Question

In a population, the correlation coefficient between family income and child IQ is 0.30. The mean family income was $60,000. The standard deviation in income is $20,000. IQ is measured on a scale such that the mean is 100, and the standard deviation is 15.

(a) Using this information, predict the expected IQ of a child whose family income is $70,000
(b) How reliable do you expect this prediction to be? Why? (your answer should be a property of correlation, not an about IQ)
(c) The family income now rises does the correlation predict that the child will have a higher IQ? Why? opinion

Answer 1

Explanation:

Solution A:

regression eq is

y=a+bx

IQ=a+b*Income

where b=r*sy/sx

=0.3*15/20000

=0.000225

a=ybar-bxbar

a=100-0.000225*60000

a=86.5

y=a+bx

y=86.5+0.000225*x

IQ=86.5+0.000225*income

For given income of 70000 we need to predict IQ

substitute income =70000 in regression equation obtained above we get

IQ=86.5+0.000225*70000

predicted IQ=102.25

Solution b:

since r=0.30

r sq=0.30*0.30

=0.09

=0.09*100

=9%

that is explained variance by regression eq is

9%

unexplained variance=100-9=91%

9% variance in IQ is explained by regression equation.

Solution-c:

correlation does not imply causation with correlation cannot predict that the child will have a higher IQ

we can get only the relationship between two variable with correlation,but we cant predict