This brief document can be used to guide students as they learn how to find regression equations for paired data. Or, since there are several features of the calculators that are used in the example, this could be used as an illustration for a general introduction to a wide range of the capabilities of the graphing calculators. It is written for both the TI-82 and TI-83. As a result the user may find that there are some minor variations between these instructions and the particular calculator in use.

Entering discrete data.

Sample exercise 1. For the male students in this room, describe (in the most descriptive and accurate manner that you can) how the weight of the students is related to the height. Use this information to predict the weight if the height of a given student is known to be 67 inches tall. (Rather than collect the data for all the students today, we will use data from five UWWC students who were in a section of MATH 110, Sept 18, 1996. Any two sets of related data could be used in place of the height and weight of this example.)

 
Put the heights in a calculator list, L1.

Use STAT, EDIT, Edit.

Highlight L1 and enter CLEAR, ENTER to clear the existing entries in the list.

Move the highlight to the first position in the list and start entering heights.

Move down the list by pressing the down arrow or ENTER.

Do not enter the 67 since there is no corresponding weight.

Put corresponding weights in list L2 in a similar manner.

Note: This can also be done by going to the home screen and entering {135,180,180,160,140}, STO >, L2. (L2 is entered with 2^nd 2.)

Since we are dealing with heights to the nearest inch, we should change the display to show only one place past the decimal. This is done as follows.

Select MODE, Normal, 1. (The rest of the mode settings should be on the first option in each line.)

If you go back to the display of data in the two lists with STAT, EDIT, Edit, you will see the numerical representation of all the heights shown with the corresponding weights in the next column.

Optional: Operations on lists.

Suppose that these five students all go on a rigorous exercise program and each on loses 10 pounds. Can we display that in our chart?

First method. On the home screen enter L2 – 10, STO >, L3. Now pull up list 3 and note the results.

Second method. On the Stat, Edit screen where the lists are shown highlight L3 and clear it. With the L3 heading highlighted, enter L2 – 10, ENTER. Notice the values that appear in the list for L3.

In a similar you can square a list (which squares each number of the list), multiply it by a constant, or perform any other operation using the list as you would a single number.

Graphing discrete data.

Now Back to our height & weight data. To graph the data, follow the procedure described here, which produces the traditional scatterplot or scattergram for a set of discrete points.

Turn off the Y functions by selecting VARS, Y-VARS, 4, 2, ENTER.

Set up a statistical plot by selecting STAT PLOT, 1, ENTER, On, ENTER. Select the first option under "Type" (the miniature graph of discrete points.) and press ENTER. Select L1 and L2 for x and y lists respectively since the independent variable is height and it is in list 1 and the dependent variable, weight, is in list 2. Now highlight one of the selections for the type of Mark (probably the box is best) and press ENTER.

Return to the home screen by pressing QUIT.

Set the appropriate graphing window by selecting WINDOW, setting Xmin and Xmax for 0 and 80 respectively (why?), set the x scale for 10, and set y to go from a minimum of 0 to a maximum of 200 with a scale of 20.

Press GRAPH.

The discrete points should be shown on the graph with the horizontal axis depicting the height and the vertical axis showing the weight of each student.

Finding the regression line (curve or "best fit").

It appears that the points in this example lie reasonably close to a straight line. Can we find what is known as the "best fit line" or "regression line" through the points? Yes, there are several ways.

Use the TI-82/83 calculator to find and graph the regression line for a set of paired data.

Select STAT, CALC, LinReg(ax+b), L1, comma, L2, ENTER.

Record the values for a and b and use them to set up a Y function by entering Y=, ax+b. (You may have to clear the Y function first or move to something other than Y1.)

Enter GRAPH.

• TRACE the line until the value of X is as close as possible to the given X value and then read the corresponding Y value.
• Calculate it by selecting CALC, CALCULATE, value, known value for X, ENTER.
• Use a table of values by selecting TBLSET, enter the known X for TblStart, TABLE, and then read the desired value. If there are several weights to determine go back to TBLSET and change the option for Indpnt (independent) to Ask. Now when you go to TABLE you can enter a value you want for the height and the corresponding predicted weights will be displayed.
• Calculate it by writing the equation and substituting the appropriate value(s) for x.


Nonlinear data.

By looking at the graph estimate the type of function that you think will fit best. Rather than selecting LinReg(ax+b) as you did above, select one of the other types of regression. For example, if the data appears to be from a population with exponential growth, you find the regression curve by selecting STAT, CALC, ExpReg(L1,L2). Of course L1 and L2 can be any lists where the x and y values are stored. If some pairs occur more than once the frequency can be stored in a third list, say L3. Then the entry is of the form ExpReg(L1,L2,L3,Y1). The Y1 is optional. Whatever Y function is included is where the regression function will be stored.

The TI-83 has several regression functions available that the TI-82 does not include.

Questions, or suggestions for modifying this document, should be sent to Gary Britton, gbritton@uwc.edu.