Linear Regression (Jump to: Lecture | Video )

In a previous lecture on Pearson's r, we found two sets of data to be highly correlated:

Figure 1.

If we know that two variables are strongly correlated, we can use one variable to predict the other using the following equations:

Figure 2.

Here, we first calculate beta1 and beta0 and place them in the top equation. Then, if we plug an x into the equation, we can predict what our y value will be.

The stronger your correlation (that is, the closer r is to -1 or 1), the more accurate your prediction will be.

First, we solve for beta1:

Figure 3.

We then use beta1's value to solve for beta0:

Figure 4.

Now, putting those values into the original equation, we have our completed regression equation:

Figure 5.

Predict the yearly income of someone who is 33 years old.

Figure 6.

We would expect someone who is 33 years old to make approximately $36,963 a year.

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