Are the size and weight of your brain indicators of your mental capacity? In this study by Willerman et al. (1991) the researchers use Magnetic Resonance Imaging (MRI) to determine the brain size of the subjects. They selected a sample of 40 right-handed Anglo introductory psychology students at a large southwestern university who had indicated no history of alcoholism, unconsciousness, brain damage, epilepsy, or heart disease. These subjects were drawn from a larger pool of introductory psychology students with total Scholastic Aptitude Test Scores higher than 1350 or lower than 940 who had agreed to satisfy a course requirement by allowing the administration of four subtests (Vocabulary, Similarities, Block Design, and Picture Completion) of the Wechsler (1981) Adult Intelligence Scale-Revised. The MRI Scans were performed at the same facility for all 40 subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with non-zero gray scale in each of the 18 images and the total count served as an index for brain size. Using a 0.05 significance level, we need to determine whether brain size can be predicted from the following variables: (1) FSIQ: Full Scale IQ scores based on the four Wechsler (1981) subtests, (2) VIQ: Verbal IQ scores based on the four Wechsler (1981) subtests, (3) PIQ: Performance IQ scores based on the four Wechsler (1981) subtests, and (4) Height: Height in inches.

What percentage of the variation in brain size can be explained by the linear association between brain size and the collection of variables given in this problem?

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