Question

The following data show the curb weight, horsepower, and ½-mile speed for 16 popular sports and GT cars. Suppose that the price of each sports and GT car is also available. The complete data set is as follows: Curb Weight (lb.) 2577 3066 2844 3439 3246 Speed at /4 Mile (mph) Price ($1000s) 25.035 93.758 40.900 24.865 50.144 Sports & GT Car Acura Integra Type R Acura NSX-T BMW Z3 2.8 Chevrolet Camaro Z28 Chevrolet Corvette Convertible Dodge Viper RT/10 Ford Mustang GT Honda Prelude Type SH Mercedes-Benz CLK320 Mercedes-Benz SLK230 Mitsubishi 300OGT VR-4 Nissan 240SX SE Pontiac Firebird Trans Am Porsche Boxster Toyota Supra Turbo Volvo C70 Horsepower 195.000 290.000 189.000 305.000 345.000 90.7 108.0 93.2 103.2 102.1 69.742 23.200 26.382 44.988 42.762 47.518 25.066 27.770 45.560 40.989 41.120 3319 3227 3042 3240 3025 3737 2862 3455 2822 3505 3285 450.000 225.000 195.000 215.000 185.000 320.000 155.000 305.000 201.000 320.000 236.000 116.2 91.7 89.7 93.0 92.3 99.8 85.5 102.8 93.8 104.0 98.0 a. Find the estimated regression equation that uses price and horsepower to predict ½-mile speed (to 3 decimals) Speed -bo +biPrice + b2Horsepower b. Plot the standardized residuals against y. - Select your answer- b. Plot the standardized residuals against y - Select your answer -i A. 1.5 0.5 100 110 90 1.5 2.5 1.5 0.5 110 90 100 0.5. 1.5 2.5 C. 1.5 0.5 90 100 110 1.5 2.5 1.5 0.5 90 100 110 1.5 2.5 Does the residual plot support the assumption about E? -Select your answer- c. Check for any outliers There are Select your answer- observation(s) with a large standardized residual What are your conclusions? Thus, there - Select your answer-appear to be any outliers in the data

Answer 1

Solution: Use MINITAB to estimate the regression equation as given below MINITAB procedure: Step 1: Choose Stat > Regression > Regression. Step 2: In Response, enter Speed at 1/4 mile. Step 3: In Predictors, enter Price and Horsepower Step 4: In Graph, Step 5: Click OK. choose Response versus fits. MINITAB output:

Regression Analysis: Speed at 1/4 mile versus Horsepower, Price The regression equation is Speed at 1/4 mile 71.3 + 0.0845 Horsepower0.107 Price Coef SE Coef Constant 2.248 31.73 0.000 Horsepower 0.084496 0.009306 9.08 0.000 0.10719 0.03918 2.74 0.017 71.328 Price S# 2.48532 R-Sq 91.9% R-Sq (adj) 90.7% # Analysis of Variance Source Regression Residual Error 13 80.30 Total 2 915.66 57.93 74.12 0.000 6.18 15 995.95 Source DE Seg ss Horsepower 1 869.43 Price 1 46.22 Speed at obs Horsepover 1/4 mile Fİt SE Fit Residual St Resid 90.700 90.488 0.991 290 108.000 105.882 2.007 93.200 91.682 0.882 305 103.200 99.765 1.140 345 102.100 105.854 0.944 450 116.200 116.827 1.699 91.700 92.827 0.894 89.700 90.633 0.970 0.212 2.118 1.518 3.435 -3.754 -0.627 -1.127 -0.933 215 93.000 94.317 0.781 1.317 195 1.45 X 0.65 1.56 189 -0.35 -0.49 225 195 -0.56 0,33 -2.90 92.300 91.544 0.935 99.000 103.460 0.802 94.600 87.112 1.064 305 103.200 100.076 1.055 93.200 93.195 0.874 320 105.000 102.761 0.859 236 97.000 95.6770.651 0.756 -4.460 -2.512 3.124 0.005 2.239 1.323 320 155 13 14 1.39 0.00 О. 96 0.55 201 16 X denotes an observation whose X value gives it large leverage

From the above MINITAB output, the estimated the regression equation Speed at ¼mile= 71.3+0.084 5Horsepower +0.107Price Use MINITAB to plot the residuals against MINITAB output: as shown below: Versus Fts (resparse iSpeed at 1/4 mile) -2 -5 110 105 Fitted Vaue 115 120 Explanation From "Residual versus fits", there seems to be no sign of serious problem. Hence, the line isa good fit for the data. Thus, the assumptions are not violated

Frompart (b) it is clearthat there are three outiers appearin the data, but it is not affected any serious violations. Thus, it can be concluded that the model ofthe given experiment is adequate