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Probability and Statistics

Probability and Statistics

Linear Regression

As we mentioned earlier, sometimes the dots in a scatter plot cluster like they're trying to make a nice shape. Sometimes the dots try to look like a straight line:

Sometimes the dots try to look like a curve:

Sometimes the dots try to look like an incredibly strange curve:

When the dots are trying to be a straight line, the line they're trying to be is called the line of best fit. In actual statistics classes you get to learn a tedious-but-not-really-hard procedure called linear regression, which allows you to find the line of best fit. If you get stuck, shoot Goldilocks an email; we hear she's had some experience with this sort of thing.

Right now, though, we'll do things the cheap way. Actually, you have your choice of cheap ways. You can either put all the data points into your calculator and let it do the work, or you can draw a picture and guess. We told you it would be cheap.

By "draw a picture and guess," we mean exactly that. First we draw the scatter plot. Then we pick two points (not necessarily among the scatter plot dots) that look like they're pretty close to the line of best fit. We find the equation of the line between our two points, and say that's close enough. We're not trying to arrive at any precise solution here...we're just trying to get a general idea of what these dots are up to.

Sample Problem

Approximate the line of best fit for the following data.

The dots look like they're trying to be a line that slopes up and to the right, and goes through the points (1, 1) and (5, 5).

The equation of the line between these points is

y = x,

so that's our guess at the line of best fit.

When drawing these pictures, of course, it's helpful to use graph paper and a ruler, and to have super-tidy labels. We know there's neat handwriting in you somewhere. But don't stress too much, because until you learn actual linear regression, you're only approximating the line of best fit. You only need to find a reasonable answer, not necessarily the one right answer. Enjoy it while it lasts...you won't often be asked to "guess" in algebra.

Here's another type of graph involving a bell curve; learn a little bit about it in our video.

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