# Activities

• • • ##### Subject Area

• Math: Algebra I: Linear Functions

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-92 Plus / Voyage™ 200
• ##### Other Materials
This is Activity 5 from the EXPLORATIONS Book:
Discovering Math on the Voyage 200.

## 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.

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