Question

In a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and again at age 35. The following results are obtained.
Age 18: average score = 100, SD = 15
Age 35: average score = 100, SD = 15, r = 0.80
(a) Estimate the average score at age 35 for all the individuals who scored 115 at age 18.
(b) Predict the score at age 35 for an individual who scored 115 at age 18.

Answer 1

Answer:

112

Step-by-step explanation:

Given that in a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and again at age 35.

Age 18: average score = 100, SD = 15

Age 35: average score = 100, SD = 15, r = 0.80

Let us obtain regression equation of y on x.

Let y be the scores at age 35 and x at age 18

Slope = $r(s_y/s_x) = 0.8(\frac{15}{15} )=0.80$

The line passes through (100,100) being average of x and y

Hence regression line would be

$y-100=0.8(x-100)\\y = 0.8x+20$

a) Here given that x =115

Hence $y=0.80(115)+20\\=112$

the average score at age 35 for all the individuals who scored 115 at age 18, would be 112.

b) Prediction also would be the same 112.