In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

When I teach regression, I typically use this example to illustrate the regression effect:

Suppose that the heights of fathers and their adult sons both have mean 69 inches and standard deviation 3 inches. Suppose also that the correlation between the heights of the fathers and sons is 0.5. Predict the height of a son whose father is 63 inches tall. Repeat if the father is 78 inches tall.

Using the formula for the regression line

,

we obtain the equation

,

so that the predicted height of the son is 66 inches if the father is 63 inches tall. However, the prediction would be 73.5 inches if the father is 76 inches tall.

To make this more memorable for students, I’ll observe:

As expected, tall fathers tend to have tall sons, and short fathers tend to have short sons. For example, my uncle was 6’6″. His two sons, my cousins, were 6’4″ and 6’5″ and were high school basketball stars.

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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