Question

(1)        The following table reports the curb weight, horsepower, and the speed at ¼ mile for 16 sports and GT cars (1998 Road & Track Sports & GT Cars).

                                                                                                                        Speed at

Sports & GT Car                     Curb Weight               Horsepower                 ¼ Mile mph

Acura Integra Type R                         2577                            195                  90.7

Acura NSX-T                                      3066                            290                  108.0

BMW Z3 2.8                                       2844                            189                  93.2

Chevrolet Camaro z28                        3429                            305                  103.2

Chevrolet Corvette Convertible          3246                            345                  102.1

Dodge Viper RT/10                            3319                            450                  116.2

Ford Mustang GT                               3227                            225                  91.7

Honda Prelude Type SH                     3042                            196                  89.7

Mercedes Benz CLK320                    3240                            215                  93.0

Mercedes Benz SLK230                     3025                            185                  92.3

Mitsubishi 3000GT VR-4                   3737                            320                  99.0

Nissan 240X SE                                  2862                            155                  84.6

Pontiac Firebird Trans AM                 3455                            305                  103.2

Porsche Boxster                                  2822                            201                  93.2

Toyota Supra Turbo                            3505                            320                  105.0

Volvo C70                                          3285                            236                  97.0

COMPUTER OUTPUT – RESULTS

                                              CAR SPEED at 1/4 mile

                       REGRESSION FUNCTION & ANOVA FOR MPH

       MPH = 74.62398 - 0.000806 CURBWT   +   0.099174 HPOWER

       R-Squared                            =   0.874119

       Adjusted R-Squared            =   0.854753

       Standard error of estimate   =   3.105472

       Number of cases used         =   16

                                      Analysis of Variance

                                                                                                                        P-value

       Source                SS                  df           MS                F Value         Sig Prob

       Regression        870.58290        2         435.29150       45.13618        0.000001

       Residual            125.37150       13            9.64396

       Total                  995.95440       15

                                         CAR SPEED at 1/4 mile

                         REGRESSION COEFFICIENTS FOR MPH

                                                                                    Two-Sided

         Variable          Coefficient          Std Error          t Value            Sig Prob

         Constant            74.62398             6.34292         11.76493          0.000000

         CURBWT         -8.05781E-04      0.00233          -0.34516          0.735491 *

         HPOWER           0.09917             0.01237           8.02039           0.000002

                     * indicates that the variable is marked for leaving

         Standard error of estimate    =     3.105472

         Durbin-Watson statistic       =      1.690434

USE THE ABOVE COMPUTER OUTPUT TO RESPOND TO THE QUESTIONS BELOW

QUESTIONS:

A stepwise multiple regression was run using the following model

            MPH = b + b (Curbwt ) + b (Hpower ) + e

(a)        From the computer output, what is the estimated multiple regression equation?

ANSWER

(b)        Clearly state your null and alternative hypotheses for testing the significance of both independent variables and carry out the test. What is your conclusion?

ANSWER

(c)        Test for the significance of each individual independent variable. What is your conclusion? Which of the two independent variables should be dropped and why?

ANSWER

(d)       Give an interpretation to the R-Squared value of the full model.

ANSWER

(e)        The 1999 Porsche 911 has been advertised as having a curb weight of 2910 and an engine of 296 horsepower, use the full model and the final model to predict the speed at ¼ mile of this car.

ANSWER

Answer 1

SolutionA:

estimated multiple regression equation is

MPH = 74.62398 - 0.000806 CURBWT   +   0.099174 HPOWER

(b)        Clearly state your null and alternative hypotheses for testing the significance of both independent variables and carry out the test. What is your conclusion?

H0: no linear reltionship

H1:Atleast one independent variable affects y

test statistic:
F= 45.13618      

p= 0.000001

p<0.05

Reject Null Hypothesis.

Accept alternative Hypothesis.

COnclusion is

Model is significant and can be used to predict MPH from CURBWT and HPOWER.

(c)        Test for the significance of each individual independent variable. What is your conclusion? Which of the two independent variables should be dropped and why?

For CURBWT p= 0.735491

p>0.05
CURBWT is not significant variable.

for HPOWER p=0.000002

p<0.05

HPOWER is significant variable.

(d)       Give an interpretation to the R-Squared value of the full model.

R sq= 0.874119

= 0.874119*100

=87.41% variation in MPG is explained by independent variables CURBWT and HPOWER

Good model