The accompanying data on x 5 head circumference z score (a comparison score with peers of the same age—a positive score suggests a larger size than for peers) at age 6 to 14 months and y 5 volume of cerebral grey matter (in ml) at age 2 to 5 years were read from a graph in the article described in the chapter introduction (Journal of the American Medical Association

[2003]).

Cerebral Grey Matter (ml) 2–5 yr Head Circumference z Scores at 6–14 Months 680 .75 690 1.2 700 .3 720 .25 740 .3 740 1.5 750 1.1 750 2.0 760 1.1 780 1.1 790 2.0 810 2.1 815 2.8 820 2.2 825 .9 835 2.35 840 2.3 845 2.2

a. Construct a scatterplot for these data.

b. What is the value of the correlation coef fi cient?

c. Find the equation of the least-squares line.

d. Predict the volume of cerebral grey matter at age 2 to 5 years for a child whose head circumference z score at age 12 months was 1.8.

e. Explain why it would not be a good idea to use the least-squares line to predict the volume of grey matter for a child whose head circumference z score was 3.0.