Question 6.87

52. A vehicle’s tire pressure can affect tire wear (in terms of the length of life of the tire). When tire pressure is low, the tire flattens out and more of its surface contacts the road. This causes more friction between the tire and the roadway and increases the amount of wear on the tire. Data collected on tire pressure and tire wear appear in the table below:

Tire Pressure (psi), Tire Wear (in thousands of miles driven),
30 29.8
30 30.2
31 32.4
31 34.5
32 36.2
32 35.0
33 38.4
33 37.6
  1. Fit a least-squares regression line to these data. What is the equation?
  2. Make a scatterplot of the data with a graph of the least-squares regression line superimposed. Does the line do a reasonable job of describing the pattern in these data?
  3. Use the equation of the least-squares line to predict the tire wear corresponding to a tire pressure of 40 psi. Is this an example of interpolation or extrapolation?

  4. Four more data values shown in the table below were collected for tire pressures higher than 33 psi. Redraw your scatterplot so that it includes these additional data values. Does the least-squares regression line from part (a) do a reasonable job of describing the pattern in the complete dataset? Explain.

    Tire Pressure (psi), Tire Wear (1000 miles),
    34 38.0
    34 37.2
    35 35.3
    35 34.6
  5. Based on your answer to part (d), comment on the accuracy of your prediction in part (c).