Mode Screen

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 .

Blank Screen

If the screen is not blank, press the key again and it should become blank. 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 WINDOW settings to be sure that those settings are set the way we want them to be set.

Window Screen	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, Figure 1, reflects a change of values that will have X running from -1 to 20, and y going from -10 to 30.
Figure 1	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 because puts the origin, (0,0), onto the graph. The Yscl value was set to 2 so that the "tick" marks on the Y-axis are not on top of one another. We chanck out the sup[posedly empty graph by pressing the key. The result is on the calculator used here is given in Figure 2.
Figure 2	If your screen looks like Figure 7 instead of having extraneous lines on it, as does Figure 2, then feel free to skip to Figure 7. The lines here, on Figure 2, are left over from some earlier work on this calculator. We want to clear off those lines. In order to do that we need to see the equations that generate the lines. To do this we move to the Y= screen by pressing the key.
Figure 3	There are two methods to removing the lines from the screen. The first is to just press the key to erase the line that is highlighted. For Figure 3, the highlighted line is the first line. Pressing that key will produce Figure 4.
Figure 4	Figure 4 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. Here we can demonstrate an alternative method to hiding the graph for this second equation. Note, back in Figure 3 and in Figure 4, that the equal sign is given in reverse shading, i.e., the character has a black background and the equal sign is in white. This indicates, in Figure 3, that the first two equations are "active" while in Figure 4 the only "active" equation is the second one. We can use the key to move the cursor highlight doen to the second equation and then the key to move the cursor over the equal sign. The result should be Figure 5.
Figure 5	Now that we have the cursor on the second equation, we implement the alternative method by pressing the key. When the cursor is over the equal sign, pressing the Enter key will reverse the "active"/"inactive" status of the equation. The result is in Figure 6.
Figure 6	Here we see that the first equation is removed and the second one is in an "inactive" status. We could reactivate this second one if we desired by again changing its status. The old first equation is lost and we would have to re-enter it to get it back on the screen. At this point we press the key to leave this window and see the benefits of our work.
Figure 7	Now we have a blank graph with appropriate axes. Press the key to return to the normal screen. We are ready to enter the data from the table given at the start of this page. Here is that table again: x 5 8 9 11 15 y 11 18 18 20 28
Figure 8	To do this regression we need to enter the data as two lists, the x values go into one list and the y values go into another. A "list" on the TI-83 is a sequence of numbers, separated by commas, and enclosed in curly braces. We use the sequence button to generate the left curly brace. 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 . We close the list with the sequence . Now we want to store the list that we entered. press the key for the "store" character, the right pointing arrow. We will store the list in one of the built-in lists, namely L1. To do this press This produces the screen shown in Figure 8.
Figure 9	Then, to finish the process, press . The result should be the screen to the left, in Figure 9. The TI-83 displays the list again.
Figure 10	Now we need to give enter the y values into a list that we will store in L2. The key sequence to do this is to get the {, and to get the }. Then, , followed by
Figure 10a	Let us take a look at out points. We press the but the result may look like figure 10a. [If it looks like Figure 14 you can skip to that Figure.) The problem with Figure 10a is that we might not have told the TI-83 to turn on the plotting of points stored in the lists L1 and L2. We need to look at the calculator settings for STAT PLOT
Figure 11	In order to be sure that the calculator is set to display or plot our points. press to open the screen in Figure 11. In that screen we see that all three of the plots are OFF. We want to turn on the first one. That is the highlighted option so we press to move to Figure 12.
Figure 12	It is hard to show the blinking light in Figure 12, but it is on the On option. Use the key to select that option. This moves is to Figure 13.
Figure 13	We are ready to see the plot of the points. To do this press the key.
Figure 14	Finally, we see the plot of the points from the problem we were given. We still have to find and eventually graph the linear regression equation.
Figure 15	To open the Figure 15 screen, press the key.
Figure 16	Press to move the highlight to the CALC option. In this screen we want option 4. We could do this simply by pressing the 4 key or by using the down arrow to move the highlight to the 4th option, as shown in Figure 16, and then press the key to move forward.
Figure 17	The TI-83 merely pastes the selected command from Figure 16 onto the main screen. To perform that command, press the .
Figure 18	The LinReg(ax+b) command has the TI-83 do a linear regression on the set of points stored in the L1 and L2 lists. The results are displayed in Figure 18. From that we see that the regression equation is y = 1.612318841*x+3.52173913 The next step is to see the graph of this equation. If we press the key, we get the graph in Figure 18a.
Figure 18a	This is not what we want. There should be a line, the graph of the regression equation, here. The problem is that although the TI-83 calculated the regression equation, it did not put that equation into the Y= screen. To see that screen press the key to move to Figure 19.
Figure 19	Figure 19 shows the Y= screen. We need to place the regression equation here. We could just type in the equation, but that is asking for a lot of key-strokes. Beside the inconvenience, we would have to have written down the equation since we can no longer see it on the calculator screen. The TI-83 provides an alternative to typing the equation. We press the key to get Figure 20.
Figure 20	Figure 20 provides a selection of variables. We want the Statistics sub-menu, option 5. We could press the 5 key to do this or we could use the down arrow to move the highlight to option 5, This is the approach shown here to move to Figure 21.
Figure 21	Press to select the move to the Statistics sub-menu.
Figure 22	Here we have many options, but the one we want is not on this screen. Instead, we will need to press the right arrow twice, , to highlight the EQ selection. This will move us to Figure 23.
Figure 23	Fortunately, the thing we want is the first item, RegEQ. We could select it by pressing the 1 key or, since it is currently highlighted, press the key.
Figure 24	The result of our Figure 23 action is that the calculator has pasted the entire regression equation into our Y= screen. We are ready to look at the graph. Press to see the graph.
Figure 24a	Finally we have a graph of the plot of points and of the regression equation.

Of course, the next problem is to find the correlation coefficient for this regression. The good news is that the TI-83 would have been happy to find this if we had set it up properly. We need to turn on the Diagnostics. To do this the TI-83 has a special command. To find that command we need to look in the CAATALOG which we do by pressing .

Figure 25	Figure 25 shows the start of the CATALOG. We are looking for the DiagnosticOn command. We could use the cursor key to move down through the list of commands, but a small shortcut is to press the key to skip to the D's in the list. [We choose the x-1 key because it is assigned to the alphabetic letter D.]
Figure 26	Now that we are closer to our goal, repeat pressing the key to move the highlight down to the DiagnosticOn command, as shown in Figure 27.
Figure 27	Press to select the DiagnosticOn option.
Figure 28	The command has been pasted onto the main screen. Press to execute the command.
Figure 29	The caculator responses with DONE.
Figure 30	We now return to the STAT window by pressing the key. We move to highlight the CALC sub-menu by pressing the key. We highlight the fourth option by moving the cursor down using the key. Then we press the key to paste the command onto the main screen, as in Figure 31.
Figure 31	Press key to execute the command.
Figure 32	Figure 32 gives the same regression equation, but it also givess the value of the correlation coefficient, r, along with the value of r2.

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	5	8	9	11	15
y	11	10	18	20	28

Figure 33	Press to get to the STAT window and then, since the first option, Edit is highlighted, press to get to FIgure 34.
Figure 34	The calculator displays the lists that are defined. Use the key to move to the second list and then to highlight the incorrect value, 18.
Figure 35	Press to enter the correct value for this item. This will be displayed at the bottom of the screen, as it appears in Figure 36.
Figure 36	Now press to accept that new value.
Figure 37	The list has been changed and all of the correct values are here.
Figure 38	Pressing redisplays the data. We can see that the second data point has moved. However, the regression line has not changed. This is because we have not redone the calculation of the regression line based on the new data.
Figure 39	Press the key and the calculator pastes the command onto the main screen. We can see this in Figure 39, along with the results from our previous run of the command.
Figure 40	Press to run the command.
Figure 41	New results appear on the screen represented in Figure 41. Note that all of the values have changed.
Figure 42	We might think that we can look at the new regression line, so we press only to see that the graph has not changed.
Figure 43	Returning to the Y= screen via the key we see that the old equation is still there. We could replace it or make it inactive, but for our purposes we will just let it stay there.
Figure 44	Instead we will move the highlight down to the Y3= line.
Figure 45	Then use the key to open the window shown in Figure 45. Then use the cursor down charactrer to move the highlight to item 5, Statistics.
Figure 46	Use the cursor right key to highlight the EQ sub-menu.
Figure 47	Press the key to paste the equation into the Y3= field.
Figure 48	Now press to display the graph, where we see both the new regression line and the old one, and the new points.

©Roger M. Palay
Saline, MI 48176
August, 2010