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