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-85. 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 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. If there are graph lines on the screen we will want to remove them. Removing such graphs will be demonstrated below, around Figure 4b. We would like to check on the range of values, so we select the RANGE 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.
Figure 4b
Get out of the RANGE display by using . This will take you back to a blank screen, as in Figure 2. If the screen is blank, as was Figure 2, then you may want to skip ahead to Figure 5.

Figure 4b demonstrates a graph that has the appropriate range, but also has some left over lines on it. We will want to remove those lines since they will interfere with our work here.

Figure 4c
Our first step in the process of removing the left over lines is press the key to select "y(x)=" from the menu. This will bring up a screen similar to the one shown in Figure 4c. On your screen you may have one or more equations. Figure 4c shows two. We can eliminate the first equation by pressing the key.
Figure 4d
Figure 4d shows the effect of pressing the key. Having cleared the first equation, we can use the down arrow key to move to the next equation if there is one. If there are no more equations, then we are done and we can close this screen and then move directly to Figure 5. We can close this window by using the key.
Figure 4e
Now that we have the cursor on the second equation, we repeat the process by pressing the key to eliminate that equation.
Figure 4f
Once all of the equations have been removed, we can use the key to leave this window.
Figure 5
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 85 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-85 has already moved into alphabetic mode as signaled by the change in the cursor.
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-85 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-85 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 14
We want to do some calculations in the statistical area. We use to select CALC from the menu. This will open a new menu and it will display two prompts at the top of the screen. The new menu gives the names of LISTs that have been defined on the calculator. This menu will change over time as new LISTs are created or old ones are deleted.
The TI-85 wants to do statistical calculations using a list for the x values and one for the y values. The screen that is presented in Figure 14 is telling us that the default is set to use the predefined list called xStat for the list of x values, and the predefined list called yStat for the y values. However, we put our lists into L5 and L6. We need to tell the calculator to use those lists instead of the default.
Figure 15
The following steps assume that L5 is menu item 3 and L6 is menu item 4. That may not be the case on your calculator. You may even need to use the MORE key to locate L5 and L6 in the menu. Press to select L5 from the menu to replace xStat for the xlist Name. The display should be similar to Figure 15.
Figure 16
Press and the cursor will move to the second line. Press L6 from the menu to replace yStat for the ylist Name. Press to accept these changes.
Figure 17
The TI-85 reponds with the screen in Figure 17. The x values will be taken from L5, and the y values will come from L6. Furthermore, the menu has changed to show the various statistical commands that we can give.
Figure 18
Since we want to do a linear regression, press to select LINR from the lower menu. The TI-85 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
In this form "b" is the "slope" of the line and "a" is the y-coodinate 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 18 (repeated)
 Figure 18 identifies that there are 5 pairs of data points (N=5), and that the regression equation is
y = 3.5217 + 1.6123 x
with values rounded to 4 decimal places. The corr=.984667514236 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.
Figure 19
 Figure 18 shows an upper and a lower menu. To move ahead, we want to select the "DRAW" option from the upper menu. We can do this directly by pressing the keys. This will leave the menus as shown in Figure 19.

We are interested in first seeing the actual points of the xy-data chart, and of our two lists. We do this in Figure 19 by pressing the key to select the "SCAT" menu option (to show a "scatter" graph of the data pairs).

Note that Figure 19 shows the calculator display after selecting the SCAT option. Each pair of data points is represented by one point on the screen. The goal of the linear regression is to produce a line that "best fits" this data. The line that we found was given by

y = 3.5217 + 1.6123 x
and now we would like to see that line.
Figure 20
To draw the regression line, press to select the DRREG menu option. The regression line will appear, as seen in Figure 20. Now you can see the advantage of setting up the RANGE of 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 28, which corresponds to Figure 20, but with yMin set at 0.
Figure 20
Although Figure 19 shows the equation, it does not show the data points. By using the SCAT command from the lower menu we can have the graph display those points. Press to select SCAT. Figure 20 shows the result. Although it is hard to see the points, they are there. Furthermore, because the line is such a good "fit", the points are right next to the line.
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 get out of this and look at some of the values that the TI-85 computes as part of the LINR function. Press to move to close one menu and have the display be as in Figure 21.
Figure 22
What we want to do is to return to the STAT menu, now that some standard variables have been created. On the TI-85 we will close down the current menu and then re-initialize the STAT menu. Thus, press to arrive at Figure 22. Note that you may well have some residual text in the screen above the menu. Our only goal is to get the new menu to display.
Figure 23
In the new menu of Figure 22, the last item is VARS. We press to select VARS. This opens a new menu, as shown at the bottom of Figure 23. The variables that we want to see are not in this part of the new menu. Therefore, press to move to Figure 24.
Figure 24
We want to see the sum of the x2. Therefore, press to select that item from the menu.
Figure 25
The calculator responds by displaying the symbol for the sum of the x-squared values as in Figure 25. This symbol is really the name of a variable held by the calculator. If we now press .
Figure 26
The calculator responds by displaying the value of the variable on the next line. In this case the sum of the x-squared values is 516. We can inspect other special variables in the same way.
Figure 27
We move from Figure 26 to Figure 27 by pressing and . From this we can see the value of the sum of the y-square values, which is not used in the formula, and the sum of the x values, which is.

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 28
Figure 28 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 28 was set to 0. Notice how the menu lines cover the bottom of the graph.

©Roger M. Palay
Saline, MI 48176
February, 1998