The data file named Galton.dat on this book's Web site contains Galton's data on heights of parents and children discussed in the section on regression to the mean. In these data, Galton multiplied mothers' and daughters' heights by 1.08 to give them the same mean as male heights, and then averaged the heights of both parents to produce the mid-parent height. The data are taken from Stigler (1999).

(a) Regress child height against parent height.

(b) Calculate the predicted height for children on the basis of parental height.

(c) The data file contains a variable called Quartile ranging from 1 to 4, with 1 being the lowest quartile. In SPSS use Analyze/Compare Means/One-way ANOVA to give child means corresponding to each quartile. (Make Child the dependent variable and Quartile the independent variable.) Do the same for parent means.

(d) Do the children of parents in the highest quartile have a lower mean than their par- ents, and vice versa for the children of parents in the lowest quartile?

(e) Draw a scatterplot with parent quartile means on the X axis and child quartile means on the Y axis and also draw a 45 degree line that would represent parents having children with the same mean height.