Question: A diabetic is interested in determining how the amount of aerobic exercise impacts his blood sugar. When his blood sugar reaches 170 mg/dL, he goes out for a run at a pace of 10 minutes per mile. On different days, he runs different distances and measures his blood sugar after completing his run. Note: The preferred blood sugar level is in the range of 80 to 120 mg/dL. Levels that are too low or too high are extremely dangerous. The data generated are given in the following table.
a. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between distance run and blood sugar level?
b. Find the predictive regression equation of blood sugar level on the distance run.
c. Give a brief interpretation of the values of a and b calculated in part b.
d. Plot the predictive regression line on the scatter diagram of part a and show the errors by drawing vertical lines between scatter points and the predictive regression line.
e. Calculate the predicted blood sugar level count after a run of 3.1 miles (5 kilometers).
f. Estimate the blood sugar level after a 10-mile run. Comment on this finding.