Question

1. 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 and independent consumer survey to help drivers help each other by sharing their long-term driving 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.
   1. Develop the estimated regression equation that can be used to predict the Buy Again rating given based on the Steering rating. At the .05 level of significance, test for a significant relationship.
   2. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain.
   3. Develop an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating.
   4. Is the addition of the Tread Wear independent variable significant? Use a = .05.

2. Tire	Steering	Tread Wear	Buy Again
   Goodyear Assurance Triple Tred	8.9	8.5	8.1
   Michelin HydroEdge	8.9	9.0	8.3
   Michelin Harmony	8.3	8.8	8.2
   Dunlop SP60	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

Answer 1

using excel>data>data analysis>Regression

we have

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.9182
R Square	0.8430
Adjusted R Square	0.8332
Standard Error	0.8411
Observations	18
ANOVA
	df	SS	MS	F	Significance F
Regression	1	60.7866	60.7866	85.9295	0.0000
Residual	16	11.3184	0.7074
Total	17	72.1050
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-7.5218	1.4668	-5.1282	0.0001	-10.6312	-4.4124
Steering	1.8151	0.1958	9.2698	0.0000	1.4000	2.2302

a ) the estimated regression equation that can be used to predict the Buy Again rating given based on the Steering rating is

Buy Again = -7.5218+1.8151

since p-value of F stat is 0.0000 which is less than 0.05 so  relationship between Buy again and steering rating is significant

b ) the estimated regression equation developed in part (a) provide a gives good fit to the data because about 84.30% variation in Buy again can be explained by steering rating .

uisng excel>data>data analysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.9653
R Square	0.9318
Adjusted R Square	0.9227
Standard Error	0.5727
Observations	18
ANOVA
	df	SS	MS	F	Significance F
Regression	2	67.1848	33.5924	102.4121	0.0000
Residual	15	4.9202	0.3280
Total	17	72.1050
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-5.3877	1.1095	-4.8558	0.0002	-7.7526	-3.0228
Steering	0.6899	0.2875	2.3992	0.0299	0.0770	1.3028
Tread Wear	0.9113	0.2063	4.4166	0.0005	0.4715	1.3511

c ) an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating is

Buy Again = -5.3877+0.6899*Steering + 0.9113 *Treadwear

d ) yes, the addition of the Tread Wear independent variable is significant because p-value of Treadwear is less than 0.05