Does Size Matter? Researchers wondered whether the size of a person’s brain was related to the individual’s mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. MRI scans were performed at the same facility for the subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with a nonzero gray scale in each of the 18 images, and the total count served as an index for brain size.

(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Comment on what you see.

(b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly related?

(c) A lurking variable in the analysis is gender. Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable, but use a different plotting symbol for each gender. For example, use a circle for males and a triangle for females. What do you notice?

(d) Compute the linear correlation coefficient between MRI count and IQ for females. Compute the linear correlation coefficient between MRI count and IQ for males. Are MRI count and IQ linearly related? What is the moral?