In a study, nine tires of a particular brand were driven on a track under identi

Question

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)

r^2= 0.953

Which statement is true?

A. About 95.3% of the variation in tread depth is explained by the regression on miles.

B. According to the least-squares regression line, the groove depth of a new tire (driven 0 miles) is predicted to be 360.64 mils.

C. All the answer choices are correct

D. 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

Explanation / Answer

OPTION C: C. All the answer choices are correct [ANSWER]

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The r^2 value is the percentage of variation that can be eplained by the regression, so A is correct.

The intercept is the groove depth at 0 miles, so B is correct.

The slope is the increase/decrease in the groove depth per unit increase in miles. Hence, option D is also correct.

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