A study of child development measures the age (in months) at which a child begin

Question

A study of child development measures the age (in months) at which a child begins to talk and also the child's score on ability test given several years later. The study asks whether the age (x) at which a child talks helps predict the later test scores (y). A sample of 69 children produced the estimated regression line of y on x is:    y =115 - 1.7 x.

a)According to this regression line what do we expect when a child starts talking one month later?

b)What is the predicted score for a child who begins to talk at 8 months age?

c)If the observed score for a child who begins to talk at 8 months age is 102, what is the value of the residual error?

d)In this problem, which of the following is a plausible value of correlation coefficient between x and y?

Explanation / Answer

Ans:

a)when x=1 month

y'=115-1.7*1=113.3

b)

y'=115-1.7*8=101.4

c)

Residual error=Observed -perdicted=102-101.4=0.6

d)There is strong negative correlation(approximately -0.80) between age and scores,as the age increases,test score decreases

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