Education Technology

What Is a Linear Regression?

Activity Overview

In this activity, students create lists of data points, plot them on a graph, and determine the regression equation of the best fitting line. They also understand exactly how the linear regression is determined.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 31 - 39 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

    Finding a Linear Equation:

  • Given a set of data points
  • Enter the x- and y- coordinates as lists
  • Graph the data as a scatter plot
  • Define a linear equation in the form y = mx + k
  • Use method of least squares to find the best fit
  • Observe that when the points are close to the line, the sum of the squares of distance from the line is the least
  • Enter arbitrary values of m (the slope), and k (the y-intercept) and plot the lines
  • Repeat the step until a line of best fit is obtained
  • Use the method of least squares on the calculator to determine the line of best fit

  • Calculating an Algebraic Equation for SS:
  • Observe that the equation to define the numerical value of best fit SS is quadratic for both m and k
  • Enter the terms of m and k and display the value of SS with undefined values of m and k
  • Observe the equation is a quadratic equation of the form y = ax2 + bx + c, which is the equation of a parabola, with a > 0
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary