Question

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 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?

Answer 1

To develop an estimated regression equation, plot the data points, calculate the equation for the line of best fit, and use the coefficient of determination to determine the percentage of variation in the Buy Again rating that can be predicted.

Step-by-step explanation:

To develop an estimated regression equation to predict the Buy Again rating based on the Steering and Tread wear rating, you would use linear regression analysis. Here are the steps:

Plot the data points on a scatter plot, with the Steering rating on the x-axis and the Tread wear rating on the y-axis.

Calculate the equation for the line of best fit that minimizes the distance between the data points and the line. This equation will give you the estimated regression equation.

The equation will be in the form of: Buy Again rating = b0 + (b1 * Steering rating) + (b2 * Tread wear rating), where b0 is the y-intercept and b1 and b2 are the coefficients for the Steering and Tread wear ratings respectively.

To determine the percentage of the variation in the Buy Again variable that can be predicted by the Steering and Tread wear rating, you can use the coefficient of determination (R-squared). It measures the proportion of the total variation in the Buy Again rating that can be explained by the variation in the Steering and Tread wear ratings.