Question

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15.54 The Tire Rack, America’s leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 maximum performance summer tires. The variable Steering rates the tire’s steering responsiveness, Tread Wear rates quickness of wear based on the driver’s expectations, and Buy Again rates the driver’s overall tire satisfaction and desire to purchase the same tire again.

Tire	Steering	Tread Wear	Buy Again
Goodyear Assurance TripleTred	8.9	8.5	8.1
Michelin HydroEdge	8.9	9.0	8.3
Michelin Harmony	8.3	8.8	8.2
Dunlop SP 60	8.2	8.5	7.9
Goodyear Assurance ComforTred	7.9	7.7	7.1
Yokohama Y372	8.4	8.2	8.9
Yokohama Aegis LS4	7.9	7.0	7.1
Kumho Power Star 758	7.9	7.9	8.3
Goodyear Assurance	7.6	5.8	4.5
Hankook H406	7.8	6.8	6.2
Michelin Energy LX4	7.4	5.7	4.8
Michelin MX4	7.0	6.5	5.3
Michelin Symmetry	6.9	5.7	4.2
Kumho 722	7.2	6.6	5.0
Dunlop SP 40 A/S	6.2	4.2	3.4
Bridgestone Insignia SE200	5.7	5.5	3.6
Goodyear Integrity	5.7	5.4	2.9
Dunlop SP20 FE	5.7	5.0	3.3

1. Clearly specify the dependent variable and the independent variables, and develop an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating.
2. What are the estimates for parameters of the independent variables?
3. What are the p-values of the t tests for the independent variables?
4. What is the p-value of the F test?
5. At the .05 level, are there significant relationship between the dependent variable and the independent variables?
6. What is the multiple coefficient of determination?
7. What is the adjusted multiple coefficient of determination?
8. Interpret the results.

Answer 1

Sol:

a).

Buy again is the dependent variable and steering and tread wear rating are independent variables.

Buy again=

b to d)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.97
R Square	0.93
Adjusted R Square	0.92
Standard Error	0.57
Observations	18
ANOVA
	df	SS	MS	F	Significance F
Regression	2	67.18	33.59	102.41	0.00
Residual	15	4.92	0.33
Total	17	72.11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-5.39	1.11	-4.86	0.00	-7.75	-3.02
Steering	0.69	0.29	2.40	0.03	0.08	1.30
Tread Wear	0.91	0.21	4.42	0.00	0.47	1.35

e)

H0: None of the independent variables affect the dependent variable.

H1: Atleast one of the independent variables affects the dependent variable

Sign F is less than 0.05 and hence reject the null hypothesis. Thus, we conclude that atleast one of the independent variables affects the dependent variable. Fcrit is 3.68 and F is 102.41. Hence, F>Fcrit and hence reject the null hypothesis

f)

r^2=0.93

g)

adj r^2=0.92

h)

Intercept: Buy again would remain constant at -5.39 in absence of other factors as well

Steering: For every increase of 1 in steering, buy again would go up by 0.69 keeping everything else constant

Tread Wear: For every increase of 1 in tread wear, buy again would go up by 0.91 keeping everything else constant.

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