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 after 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 6.2 8.4 7.0 7.5 8.1 6.9 10.0 9.7 y 9.8 10.7 10.3 11.9 14.2 7.0 14.6 12.2 x 5 63.8; x2 5 521.56; y 5 90.7;
y2 5 1070.87; xy 5 739.65

(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 coeffi cient r and the sample coeffi cient of determination r2. Explain the meaning of r2 in the context of the application.

(d) If x 5 9.0, use the least-squares line to predict y.