(1) The following table reports the curb weight, horsepower, and the speed at ¼
ID: 2948673 • Letter: #
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
Explanation / Answer
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.
ANSWER
R sq= 0.874119
= 0.874119*100
=87.41% variation in MPG is explained by independent variables CURBWT and HPOWER
Good model
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