Question

Tire	Steering	Tread Wear	Buy Again
Goodyear Assurance TripleTred	8.9	8.5	8.1
Michelin HydroEdge	8.9	9	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	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	6.5	5.3
Michelin Symmetry	6.9	5.7	4.2
Kumho 722	7.2	6.6	5
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	3.3

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. The following data show survey ratings (1 to 10, with 10 being the highest) for 18 summer tires. Develop an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering and Tread wear rating. How many percent of the variation in the Buy Again variable could be predicted by Steering and Thread wear rating?

Note: put answers into decimal form, if your answer is 90.8765%, enter in 0.908765.

Answer 1

The multiple regression model that we want to estimate is

where is the intercept, are the slope coefficients and is a random disturbance

Using Excel, data--->data analysis--->regression

get this

ans: an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering and Tread wear rating is

the coefficient of determination R-square is

This indicates that 93.1764 percent of the variation in the Buy Again variable could be predicted by Steering and Thread wear rating.

ans: 0.931764