Following are data on price, curb weight, horsepower, time to go from 0 to 60 miles per hour, and the speed at 1/4 mile for 16 sports and gt cars.
Sports & GT Car/ Price ($1000s)/ Curb Weight (lb.)/ Horsepower /0-60 mph (seconds) /Speed at 1/4 mile (mph):
Acura Integra Type R/ 25.035 /2577/ 195/ 7/ 90.7
Acura NSX-T/ 93.758/ 3066/ 290/ 5/ 108
BMW Z3 2.8/ 40.900/ 2844/ 189/ 6.6/ 93.2
Chevrolet Camaro Z28/ 24.865/ 3439/ 305/ 5.4/ 103.2
Chevrolet Corvette/ 50.144/ 3246/ 345/ 5.2/ 102.1
Dodge Viper/ 69.742/ 3319/ 450/ 4.4/ 116.2
Ford Mustang GT/ 23.200/ 3227/ 225/ 6.8/ 91.7
Honda Prelude Type SH/ 26.382/ 3042/ 195/ 7.7/ 89.7
Mercedes-Benz CLK320/ 44.988/ 3040/ 205/ 7.2/ 93
Mercedes-Benz SLK230/ 42.762/ 3025/ 185/ 6.6/ 92.3
Mitsubishi 3000GT VR-4/ 47.518/ 3737/ 320/ 5.7/ 99
Nissan 240SX SE/ 25.066/ 2862/ 155/ 9.1/ 84.6
Pontiac Firebird Trans Am/ 27.770/ 3455/ 305/ 5.4/ 103.2
Porsche Boxster/ 45.560/ 2822/ 201/ 6.1/ 93.2
Toyota Supra Turbo/ 40.989/ 3505/ 320/ 5.3/ 105
Volvo C70/ 41.120/ 3285/ 236/ 6.3/ 97
Develop a regression model with curb weight, horsepower, time from 0-60 mph, and the speed at 1/4 mile as 4 different independent variables to predict the car price. Typically, you should keep only significant variables in your final estimated regression model. That is, if you find statistically insignificant variables, you should remove them from the model and then re-run the model again (one at a time). However, for this particular homework problem, please keep all 4 independent variables in the final estimated equation even if some of the independent variables might not be statistically significant at the .10 alpha level.
a. Please specify the regression model?
b. At a .10 level of significance, please report your conclusions related to the hypotheses specified in part (a).
c. Again, please focus your attention on the estimated regression equation (with one dependent variable and four independent variables). Please predict the price of a sports car that takes only 7 seconds from 0 to 60 mph, along with the following features: 2,850 lbs, 200 horsepower, 100 mph 1/4 mile. In addition, please report the 95% prediction interval related to the estimated price.
Using MINITAB:
The COMMANDS are:
Stat >> Regression >> Regression >> Fit Regression:
MINITAB window would be:
Click on Graphs:
Click OK.
Then Click OK.
MINITAB output:
a)
In the output above, the regression model is:
Price ($1000s) = -208 - 0.0140 Curb Weight (lb.) - 0.156 Horsepower + 1.38 0-60 mph (seconds) + 3.34 Speed at 1/4 mile (mph)
That is,
= -208 - 0.0140 Curb Weight (lb.) - 0.156 Horsepower + 1.38 0-60 mph (seconds) + 3.34 Speed at 1/4 mile (mph)
b)
Conclusion:
In the output above, we can see that the predictor variable of Speed at 1/4 mile (mph) is significant because of their p-value is 0.096. However, the p-value for Curb Weight (lb.) (0.442), the p-value for Horsepower (0.342), the p-value for 0-60 mph (seconds)(0.874) are greater than the alpha level of 0.10, which indicates that it is not statistically significant.
Typically, we use the coefficient p-values to determine which terms to keep in the regression model. In the model above, we should consider removing the Curb Weight (lb.) (0.442), Horsepower (0.342), 0-60 mph (seconds).
c)
For the given values of
0 to 60 mph = 7 seconds,
curb weight = 2,850 lbs,
horsepower = 200,
mph 1/4 mile = 100
The Prediction for Price ($1000s) is obtained as:
Substitute these values into the above equation
Thus, the Prediction for Price ($1000s) of a sports car that takes only 7 seconds from 0 to 60 mph, along with the following features: 2,850 lbs, 200 horsepower, 100 mph 1/4 mile is $64.56 (in $1000).
Using the MINITAB we can find the 95% prediction interval related to the estimated price.
The COMMANDS are:
Stat >> Regression >> Regression >> Predict:
MINITAB window would be:
Click OK.
MINITAB Output:
Following are data on price, curb weight, horsepower, time to go from 0 to 60 miles...
eBook The following data show the curb weight, horsepower, and fs-mile speed for 16 popular sports and GT cars. Suppose available. The complete data set is as follows: that the price of each sports and GT car is also Sports & GT Car Acura Integra Type R Speed at Mile Horsepower (mph) 90.7 ($1000s) 25.035 93.758 40.900 24.865 50.144 (lb.) 195.000 290.000 189.000 305.000 345.000 BMw 23 2.8 Chevrolet Camaro Z28 Chevrolet Corvette Convertible Dodge Viper RT/10 Ford Mustang GT...
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...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares Squares F Regression 2 60 Error 18 120 Total 20 180 Determine the Regression Mean Square (MSR): Determine the Mean Square Error (MSE): Compute the overall Fstat test statistic. Is the Fstat significant at the 0.05 level? A linear regression was run on auto sales relative to consumer income. The Regression Sum of Squares (SSR) was 360 and...