Best-fit Line and Regression Line

This tutorial is going to teach you about lines of best fit. Specifically you will focus on:

1. Best Fit Line/Regression Line

1. BEST FIT LINE/REGRESSION LINE

The idea of a line of best fit is that there's going to be a line that sort of roughly approximates what's going on with the data in the form of a single line.

You're not going to talk about how to calculate a line of best fit, but you're going to understand what it's going to be used for.

Imagine a line going through the pack of points. That line is going to be called a best fit line, or a trend line, or a regression line. One easy visual way to do it is place an oval over the top of your points.

Best-Fit Line/Trend Line/Regression Line

A line that closely approximates the response values for given explanatory values when the form of the scatterplot is linear.

At the oval can be symmetric along what we call the minor axis, which is essentially cutting it the hamburger way. or you can cut it along the longer, major axis, which is typically called the hot dog way. You're going to essentially cut it the hot dog way. That's a pretty good approximation at a line of best fit.

It has a couple of different properties to it.

Roughly half the points fall above and below the line.

In this particular example, about five of them fall pretty near the line, and there are three that are substantially below, and three that are substantially above.

Just having points above or below the line isn't good. This is a poor choice of a trend line.

Not only does it not cut the oval hot dog way, but there's a pattern to how the points are above or below the line. If you know that a point is above the line, you know that it's on the right. And if you know that a point is below the line, you know that it's on the left.

You don't want it to look like that. This is a better trend line, because these points that are above are sort of peppered throughout. The ones that are below are sort of peppered throughout. You don't want a pattern to how the points are off from the line.

So what is a trend line used for?

A line of best fit is used to give approximations for values of x. Give approximations to values of y. Even on places where there is an existing value of y. For instance for 7, there's a difference between the actual value of y at 7, and what the line predicts as the value of y at 7.

What does this line predict for if x was 6 and 1/2? Go up from 6 and 1/2 until you get to the line, and figure out how high it is at that point. It's at about 625. You can say that the prediction for x being 6 and 1/2 is y being 625.

A line of best fit can understand the general trend of what's going on. How the y values relate to the x values. A good trend line will cut down the middle, and have sort of a peppering of points above and below it, random scatter, as opposed to some systematic flaw in it.

Good luck.