Steps to a Linear Regression on the TI-83

Note that the TI-83 and the TI-83 plus have slightly different keys. This page uses the keys associated with the TI-83. The differences are that the TI-83 key is replaced by the TI-83 Plus key, and the TI-83 key is replaced by the TI-83 Plus key.

This page is not a complete introduction to finding linear regressions on the TI-83. Rather, this is a quick tour of the processes needed to generate the graphs that are in the text at the start of Chapter 2, Section 3. Additional material related to regression in general can be found on the Linear Regression page. Additional work on doing regression on the TI-83 can be found on the Linear Regression on the TI-83 page.

In the text we are given the following table

x (miles)	3	5	9	11	12	15	20	25
y (time)	6	9	13	16	16	21	28	31

and we are asked if the data is related. Then the text gives a plot of the data points and eventually draws the line of best fit for those data points. On this page we will develop those same plots with the same points and the same line.

Figure 1	We start off in Figure 1 by entering our two sets of values. We need to store these values in lists. The TI-83 has a number of built-in lists, called L1 through L6. We will store the first set of values in a list called L1 and the second in L2. The result is shown in Figure 1.
Figure 2	We will do a little preparation work before we process and display the data from our two lists. In particular, we would like to be able to plot the values in the list. We will need to set the "WINDOW" values in the graphing calculator to handle the values in our lists. In Figure 2 we open the WINDOW menu by pressing the key. Figure 2 displays the current limits to the WINDOW values. These are the values that were last used on this particular calculator. If we look back at our two lists, we see that none of the points will be shown on a screen with the current setting. Therefore, we will want to change those settings.
Figure 3	Changing the Xmin to ^–5, the Xmax to 40, and the Xscl to 5 will handle the MILES list, and having Ymin set to ^–4, Ymax set to 40, and Yscl set to 4 will handle the TIME list values.
Figure 4	In Figure 4 we have used the key to get out of the WINDOW menu and start the STAT menu.
Figure 5	Our interest here is in doing a calculation. Therefore, we use the key to move to the CALC menu, as is shown in Figure 5. We can see the LinReg(ax+b) option, number 4, in the menu list. We can select that option by pressing the key.
Figure 6	Our action has caused the command LinReg(ax+b) to be pasted onto the screen. However, the command that we want to form is LinReg(ax+b) L1, L2
Figure 7	In Figure 7 we complete the command by pressing . Then we press to execute the command.
Figure 8	Figure 8 gives the output from the LinReg command. This is nice output, but it is not the same as the results generated by a TI-86 for the image in the text book. There the result appears as There are a number of important differences here. First, the parameters "a" and "b" have reversed meanings on the two calculators. On the TI-86 "a" is used as the intercept value, and "b" is used as the slope. In the TI-83, using the LinReg(ax+b) command, the "a" is used for the slope and the "b" is used as the intercept value. Second, the TI-86 has a few extra digits of accuracy. And, third, the TI-86 output has a few more lines, of output, one giving the "correlation coefficient" and the other giving the number of items in each original list.
Figure 9	The TI-83 used to produce the output above was operating in the default mode. In that mode the diagnostic setting is turned "off". There is no penalty for turning that setting "on". To do that we open the CATALOG by pressing . Figure 9 shows the start of the CATLOG listing of commands.
Figure 10	We can jump down the CATLOG listing of coomads, to the D's, by pressing the key. Figure 10 reflects such a change.
Figure 11	Once we are in the "D's", we will use the key to move the highlight to the desired command, DiagnosticOn, shown in Figure 11.
Figure 12	Pressing selects that command and places it onto the screen, Then we press to actually perform the command. The TI-83 responds with "Done".
Figure 13	We can use the key sequence enough times to recall the LinReg(ax+b) command, or we could construct it again. Either approach can be used to produce Figure 13. We press the key to perform that command and produce Figure 14.
Figure 14	Comparing the output in Figure 14 with the output given in the book, namely, we can see that the correlation coefficient given in the book is produced on the output of Figure 14 as the "r=" value. IF we square that value then we do get the "r²=" value. The TI-83 does not produce the "n=" value as a result of the LinReg command. The TI-83 has slightly less precision than does the TI-86, but the answer is quite accurate enough. And, although we used the LinReg(ax+b) command, the TI-83 also has, later in the same menu, the LinReg(a+bx) command:
Figure 15	Thus far we have produced the numbers for the regression equation, but we have not produced the plot of the data points and we have not drawn the reqgression equation. In Figure 15 we press to open the STAT PLOT menu. The screen shows that all 3 plots are turned off. We want to use Plot1 to graph the data points. Therefore, we will press to select that Plot and to open the screen shown in Figure 16.
Figure 16	Here the blinking cursor is covering the "On" value, and we note that the "Off" value is the currently selected setting. We can change the setting to "On" by pressing the key. This will change the display to that shown in Figure 17.
Figure 17	The plot has been turned "On". Furthermore, all of the other settings happen to be just what we want. The plot will be a "scatter" plott with X values taken from L1 and Y values taken from L2, and the points will be marked on the graph by small squares. We can leave Figure 18 and produce the plot by pressing the key. The result is shown in Figure 18.
Figure 18	Figure 18 contains the scatter plot of our data points. The image is similar to the image given in the text. The differences are due to the fact that the image here was produced on a TI-83 while the image in the text was produced on a TI-86.
Figure 19	Now, to add the regression equation to the plot we need only define it as a function. We press to open the "Y=" screen, shown in Figure 19, and we continue by entering the values for the regression equation. Those are exactly the values produced in Figure 14.
Figure 20	Once the regression equation has been defined, we can press to plot the points and draw the defined equation. The result is shown in Figure 20.
Figure 21	Figure 21 has been included here as a small demonstration of the power of the TABLE feature of the TI-83. To generate Figure 21 it was necessary to press . The result is the table shown in the Figure, a table that gives values for X and corresponding, calculated values for Y based on the regression equation that we entered as "Y1=".