13.27 A diabetic is interested in determining how the amount of aerobic exercise impacts his blood...

 

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13.27 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 dif- ferent 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 ex- tremely dangerous. The data generated are given in the following table. 2 Distance (miles) 2 2.5 2.5 3 3 3.5 3.5 4 4 4.5 4.5 Blood sugar (mg/dL) 136 146 131 125 120 116 104 95 85 94 83 75 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 draw- ing 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. 13.27 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 dif- ferent 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 ex- tremely dangerous. The data generated are given in the following table. 2 Distance (miles) 2 2.5 2.5 3 3 3.5 3.5 4 4 4.5 4.5 Blood sugar (mg/dL) 136 146 131 125 120 116 104 95 85 94 83 75 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 draw- ing 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.

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