Researchers wondered whether the size of a persons brain was related to the individuals mental capacity. They

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?

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Gender MRI Count I Gender MRI Count IQ Female Female 951,545 137 Male 1,001,121 140 Female 991,305 138 Male 1,038,437 139 Female Female Female 852,244 132Male 1,079,49 141 Female Female Female Female 816,932 133 Male 949,395 140 833,868 132 Male 856,472 140 Male 965,353 133 955,466 133 790,619 135 Male 866,662 130Male 857,782 133 Male 948,066 133 Male 924,059 135 955,003 139 935,494 141 949,589 144