Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 77

Linear Regression: Blood Glucose Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour alter drinking sugar water (after the 12-hour fast). Units are in mg/10 ml. A random sample of eight adults gave the following information (Reference: American Journal of Clinical Nutrition , Vol. 19. pp. 345-351).

x = 63.8; x 2 = 521.56; y = 90.7;
y 2 = 1070.87; xy = 739.65
(a) Draw a scatter diagram for the data.
(b) Find the equation of the least-squares line and graph it on the scatter diagram.
(c) Find the sample correlation coefficient rand the sample coefficient of determination r 2. Explain the meaning of r 2 in the context of the application.
(d) If x = 9.0, use the least-squares line to predict y.