Before the presidential election of 2004, there was much discussion of the relative intelligence of the two candidates, George W. Bush and John Kerry. After critics of Bush suggested that his IQ was on the low side, his defenders used a regression on his SAT score (1206) to estimate his IQ to be 124. Kerry's IQ was presumably about 122, based on his purported SAT score of 1190.
a. Correlation between SAT score and IQ is somewhere between 0.5 and 0.6. Is the relationship weak, moderate, or strong?
b. Standard deviation for IQ is about 15, and s (typical error size) for the prediction of IQ based on SAT score would be about 10. What is the range of IQ scores that are within about one s of the prediction for Bush's IQ, 124?
c. What is the range of IQ scores that are within about one s of the prediction for Kerry's IQ, 122?
d. Comment on the validity of a claim that Bush's IQ was about 2 points higher than Kerry's, based on their SAT scores.
e. Which should we be able to predict more accurately: IQ of one individual whose SAT score was 1206, mean IQ of all those whose SAT score was 1206, or both the same?
f. Based on samples, we can get a rough idea of the equation for the regression line that relates IQ to SAT for everyone who took the SAT test, but the actual intercept and slope for the entire population are unknown. Are these denoted b0 and b1 or b0 and b1?