Steps to a Linear Regression on the TI-86

This page is devoted to presenting, in a step by step fashion, the keystrokes and the screen images for doing a linear regression on a TI-86. The example used is to find the best fit line for the data given as
x 5 8 9 11 15
y 11 18 18 20 28

First we want to be sure that the calculator has the correct mode settings. To do this, use to display a screen similar to this.
Figure 1
All of the options on the left, and only the options on the left, should be highlighted. If your screen does not appear like this, then you should fix it. Use the cursor control keys to move up and down, left and right on the screen. Then use the key to select the desired option. To get out of the review of modes, press the .
This should cause a blank screen to appear, as in the following figure.
Figure 2
Next, we want to prepare for an eventual graph of the solution. Therefore, before we even start working on the data, we look it over and determine that we want to graph x values from -1 to 20, and y values from -10 to 30. We need to check the range settings (i.e., what is the window of the graph that we will be able to see) in the graph mode to be sure that those settings are set the way we want them to be set.
We can move into the graphics mode by pressing . This will bring up the graphing screen such as
Figure 3
The only important point of this screen is that it shows the menu on the bottom line. We would like to check on the range of values, so we select the WIND option by typing . This produces a screen similar to the following picture.
Figure 4
You may have different values. That is just fine because we will now set the values to the ranges that we want. Do this by using the cursor control keys to move up or down the list, typing in new values where needed. The following screen reflects a change of values that will have x running from -1 to 20, and y going from -10 to 30.
Figure 4a
Note that I chose the yMin to be -10, even though our values do not go down that far. The choice was made so that the y-axis would be elevated off the bottom of the display. This helps later when the graph is displayed and there are menus along the bottom of the screen that cover up the graph. By using -10 for yMin, the menus will be covering up areas that are not important to the values being graphed.

There is one more value to display, as noted by the down arrow at the left of "yScl". That last value is "xRes" and it should be set to 1.

Figure 5
Get out of the WIND display by using . This will take you back to a blank screen, as in Figure 2. Now use the buttons to open the LIST menu. This should produce a screen as seen to the left in Figure 5. Note that the menu has the { and } characters assigned to the and keys, repectively. Lists on the TI-86 are enclosed in curly braces. There is no key assigned to the curly brace. Thus, when we want to type a curly brace we need to open the LIST menu so that we can use the F1 and F2 keys.
Figure 6
Now, use the button to generate the left curly brace. The screen shoud appear as in Figure 6. We will now complete the list which will hold our x values. To do this we type the elements of the list, separated by a comma. In our example we want the values 5, 8, 9, 11, and 15. So we enter
Figure 7
Then, to finish off the list, we will add the closing curly brace by typing . The result should be the screen to the left, in Figure 7. Having created a list, we want to save it, or rather we want to STORE it in a variable. The key generates the store arrow on the screen.
Figure 8
Now we need to give the list a name. We will use L5 for this list. The TI-86 has already moved into alphabetic mode as signaled by the change in the cursor (the cursor was not captured in the image in Figure 8 but it appears as a flashing black box with a white uppercase A inside of it.
Figure 9
To arrive at the name L5, press to produce the "L". Then, to get out of alphabetic mode, press and follow that by pressing . This should leave the screen looking like Figure 9. Finally, press .
 
Figure 10
The TI-86 responds by displaying our L5 list as the answer, this time without the commas. Now we need to enter the second list, the y values, and store it in a variable we will call L6.
Figure 11
Use to get the {, and to get the }. Then,
Figure 12
Use the key to submit the new list. Again, the TI-86 responds by displaying the newly entered list, as in Figure 12.
Figure 13
Now that the data has been entered, we need to use the statistical functions to do the linear regression. Press . This will close the LIST menu of Figure 12 and generate the STAT menu at the bottom of Figure 13.
Figure 13a
We want to do some calculations in the statistical area. We use to select CALC from the menu. This will open a new menu, as in Figure 13a, that includes the LinR command in the third position.
Figure 14
Press the to generate the LinR command. Figure 14 shows that "LinR" command on the screen, just as if you had entered it by keystrokes, which you could have done.
The TI-86 wants to do statistical calculations using a list for the x values and one for the y values. There are many possible lists to use. If the command remains as "LinR" then the TI-86 assumes that the two lists are in the predefined names xStat and yStat. However, we put our lists into L5 and L6. We need to tell the calculator to use those lists instead of the default. To do this we need to follow the "LinR" command by the names of the two lists we want, separated by a comma.
Figure 15
We could type the names of the lists directly, or we could move back to the LIST menu, select the NAMES sub-menu, and then select the lists from that display. We will use this second approach. To get to the LIST menu press . This should produce the screen in Figure 15.
Figure 16
To open the NAMES sub-menu, press . Now there should be two menus, as in Figure 16. Note that the particular arrangement of lists in that bottom menu will change over time as new lists are created and old ones are deleted. You may even need to use the key to look through a continuation of the menu if there are more than 5 LISTs. Also, the TI-86 maintains 3 standard lists, xStat, yStat, and fStat.
Figure 17
Press to generate the L5,L6 as seen in Figure 17.
Figure 18
To do the specified linear regression, press . The TI-86 should respond with the screen shown in Figure 18.
Extreme caution needs to be used in reading the values on the screen in Figure 18. The regression equation is meant to be of the form
y = a + bx
as shown on the screen. In this form "b" is the "slope" of the line and "a" is the y-coordinate of the y-intercept. This naming tends to confuse people, especially those of us who have just had the slope-intercept formula (y=mx+b) drilled into our heads. The "b" in the regression equation (y=a+bx) has nothing to do with the "b" in the slope-intercept form. Also, be aware that statisticians prefer to give the constant (intercept) first, rather than at the end of the equation. So, again, the regression equation, the line of best fit for the given data points, is given as
y = a + bx
where "a" is the constant that gives us the y-coordinate of the y-intercept, and "b" is the slope of the line.
Figure 18a
Figure 18 identifies the regression equation as
y = 3.5217 + 1.6123 x
with values rounded to 4 decimal places. The corr=.984667514 gives a measure of just how good the fit is. The closer this value is to 1.0 or to -1.0, the better the fit. The next step is to do some plotting of the graphs for this data. The commands will close the menu of Figure 18 and generate the menu on Figure 18a.
Figure 19
Having returned to the STAT menu in Figure 18a, we can now plot the points by using the DRAW menu item. We do this by pressing . This will display the graph, as seen in Figure 19.
Figure 20
Although Figure 19 shows the data points, it does not show the regression line. The DRAW menu command not only plotted the points, but it opened a new sub-menu. Unfortunately, the command that we want is not among the first 5 choices. Therefore, we need to press to see more options. This has been done to get to Figure 19a.
Figure 20
The choice that we want, DRREG, is now displayed. Press to select DRREG. This draws the line described by the regression equation. Now you can see the advantage of setting up the WIND values for the graph back in Figure 4A, as well as setting the yMin value to -10. The menu in Figure 19 covers the bottom of the graph, but we can still see the first quadrant. You might want to look ahead at Figure 27, which corresponds to Figure 20, but with yMin set at 0.
Figure 21
At this point we are done looking at the regression line and the scatter points. Rather than zoom in to get a better look, let us look at some of the values that the TI-86 computes as part of the LinR command. Press to select the VARS option from the top menu of Figure 20, generating Figure 21. These variables represent such values as the mean of the x values, the standard deviation of the x values (assuming x is a population), the standard deviation of the x values (assuming x is a sample, and so on.
Figure 22
We want other values than are shown in Figure 21. Press to display more variables. We want to see the sum of the x-square values. It is in this menu, in position 3.
Figure 23
Pressing will select that option, close the graph, and display the symbol for the sum of the x-square values. This is shown in Figure 23. Press the key to perform the command, and move to Figure 24.
Figure 24
We can see, in Figure 24, that the sum of the x-square values is 516. It would be nice to see some more values, but that menu has disappeared from the screen.
Figure 25
We can recall the STAT menu by selecting . Then, press for the VARS, and then to find more of the variables. Now we can select any of the other variables.
Figure 26
The contents of Figure 26 were generated by and

For completeness, I have constructed the following table to show all of the values that would have to be computed to use the formula given in the book.

  x y x^2 xy y^2
  5 11 25 55 121
  8 18 64 144 324
  9 18 81 162 324
  11 20 121 220 400
  15 28 225 420 784
           
TOTAL 48 95 516 1001 1953
Certainly, this is a major task and we only had five pairs of data points.

Figure 27
Figure 27 is given to show you the result of having the range values set more closely to the data points. In particular, the yMin value for Figure 27 was set to 0. Notice how the menu lines cover the bottom of the graph.

PRECALCULUS: College Algebra and Trigonometry
© 2000 Dennis Bila, James Egan, Roger Palay