Ask Question
28 July, 01:45

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

+2
Answers (1)
  1. 28 July, 01:53
    0
    Step-by-step 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
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers