Ford Focus SE Small Sedan 20,280 0.52 68 1.3 Ford Fiesta SE Small Sedan 16,595 0.47 61 1.25 Volkswagen Jetta SE (2.5) Small Sedan 20,300 0.54 60 1.24 Volkswagen Jetta TDI Small Sedan 25,100 0.5 68 A P H H N W N NW 1.18 Chevrolet Cruze LS (1.8) Small Sedan 18,375 0.57 67 0.96 Chevrolet Cruze 1LT (1.4T) Small Sedan 20,530 0.6 69 0.91 Nissan Altima 2.5 S (4-cyl.) Family Sedan 23,970 0.59 91 1.75 Kia Optima LX (2.4) Family Sedan 21,885 0.58 81 1.73 Subaru Legacy 2.5i Premium Family Sedan 23,830 0.59 83 1.73 Ford Fusion Hybrid Family Sedan 32,360 0.63 84 1.7 Honda Accord LX-P (4-cyl.) Family Sedan 23,730 0.56 80 1.62 Mazda6 i Sport (4-cyl.) Family Sedan 22,035 0.58 73 1.6 A W A WADUIA. Hyundai Sonata GLS (2.4) Family Sedan 21,800 0.56 89 1.58 Ford Fusion SE (4-cyl.) Family Sedan 23,625 0.57 76 1.55 Chevrolet Malibu LT (4-cyl.) Family Sedan 24,115 0.57 74 1.48 Kia Optima SX (2.0T) Family Sedan 29,050 0.72 84 1.43 Ford Fusion SEL (V6) Family Sedan 28,400 0.67 80 4 1.42 Nissan Altima 3.5 SR (V6) Family Sedan 30,335 0.69 93 4 1.42 Hyundai Sonata Limited (2.0T) Family Sedan 28,090 0.66 89 1.39 Honda Accord EX-L (V6) Family Sedan 28,695 0.67 90 . W W 1.36 Mazda6 s Grand Touring (V6) Family Sedan 30,790 0.74 81 1.34 Ford Fusion SEL (V6, AWD) Family Sedan 30,055 0.71 75 1.32 Subaru Legacy 3.6R Limited Family Sedan 30,094 0.71 88 1.29\fCorrelations Price ($) Cost/Mile Road-Test Score Predicted Reliability Value Score Price ($) 1 Cost/Mile 0.944747183 Road-Test Score 0.457966026 0.409783273 Predicted Reliability 0.125545469 0.067864282 0.219937923 1 Value Score -0.49445174 -0.589060899 0.193994249 0.643688644 1 Price =b0 + b1 Cost/Mile SUMMARY OUTPUT Regression Statistics Multiple R 0.944747183 R Square 0.892547239 Adjusted R Square 0.89048084 Standard Error 2293.202275 Observations 54 ANOVA df SS MS F Significance F Regression 1 2271442274 2271442274 431.9335872 7.53753E-27 Residual 52 273456387.1 5258776.675 Total 53 2544898661 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -13091.15381 2017.801374 6.487830756 3.24197E-08 -17140.1685 -9042.139134 17140.1685 -9042.139134 Cost/Mile 63093.55065 3035.823233 20.78301199 7.53753E-27 57001.72566 69185.37564 57001.72566 69185.37564Price = b0 + b1 Cost/Mile + b2 Road-Test Score + b3 Predicted Reliability + b4 Value Score SUMMARY OUTPUT Regression Statistics Multiple R 0.949112741 R Square 0.900814995 Adjusted R Square 0.89271826 Standard Error 2269.656925 Observations 54 ANOVA df SS MS F Significance F Regression 4 2292482876 573120718.9 111.256573 5.97E-24 Residual 49 252415785.2 5151342.555 Total 53 2544898661 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 15928.91314 6259.706907 -2.544673956 0.014138867 -28508.26513 -3349.561144 -28508.26513 -3349.561144 Cost/Mile 58800.126 9671.527055 6.079714782 1.76367E-07 39364.46473 78235.78728 39364.46473 78235.78728 Road-Test Score 68.28667426 63.72362431 1.071606881 0.289146447 -59.77074317 196.3440917 -59.77074317 196.3440917 Predicted Reliability 493.8749565 801.2404603 0.61638794 0.540491726 -1116.278032 2104.027945 -1116.278032 2104.027945 Value Score -1002.67847 4450.236909 0.225309009 0.822675949 -9945.764361 7940.407422 -9945.764361 7940.407422You have been provided with the original data and two regression models with their corresponding outputs. a} In order to decide to compare the two regression models usign the correct measure for Goodness of fit, What measure should be used? b} Which model has a better goodness of fit (support it with numbers} c} Nevertheless, goodness of fit is not everything. You can also use the F-test to verify if the full model is significant compared against the initial reduce model. What is the null hvphothesis of the F-test? d} What is the value of the test statistc F when performing a partial F test? e} What is the number of degrees (DF) of freedom for the F-statistic'? Numerator df = Denominator df = f} What is the p-value for the F-statistic? p-value = g} Based on the outcome of the F-test what is your conclussion