Eyeball-estimate the regression line for the following scatterplot. Then determine the slope of that line. Select the answer that comes closest to your eyeball-estimate of the slope.

Question

Answer 1

I hope the point of this problem is to demonstrate that “eyeball estimates” aren’t very reliable when you have much noise! (Maybe the teacher wants to show how many students got very different answers?) I’ve been looking at scatterplots for 25 years, and question to me looks like it is purposefully designed to be hard to eyeball.

You want to imagine a line that has about as many points above it as below it. (The computer will do something more complicated that your eye cannot hope to do.) I think what you can most realistically ask is, “would this line have a positive or negative slope?” You can do this by imagining chopping the graph up into four squares: top right, top left, bottom right, and bottom left. If the data want to be fit by a line with a positive slope, you’ll see points mostly in the bottom left and top right; if it’s a negative slope, you would see them in the top left and bottom right.

Except…when I try to do that, I don’t get a clear answer in this question. Most of the dots would seem to go straight up the middle. Depending on what points happened to catch my eye, I could think it was a really steep positive slope or a really steep negative slope. I guess this slope will be very close to a vertical line, which has an infinite slope.

It looks like there were some multiple choice options that aren’t presented. I would take the biggest number available. But I wouldn’t feel bad if my answer was way off. This sort of graph is why we do these things with formulas instead of eyeballs!