Question

ch 5 in a study, nine tires of a particular brand were driven on a track under identical conditions. each tire was driven a particular controlled distance (measured in thousands of miles) and the tread depth was measured after the drive. tread depth is measured in \mils.\ here, 1 mil is 0.001 inch. the least - squares regression line was computed, and added to a scatterplot of these data. on the plot, one data point is marked with an \x.\the equation of the least - squares regression line is:tread depth = 360.64 - 11.39x (thousands of miles)also, r² = 0.953. which of the following statements is true?according to the least - squares regression line, we would predict a decrease in groove depth of 11.39 mils for each 1000 miles driven on a tire.according to the least - squares regression line, the groove depth of a new tire (driven 0 miles) is predicted to be 360.64 mils.about 95.3% of the variation in tread depth is explained by the regression on miles.

Explanation:

• For the regression equation \(y = 360.64-11.39x\) (where \(y\) is tread depth and \(x\) is thousands of miles), the slope \(- 11.39\) means that for each unit increase in \(x\) (each 1000 miles), \(y\) (tread depth) decreases by 11.39.
• When \(x = 0\) (new tire, 0 miles driven), substituting into the equation \(y=360.64-11.39\times0 = 360.64\).
• The coefficient of determination \(r^{2}\) represents the proportion of the variance in the dependent variable (tread depth) that is predictable from the independent variable (miles). So, \(r^{2}=0.953\) means about 95.3% of the variation in tread depth is explained by the regression on miles.

Answer:

All three statements are correct.