Chapter 4.2, Problem 100E

To determine

To explain how well does one twin’s IQ predict the other’s.

Explanation of Solution

In the question, it is given that a researcher studied a group of identical twins who had been separated and adopted at birth. Thus, by the information given in the question first construct a scatterplot for the same as follows:

  

In this scatterplot, Twin A is on the horizontal axis and Twin B is on the vertical axis. The scatterplot slopes upwards, thus there is a positive association between the variables. Moreover, the points seem to roughly lie about a line and thus the association is linear. Now, let us construct a residual plot for the linear regression line. A residual is the difference between the actual value and the predicted value by the linear regression line. Thus, it is as follows:

  

In the residual plot, Twin A is on the horizontal axis and the residual is on the vertical axis. And there is no obvious pattern in the scatterplot, thus the linear regression line seems to make good predictions for the IQ scores of Twin B.