Mathematical Modeling

on the TI-89

Finding a mathematical equation to represent real-world data is the first step in applying the power of mathematics to real-world problems. This process is called mathematical modeling. Here is a short tutorial on mathematical modeling on the TI-89.

Entering Data into the TI-89

Push the key and select "6: Data/Matrix Editor."

Select:

"3: New" to create a new data or list variable.

"2: Open" to select an existing data or list variable.

"1: Current" to select the data or list variable that was last used.

Since this is your first time in the data/matrix editor, select "3: New."

This is the New Data Dialog. Leave the type as "Data" and folder as "main". Type the name of your variable in the Variable field - "temp" is a good name for this exercise. You do not need to press [alpha] to type in this field.

Now you can enter the data values into your variable. It seems easiest type the x-values into the "c1" column first, then go back and type the y-values into the "c2" column.

(The data shown here is from Stewart, p. 27, Example 2. Note that I have used "0" for "1980," "2" for "1982" to simplify the data somewhat.)

Fitting an Equation to the Data:

To fit an equation to your data, press (Calculate). In the Calculate Dialog that opens, set:

Calculation Type to "LinReg"

x to "c1"

y to "c2"

Store RegEQ to y1(x)

then press .

Here are the results of the linear regression calculation on the data from this example. Correlation ("corr") and "R²" are measures of how closely the data fit the given line. For our purposes, a correlation close to 1 or -1 means "good fit."

(The y-intercept shown here differs from the one in the text (which is -2707.25) since my x-values are adjusted from the ones in the text.)
calculated results

You can press (Y=) to check that, sure enough, the regression equation has been saved to y1. You can go ahead and graph this line, but it won't show your data points.

To get back to your data, press .

Graphing the Data:

To set up a data plot:

if you are currently on the Data/Matrix screen, press (Plot Setup).

if you are on the "Y=" screen, scroll up to "Plots", highlight "Plot 1:", and press .

plot setup dialog

Select (Define). In the Define Plot Dialog, set:

Plot Type to "Scatter"

Mark to "Box"

x to "c1"

y to "c2"

and press .

Press (Y=) to go to the Y= Editor. Then press (Zoom) and select "9:ZoomData" to graph the data points and the regression line.
zoom data

Compare this graph to Fig. 6 on p. 28 of the Stewart text.
data plot

last update April 14, 2008 by JL Stanbrough

Push the key and select "6: Data/Matrix Editor."
Select: "3: New" to create a new data or list variable. "2: Open" to select an existing data or list variable. "1: Current" to select the data or list variable that was last used. Since this is your first time in the data/matrix editor, select "3: New."
This is the New Data Dialog. Leave the type as "Data" and folder as "main". Type the name of your variable in the Variable field - "temp" is a good name for this exercise. You do not need to press [alpha] to type in this field.
Now you can enter the data values into your variable. It seems easiest type the x-values into the "c1" column first, then go back and type the y-values into the "c2" column. (The data shown here is from Stewart, p. 27, Example 2. Note that I have used "0" for "1980," "2" for "1982" to simplify the data somewhat.)

To set up a data plot: if you are currently on the Data/Matrix screen, press (Plot Setup). if you are on the "Y=" screen, scroll up to "Plots", highlight "Plot 1:", and press .
Select (Define). In the Define Plot Dialog, set: Plot Type to "Scatter" Mark to "Box" x to "c1" y to "c2" and press .
Press (Y=) to go to the Y= Editor. Then press (Zoom) and select "9:ZoomData" to graph the data points and the regression line.
Compare this graph to Fig. 6 on p. 28 of the Stewart text.