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 = ax^{2} + 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