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This lesson aims to show how to find the linear function that better models a scatter plot or data set. Additionally, it will be shown how to use these linear functions to make predictions.

Catch-Up and Review

Here are a few recommended readings before getting started with this lesson.

Explore

Residual Sum on a Scatter Plot

Given a scatter plot, a line of fit can be used to make good predictions of values that are not known. Since there are many possible lines of fit, finding the one that most accurately represents the given data points is an important goal. The goal is finding the line of fit in which the different sums of the residuals is as close to as possible.
Interactive Line of Fit on Scatter Plot
Examine how the different sums of the residuals change when moving the line. The most commonly used residual is the sum of the squared differences.

Discussion

Line of Best Fit

Pop Quiz

Practice Finding the Line of Best Fit

Use the linear regression feature of a graphing calculator to find the equation of the line of best fit for the given data set. Compare the obtained equation with the equations shown in the applet, and choose the closest one.

Bivariate data and equations

Closure

Are Lines of Best Fit Always Useful?

In this lesson it was shown how to find the line of best fit for data sets and how to make predictions using these lines. Considering the examples discussed throughout the lesson, it is possible to make two conclusions.

  • The lines of best fit are good to make predictions only if the data have a linear correlation.
  • The stronger the correlation is, the more accurate the predictions are expected to be.
When the data have no linear correlation, making predictions based on a linear model will not be viable. Even the data points will not be accurately represented by the line of best fit.


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