Exponential and Logarithmic Equations: Background You’ll Need 4

  • Use linear regression to model data

Use Linear Regression to Model Data

When data is collected in the real world, it often does not line up perfectly along a straight line. However, the data may still follow a roughly linear pattern. In this case, we use a line of best fit to model the data. This process is called linear regression.

linear regression

Linear regression produces a line of best fit for data that is approximately linear. The equation has the form [latex]y = mx + b[/latex] or [latex]y = a + bx[/latex].

 

The regression line can be used for prediction

The line may not pass through every point (or even any point), but it minimizes the overall error (the distance from the points to the line).

Linear Regression with Technology

You can view the transcript for “Learn Desmos: Regressions [2015]” here (opens in new window).
You can view the transcript for “Linear Regression TI84 (Line of Best Fit)” here (opens in new window).

A company tracks the number of social media ads run each month and the corresponding sales. The data is shown below:

Ads (x) Sales (y)
2 7
4 9
6 14
8 17
10 21
12 24

Find a linear regression model for the data. Then use the model to predict sales if the company runs 15 ads.