In a large (hypothetical) study of the relationship between parental income and

Question

In a large (hypothetical) study of the relationship between parental income and the IQs of
their children, the following results were obtained. The intent is to predict IQ based on parental income. It was found that the scatterplot was roughly linear in nature.  
    Average income = $87,000  SD = $32,000     Average IQ = 100  SD = 17     R = 0.47

The regression equation is:
(A)  y = 0.053x + 9.78  (B) y = 0.091x + 83.66  (C) y = 0.00025x + 78.25        (D) None of these.

If I had a daughter and were to attempt to use the equation from above, to predict my daughter’s IQ score from my income, $96,000, what would her IQ be?
(A) 119   (B) 102      (C) 137   (D) 14  (E) None of these.

Explanation / Answer

Let Regression Equation be Y=a+bX.

where the slope b and intercept a are calculated in the following order:

b=r*(SDY/SDX), a=Ymean-b*Xmean.

So b=0.47*(17/32000)=0.00025

a=100-0.00025*87000=78.25

So Regression Equation is y=0.00025x+78.25.->option C.

B) Sub 96000$ in X we get Y=0.00025*96000+78.25=102.25~102->OPTION B

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