TC3 → Stan Brown → TI-83/84/89 → Least Squares Regression
revised 8 Aug 2007

# Least Squares Regression on TI-83/84

Copyright © 2005–2014 by Stan Brown, Oak Road Systems

Summary: When you have a set of (x,y) data points and want to find the best equation to describe them, you are performing a regression. There are different types: linear regression to fit a straight line, quadratic regression to fit a parabola, and so on. The basic method is called least squares regression because it considers the best-fitting line or curve to be the one that minimizes the total of the squares of residuals, which are the deviations between the data points and the fitted line or curve, measured vertically.

See also: This page assumes you’ve already made a scatter plot and know what kind of regression you need to perform. To use your TI-83/84 to make a scatter plot, see Scatter Plot, Correlation, and Regression on TI-83/84.

 Dial (x) Temp, °F (y) 0 2 3 5 6 6 −1 −3 −10 −16

For an illustration of linear regression, we’ll use the data shown at right, from Dabes & Janik’s Statistics Manual (1999).

You want to construct a linear model relating the temperature of the freezer compartment to your refrigerator’s dial setting. Designate the explanatory variable as x, the independent variable; and define the response variable as y, the dependent variable.

To perform the analysis, you’ll have a step-by-step procedure below, but here’s the overview: enter the x’s as one list of numbers and enter the y’s as a second list, then choose the proper regression command from a menu. The calculator will respond with the best-fitting line or curve of the type that you chose.

(We’ll use L1 and L2, and this procedure will automatically erase anything previously stored in those lists. If you have something in them that you want to key, you could use any other lists in your calculator.)

 First, enter the x numbers as a comma-separated list inside curly braces. The curly braces { } are shifted parenthesis ( ) keys. Press [2nd ( makes {]. (Always release the [2nd] key before pressing the other key.)   Enter 0, [,] 2 [,] 3 [,] 5 [,] 6. (No comma after the last number, please.)   Enter the closing brace [2nd ) makes }]. Store these numbers to list 1. Press [STO→], which is near the bottom left of your keyboard.  Press [2nd 1 makes L1] [ENTER]. Your screen should look like the one at right. Now enter the y numbers in list 2. Press [2nd ( makes {].   Press 6 [,] [(-)] 1 [,] [(-)] 3 [,] [(-)] 10 [,] [(-)] 16. Be careful to use the change sign key [(-)] for negative numbers, not the subtract [-] key.  [2nd 2 makes L2] [ENTER]. Check your numbers carefully. If any are wrong, press [2nd ENTER makes ENTRY] once or twice to bring back the command, then use the arrow keys to move to the wrong number. Fix it, and press [ENTER] to store the corrected list. Select your regression type. Press [STAT] and then the right arrow [►]. You’ll notice that there are many types of regression. They start with linear regression, item 4, and continue past the bottom edge of the screen. Use the up and down arrows to scroll to the type you want and then press [ENTER], or else just press the number of the selection. In this case you want linear regression. Press [4]. Add the x and y list identifiers to the regression command. Press [2nd 1 makes L1] [,] [2nd 2 makes L2]. Your screen should look like the one at right.   Finally, press [ENTER] to execute the command, and your screen should look like this one.

The linear model for the refrigerator that best fits the data is

temperature = −3.52×dial + 6.46

See also: The calculator can also give you the values of r and R², which measure the quality of the model. Scatter Plot, Correlation, and Regression on TI-83/84 gives details.

This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.

For updates and new info, go to http://www.tc3.edu/instruct/sbrown/ti83/