1. TI-84 Data Fitting Tutorial Prepared for Math Link Participants By Tony Peressini and Rick Meyer Modified for TI-84 / TI-84 Plus by Tom Anderson, Feb University of Illinois at Urbana-Champaign Copyright Board of Trustees, University of Illinois, 2006

2. TI-84 Data Fitting Tutorial—An Overview What should this tutorial help you do with your TI-84 or 84 Plus Calculator?
After completing this tutorial, you will be able to:
Enter, graph and manipulate data relating two variables
Find linear, functions for your data—that is, find the linear, exponential or power function that best fits the data (in the sense of minimizing the sum of the squares of the vertical deviations of the function graphs from the data points).
Determine how well a regression function fits the data points by statistical as well as graphical means.
You will do all this in an interactive context involving some interesting real data on stomach and lung cancer.

3. An Illustrative Problem: Cancer Data
The best way to learn the data-fitting capabilities of the TI-84 is through a real problem using real data.
The table below lists the number of deaths per year, per 100,000 women in the U. S. from lung cancer and stomach cancer during this century.
Our task is to find the linear function that best fit this data, and evaluate the "goodness of fit" for each of these functions.
Year
Lung Cancer
Stomach Cancer
1930 2 28
1940
2.5
20.5
1950
5.1 14
1960 6 9
1970 10
5.5
1980 21
4.5
1990
30.5 3

4. The Statistics Menu The TI-84 keypad is shown to the right.
In this tutorial, we will be making extensive use of the Statistics menu, (outlined in red on the keypad).
To get to the Statistics menu, press the S key. (Do that now, and continue to use your calculator to follow along as you go through the tutorial.)

5. Clearing Previous Data
To clear any previously stored data, press the 4 key while in the Statistics menu. This will display ClrList on the Home Screen as shown in Figure 1.
To clear lists L1, L2 and L3, complete the command to read
ClrList L1, L2, L3
as shown in the first line of Figure 2, you need to enter the commas as well. Then press the e key. The TI-84 will respond with the message DONE .
The lists L1 through L6 are referenced using the ` key (upper left on the keypad, outlined in red in combination) with the appropriate key 1–6 also outlined in red. For example: L4 is entered by typing ` 4 .
Figure 1
Figure 2
Exercise 1: Clear lists L4, L5 and L6.
Click here to see the Exercise 1 Answer

6. Making sure the TI-84’s STAT EDIT lists and Regression information haven’t been reprogrammed
List capabilities for the TI-84 are capable of being modified by the user.
To insure that the STAT EDIT lists appear the same on your calculator as they do in the rest of this tutorial, do the following as a precautionary measure. Press
S 5(SetUpEditor), e The screen will say SetUpEditor and DONE. These keystrokes clear out any user-defined lists which may have been in the STAT EDIT lists and would have altered the names for lists L1, L2, L3, L4, L5, and L6.
To insure that information for LinReg, which we will use later, will match our screens, perform the following keystrokes. Press
` 0 (CATALOG), cursor down to DiagnosticOn and then Press e twice. The screen will say DiagnosticOn and DONE. These keystrokes cause the value of the correlation of coefficient, r, to be shown.

7. Entering Two-Variable Data
Return to the Statistics menu by pressing the S key.
Then press the 1 key to edit the lists. Any previous values should have been cleared from the lists. The resulting screen is shown at the right.
Use the arrow keys to enter the years in L1 and the lung death rate in L2.
Leave the remaining lists empty for now. We will need them later.

8. Displaying Two-Variable Data on a Scatter Plot
Press the ` key, then the ! key (STAT PLOT) to get the STAT PLOTS menu shown at the right.
Make sure that all plots are OFF. To turn the plots off, press the 4 key, followed by the e key. The TI-84 will respond with DONE.
Press the ! key and clear any functions that may have been entered. This is accomplished by using the ARROW keys and the C key.
At this point, everything that could have cluttered our data plot has been cleared or turned off.
( Continued on the next page…)

9. Displaying Two-Variable Data on a Scatter Plot
( Continued from the previous page…)
Return to the STAT PLOT menu by pressing ` then ! .
Press the 1 key to change the options for Plot 1.
Use the ARROW keys and the e key to edit the screen so as to match the one shown at the upper right.
Press # cursor down to 9:ZoomStat and them press e to display the data (or just press # 9 ) as shown in the screen to the right. NOTE: ZoomStat automatically sizes the GRAPH window to display the data in the lists chosen.
Exercise 2: Enter the stomach cancer data into list L3, and display a plot of the data. Don’t forget to change the Ylist in the Plot 1 menu (above) to L3.
Click here to see the Exercise 2 Answer

10. Finding the Linear Regression Line for the Lung Cancer Data
Return to the Statistics Menu (by pressing S), and highlight CALC by using the > key. Press the 4 key to show LinReg(ax+b) on the Home Screen.
Complete to get LinReg(ax+b) L1,L2 and then press e to get the screen shown at the right.
The values of a and b are the coefficients of the regression line y = a x + b for the lung cancer data. The value of r is the correlation coefficient—more about its meaning later!
Exercise 3: Find the linear regression line for the stomach cancer data.
Click here to see the Exercise 3 Answer

11. Displaying the Linear Regression Line for Stomach Cancer Data
Let’s see how well the regression line for stomach cancer from exercise 3 fits the stomach cancer data by plotting both on a single graph.
STAT Plot 1 should already be set up to display the stomach cancer data which is in L3 because of exercise 2. You might wish to see, however, that STAT Plot 1 shows the Xlist as L1 and the Ylist as L3. You may also wish to rerun LinReg L1,L3 to make sure the linear regression equation for the stomach cancer data is your current function.
Press ! . All the functions should be cleared. (If not, clear them now.) The blinking cursor should be at Y1. (If not, move it there.)
Press v followed by 5 (Statistics).
Use the > key to select EQ, then press 1 (RegEQ). This will copy the most recent regression data into an equation for Y1 ( top screen shot).
Press # 9 (ZoomStat) to display the data and the graph of the linear regression equation (lower right screen).
Exercise 4: Display the linear regression line with the data for the lung cancer data (list L2).
Click here to see the Exercise 4 Answer

12. Brief comments on the "Goodness of Fit" of the Linear Regression Line
The stomach cancer data is again shown to the right with its linear regression line.
The correlation coefficient (r) for this data was calculated along with the linear regression data to be:
r =–
In general, the closer the absolute value of r is to 1, the better the fit.
In this case, the correlation coefficient does not rule out the possibility of a linear fit, but a look at the graph makes us think that we can get a better fit with some other type of regression.

13. TI-84 Data Fitting Tutorial Prepared for Math Link Participants By Tony Peressini and Rick Meyer Modified from the Fitting Data with the TI-82 or TI-83 Tutorial by Tom Anderson, Feb University of Illinois at Urbana-Champaign Copyright Board of Trustees, University of Illinois, 2001
The End
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14. Exercise 1 Answer Use the following keystrokes:
Press S then 4 to get this first screen.
Press ` 4 , ` 5 , ` 6
Press e to get this last screen.
Click here to return to the tutorial

15. Exercise 2 Answer Use the following keystrokes:
Go to the STAT PLOTS screen by doing ` ! then choose 1 .
Use the arrow keys to set Plot1 to On, and to use lists L1 and L3 (use ` 1 and ` 3 to set the Xlist and Ylist). Match the screen to the right, and then hit e to accept it.
Press # 9 to get the plot.
Click here to return to the tutorial

16. Exercise 3 Answer Use the following keystrokes:
Press S, arrow over to CALC, 4 LinReg(ax+b) ` 1 , ` 3 e .
Click here to return to the tutorial

17. Exercise 4 Answer Use the following keystrokes:
Go to the STAT PLOTS screen by doing ` ! then choose 1 .
Use the arrow keys to set Plot1 to On and to use lists L1 and L2 (use ` 1 and ` 2 to set the Xlist and Ylist). Match the screen to the right, and then hit e to accept it.
Press S , arrow over to CALC, press 4 (LinReg(ax+b)) ` 1 , ` 2 e to get the linear regression equation.
(Continued…)

18. Exercise 4 Answer (Continued from the previous page…)
Press ! (then C if you need to clear out an existing equation from Y1) v 5 (Statistics), arrow over to EQ, press 1 (RegEq) to copy the linear regression equation into Y1.
Press # 9 to get the plot.
Click here to return to the tutorial