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4 Tutorials that teach Best-Fit Line and Regression Line
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Best-Fit Line and Regression Line
Common Core: 8.SP.2 S.ID.6a S.ID.6c

Best-Fit Line and Regression Line

Author: Katherine Williams
Description:

Use a best-fit line to make predictions for a given scenario. 

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Tutorial

Source: Graph created by Katherine Williams

Video Transcription

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This tutorial talks about best-fit lines. Best-fit lines go by a couple of other names. It's called a trend line or a regression line. And your best-fit line is a way of summarizing the tendency for x to explain y for a particular scatter plot.

You could replace the word trend line there. You could say a trend line is the way of summarizing the tendency for x to explain y for a particular scatter plot. It's showing the trend.

Now, the way they're doing this is with a linear association. So the best-fit line, the trend line, the regression line, is only talking about linear association.

And then the key fact about the best-fit line, trend line, regression line, is that it splits the points. There's half the data points above the line and about half the data points below the line. This is a qualitative description, so it's not always exactly that way. And we'll learn in other tutorials how to calculate a best-fit line exactly, but just know that it's about roughly in half.

And then a great use of the best fit line is to make predictions. Once you've made your trend line, you can predict what other values would be for data points that you haven't collected.

Let's look at an example. Here, this is the best-fit line showing the average star speed in kilometers per second and the black hole mass in a measurement that is very scientific. And I actually don't know.

But what we can see is we can see we have very many data points. Each of these points represents a different observation. And then with our trend line, our best-fit line in here, we can see that some of the points are above, some are below, but very few are exactly on.

There's one point here that's exactly on and a point here that's pretty close, but not on. So with a best-fit line, you don't have to hit many of your points at all, as long as you're splitting the data.

We'll learn more about these in other tutorials. This has been your tutorial on the best-fit line.

Terms to Know
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.