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 Adult Intelligence Scale-Revised to obtain their IQ scores. MRI scans, performed at the same facility, 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. The resulting data for the females in the study are presented in the table.
MRI Count, x .. IQ, y
816,932 ...... 133
951,545 ...... 137
991,305 ...... 138
833,868 ...... 132
856,472 ...... 140
852,244 ...... 132
790,619 ...... 135
866,662 ...... 130
857,782 ...... 133
948,066 ...... 133
(a) Find the least-squares regression line for females treating MRI count as the explanatory variable and IQ as the response 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 33(d) of Section 4.1?
(c) Predict the IQ of a female whose MRI count is 1,000,000. Predict the IQ of a female whose MRI count is 830,000.