At the end of this lesson, students will be able to:
- Make a scatterplot.
- Fit a line to data and write an equation for that line.
- Perform linear regression with a graphing calculator.
- Solve real-world problems using linear models of scattered data.
Terms introduced in this lesson:
linear regression, line of best fit
Teaching Strategies and Tips
Before fitting a line to data, suggest that students always check the scatterplot first for signs of association between the variables. If the points are too scattered, any calculations will be meaningless.
Use the introduction and Example 1 to motivate linear regression.
- Data points are collected from measurement or experiment which is never perfect.
- A line of best fit is the line closest to all the data points. This means that the line minimizes the square root of the sum of the squares of the distances from each point to the line.
Provide the class with examples they can relate to. For example:
- Compile a list of students’ ages and heights.
- Use a graphing utility to make a scatterplot of age vs. height.
- Ask the class whether the data set looks approximately linear. If so, perform a linear regression using a graphing utility.
- Use the line of best fit to make predictions of height from ages. Have students gather similar age and height data from their older siblings as a way to check the model.
In Examples 3 and 4, discourage students from using any two data points to determine the equation of the line of best fit.
- Two points on the line or two data points closest to the line must be used.
- Teachers are encouraged to show that the line of best fit does not always pass through every point in the data set; in fact, it is possible that the line doesn’t go through any data point.