Technical Steps for Teaching Linear Regression in an Algebra Class

Before the invention of graphing calculators, the concept of linear regression was difficult to teach with precision. However, today's algebra students do not recall the days before graphing calculators and have grown up fluent with their use. Some teachers, though, may not have learned linear regression on a graphing calculator and may need some advice about how to use it in their algebra classroom. This article supports the concept of teaching linear regression and shares step-by-step instruction using the TI-83+ graphing calculator.

First of all, linear regression is the process of looking at a set of data points and determining the equation of the line of best fit. This is the linear equation that best represents the data points. There are other forms of regression, including quadratic regression, cubic regression, and others, but they are similar in process to teaching linear regression.

The strength of the relationship (r) of the line to the data is called the correlation coefficient. This value ranges between -1 and +1 like a fuel gauge needle ranges between empty and full. A negative one correlation represents all points in a perfectly linear pattern trending downward at a negative slope. This represents a truly strong negative correlation. In between, around a -0.6, the correlation would be considered a weak negative. As the correlation coefficient approaches 0, the description of the 'r' would be "no correlation." This pattern continues in the positive as well, with a weak positive or strong positive correlation.

To enter data on a graphing calculator and see the resulting scatter plot and line of best fit, follow the steps below.
1. Turn the "Diagnostics On" on the calculator by scrolling down within the "CATALOG" (found on the zero key.)
2. Turn on the scatter plot by pressing 2nd-y=. Make sure the scatter plot, L1, and L2 are selected
3. In the Stat-Edit menu, type the x-values (independent variable) into L1 and the y-values (dependent variable) into L2
4. Clear out any existing equations in the y= menu.
5. View the scatter plot by using Zoom - ZoomStat
6. Perform the linear regression process. To do this, press Stat, move right one menu to Calc, and select LinReg(ax+b). Press Enter.
7. Write down the 'a', 'b', and 'r' values. Use the 'a' and 'b' as slope and y-intercept of the linear equation. The 'r' value is the correlation coefficient.
8. Graph the line of best fit by entering the equation obtained in step 7 into the y= menu. Press graph.

Using this process provides an exact solution to a linear regression problem in algebra. It helps students to observe the process visually, and helps them make predictions with the "Table" menu. Real life applications and data analysis fall into this lesson nicely. Students frequently show a high participation level with this lesson due to its use of technology to help them visual concepts.

Have you taught linear regression? Do you use a graphing calculator to do so? Please comment below.

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