# Does Size Matter? Researchers wondered whether the size of a person’s brain was related to the…

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 were administered the Wechsler (1981) Adult Intelligence Scale-Revised exam to obtain their IQ scores. MRI scans, performed at the same facility, consisted of 18 horizontal magnetic resonance images. The computer counted all pixels with nonzero gray scale in each of the 18 images, and the total count served as an index for brain size. The resulting data are presented in the table.

(a) Find the least-squares regression line treating MRI count as the explanatory variable and IQ as the re-sponse variable.

(b) What do you notice about the value of the slope? Why does this result seem reasonable based on the scatter diagram and linear correlation coefficient obtained in Problem 31 of Section 4.1?

(c) When there is no relation between the explanatory and response variable, we use the mean value of the response variable, to predict. Predict the IQ of an individual whose MRI count is 1,000,000. Predict the IQ of an individual whose MRI count is 830,000.

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