4.11 Brain Size and Intelligence. For centuries, people have associated intelligence with brain size. A recent study used magnetic resonance imaging to measure the brain size of several individuals. The IQ and brain size (in units of 10,000 pixels) of six individuals are as follows: Brain size: IQ: 100 90 95 92 88 106 140 90 100 135 80 103

(a) Make a scatterplot. Which is the explanatory variable? The plot shows a positive linear pattern.

(b) Find the correlation r step by step. You may wish to round off to two decimal places in each step. First, find the mean and standard deviation of each variable. Then, find the six standardized values for each variable. Finally, use the formula for r. Explain how your value for r matches your graph in part (a).

(c) Enter these data into your calculator or software, and use the correlation function to find r. Check that you get the same result as in part (b), up to roundoff error. BRAIN