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?
Substitute 16 for x and solve for tread depth in the equation.
Thank you! :)
178
To find the predicted tread depth of a tire driven 16 thousand miles using the least-squares regression line, we can substitute the value of x (16) into the equation and solve for the tread depth.
From the given equation of the least-squares regression line:
Tread Depth = 360.64 - 11.39x (thousands of miles)
Substituting x = 16:
Tread Depth = 360.64 - 11.39(16)
Tread Depth = 360.64 - 182.24
Tread Depth = 178.40
Therefore, the least-squares line would predict that the tread depth of a tire driven 16 thousand miles would be 178.40 mils.