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 afterward the tread depth was measured. 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.
The least-squares line would predict that the tread depth of a tire driven 16 thousand miles would be
A.
260.5 mils.
B.
178.4 mils.
C.
360.64 mils.
D.
181,879 mils.
I think it's B!
You are correct!
113.9
To find the predicted tread depth of a tire driven 16 thousand miles using the equation of the least-squares regression line, we substitute x = 16 into the equation:
Tread Depth = 360.64 - 11.39(16)
Calculating this expression, we get:
Tread Depth = 360.64 - 182.24 = 178.4 mils
So the predicted tread depth of a tire driven 16 thousand miles would be 178.4 mils.
Therefore, your answer is correct. The answer is B.
To determine the tread depth of a tire driven 16 thousand miles using the given least-squares regression line equation, we simply substitute the value of x (16) into the equation and calculate the corresponding value for the tread depth.
Tread Depth = 360.64 - 11.39x (thousands of miles)
Tread Depth = 360.64 - 11.39 * 16
Tread Depth = 360.64 - 182.24
Tread Depth ≈ 178.40 mils
Therefore, the correct answer is B. 178.4 mils.