## Sketching realistic graphs

I was trying to draw Bert and Ernie the other day, and it was really difficult. I had pictures of them right next to me, but my drawings were just incredibly crude, more “linguistic” than “visual” in the sense that I was portraying key aspect of Bert and Ernie but in pictures that didn’t look anything like them. I knew that drawing was difficult–every once in awhile, I sit for an hour to draw a scene, and it’s always a lot of work to get it to look anything like what I’m seeing–but I didn’t realize it would be so hard to draw cartoon characters!

This got me to thinking about the students in my statistics classes. When I ask them to sketch a scatterplot of data, or to plot some function, they can never draw a realistic-looking picture. Their density functions don’t go to zero in the tails, the scatter in their scatterplots does not match their standard deviations, E(y|x) does not equal their regression line, and so forth. For example, when asked to draw a potential scatterplot of earnings vs. income, they have difficulty with the x-axis (most people are between 60 and 75 inches in height) and having the data consistent with the regression line, while having all earnings be nonnegative. (Yes, it’s better to model on the log scale or whatever, but that’s not the point of this this exercise.)

Anyway, the students just can’t make these graphs look right, which has always frustrated me. But my Bert and Ernie experience suggests that I’m thinking of it the wrong way. Maybe they need lots and lots of practice before they can draw realistic functions and scatterplots.