# Least Squares Regression on TI-83/84

Copyright © 2005–2015 by Stan Brown, Oak Road Systems

Copyright © 2005–2015 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 scatterplot and
know what kind of regression you need to perform. To use your TI-83/84 to
make a scatterplot, see Scatterplot, Correlation, and Regression on TI-83/84.

Dial (x) | 0 | 2 | 3 | 5 | 6 |
---|---|---|---|---|---|

Temp, °F (y) | 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.
`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.
Scatterplot, 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/