Curve Fitting using the TI-92

**Step 1: Enter data.**

To make use of the curve fitting
routines built into the TI-92, we first must enter the data. This can be done
directly using the **Data/Matrix
Editor**. To access this editor,
use the **APPS** key (left and down from the cursor control).
This causes a menu to drop down with item 6 being the Data/Matrix Editor.
Selecting this item either by moving down to it or pressing the 6 key causes a
sub-menu to open containing the options **1:Current****¼**** , 2:Open****¼**** , 3:New****¼**** ****.** Since we are starting fresh, select
the **3:New** item. The dialog box that is then displayed
allows you to select the type, the folder where the data is to be stored, and
the name (variable) to use for storing the data. This takes you to the data
screen where you can begin to input the data.

Example: To enter the data in Table I
on page 76 of Stewart’s Calculus, I entered the name *tbl1p76* as the name
of the variable (or file).

For column 1, we want the even years
from 1972 through 1990. We could type them in, hitting the **ENTER**
button each time to move to the next cell, or we can have the calculator do it
for us by using the **F4 Header** key. The formula **seq(x,x,1972,1990,2)** will do the job. In general, the syntax for this formula is **seq(***formula***, ***loop
variable***, ***start, stop, step***)**.

The data in column 2 must be typed in,
hitting the **ENTER** key each time to record the value and move to
the next cell.

It is nice to put **Titles** at
the top of the columns to remember what the numbers represent. To do this, use
the cursor control to move to the top of the column and type the heading. For
c1, I entered year, and for c2 I used CO2. The data screen now
looks something like this.

DATA | Year | CO2 | ||||

c1 | c2 | c3 | c4 | c5 | c6 | |

1 | 1972 | 327.30 | ||||

2 | 1974 | 330 | ||||

3 | 1976 | 332 | ||||

4 | 1978 | 335.30 | ||||

5 | 1980 | 338.50 | ||||

6 | 1982 | 341 | ||||

7 | 1984 | 344.3 |

**Step 2: Define plot.**

We can plot the points (*x,y*) we
have inputted where *x* is the value in c1 and *y* is the value in c2.
To do this, we use the **F2 Plot
Setup** key. This opens a dialog
box containing a listing of the defined plots. If there are already plots
defined you should either turn them off (i.e. keep them from being plotted)
using the **F4** key, or clear them (**F3** clears all). I
will assume that we want to use **Plot
1** for plotting the above data.
Be sure it is highlighted and press the **F1
Define** key. The **Plot Type**
we want is **Scatter**. The **Mark** set to
**Box** is fine, or you can select another symbol to use. For x, type in
c1
then **ENTER**. For y type in c2 and
**ENTER**. Use the cursor control to move down the list.
Hit the **ENTER** key to close the define box and return to the
first dialog box. The entry in **Plot
1** should be checked and there
should be added information on the line. Hit the ENTER key again to exit this
box.

Next we want to change the window so
that all our points will appear when plotted. This is done as before using the
green-diamond key then **WINDOW**. One set of acceptable values are xmin= 1972, xmax= 1990, xscl= 1, ymin= 325, ymax= 355,
yscl=1.

Now move to the graph screen and observe the points being plotted.

**Step 3: Linear
Regression**

To use the linear regression routine
built into the TI-92 to find the line that "best fits" the data using the
least-squares method, move back to the Data/Matrix editor by **APPS/ 6: Data/Matrix Editor/ 1:Current,
ENTER**. This should cause the
table entered above to appear on your screen. The **F5 Calc** key gives a
dialog box. The list of built in curve fitting routines is found under
**Calculation Type**. The one we want first is the **5:LinReg**.
Define x to be c1 by moving down to that cell and typing c1. Define y as c2.
**Store RegEQ to y1(x).** Hit the **ENTER** key to have
the calculations done. The results are displayed in a dialog box. It should look
something like this.

y=a× x+b

a =1.496667

b =-2624.826667

corr =.998275

R^{2}=.996552

Moving to the **GRAPH** screen shows a
plot of the original data and the line that was obtained. In this case, the fit
is excellent, although it does not always have to be so. The equation of the
line can be retrieved by using the **Y=** screen and noting
the definition of the y1 variable.

**Other routines:**

There are several other curve fitting
routines that may work if the linear fit is not very good. To do Example 2 on
page 79, define the data and use the **4:ExpReg** routine
instead of the **5:LinReg** above. This finds an exponential function that
"best fits" the data by doing a linear regression on c1 and ln(c2). The
exponential function does not fit the data well, although it fits better than a
line would. However if you try the **3:CubicReg** routine,
a cubic function will be found which fits the data even better.

**NOTE:** There is a lot more to
curve fitting than what is done here. Be careful and realize that you only have
the very beginning of a complicated topic.

Created by T. J. Sanders, tjs@usna.edu