Linear Regression on the TI-89

This is an alternative approach to 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.

The Steps to a Linear Regression on the TI-89 page produced a linear regression, a plot of the data points, and a plot of the regression line. It did this without the use of some special features of the TI-89. This page will perform a similar analysis of the same data, but this time we will use the List Editor and other special features of the TI-89.

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. Our task here is to enter the data value, obtain the regression equation, and produce a plot of the data points and the regression equation similar to the plot in the book.

Figure 1 We will start by entering the data into the calculator. To do this we will use the List Editor. We open the List Editor by first pressing the key. This brings up the window shown in Figure 1.
Of the options presented, we are interested in #6, Data/Matrix Editor. We can press the key to select that option and move to Figure 2.

Figure 2 The TI-89 responds by asking if we want to edit the current item, open an existing item, or create a new item. This is a new problem. Therefore, we press to indicate that we want a new item.

Figure 3 To define a new item, the TI-89 needs more information. Figure 3 shows the screen that the calculator uses to obtain that information.
The default is to have the new item be of type Data. This is not what we want. Therefore we press the cursor control key to move to Figure 4.

Figure 4 In Figure 4 we see a new window, one that allows us to choose the type of data that we want. In our case we want a list of values. We press to select the List option.

Figure 5 The calculator returns to the previous screen, having changed Data to List in the Type line. Because we will create the new list in the main folder, we will leave the second line as it is. We use the key to move down to the third line where we need to specify a name for our list. In Figure 5 we have supplied the name miles for the new item. We did that by pressing to shift into a locked alphabetic mode, and then to produce the letters. Finally, we press to accept our name, and then again to indicate that the information on the window is OK.

Figure 6 In Figure 6 we finally see the List Editor. We are ready to start entering the data from our two lists. Note that the calculator is still in alphabetic mode. We will have to press the key to get out of that mode. Then we can start entering the values from the first list.

Figure 7 Figure 7 captures the screen after we have entered the first 3 values from our miles list, and in the middle of the entry of the fourth value, 11, which is in the data and command entry line.

Figure 8 In Figure 8 we have finished entering the eight values for the first list, miles, and we have used the key to move over to the next column, the c2 column, where we have started to enter the corresponding values of the times list. Note that we happen to be entering the values from the end of the list toward the top of the list. Figure 8 illustrates the screen after we have entered two values and as we are about to enter the value into row 6 column 2, namely 21. The calculator has prefilled the as yet unspecified values at the top of the list with the "undef" designation.

Figure 9 As of Figure 9 we have entered all of the values into our two columns. The List Editor makes it easy for us to enter the data, to check the data, and to verify that corresponding values from the two lists are on the same row of data.
At this point we are ready to set up the plot area. To do this we press .

Figure 10 The result is the window shown in Figure 10. Actually, we do not want to be here. Rather thn set up the plot, we want to specify the kind of data analysis that is to be performed. We really want to return to the previous window, shown in Figure 9, and from there select the Calc tab. To do this we press .

Figure 11 Figrue 11 shows the "Calculate" screen. The default "Calculation Type" is TwoVar. We want to alter that selection. Therefore, we press to move to Figure 12.

Figure 12 Now we have some choices for the Calculation Type. In particular, item 5 is the LinReg or Linear Regression option. We select taht option by pressing .

Figure 13 In Figure 13 we can verify that the Calculation Type has been changed to LinReg. In addition, we have specified that the x list is in c1 and the y list is in c2. Those were the column names that we saw back in Figures 6 through 9.

Figure 14 We use the key to move down to the next option, "Store RegEQ to". The default is none. We want to change that setting. Therefore, we press to see the alternate values.

Figure 15 The new window in Figure 15 gives the alternate values for the Store RegEQ to setting. We want to select y1(x). Press to move the highlight down to that item. Then press to select it.

Figure 16 Again, the change is reflected in the Calculate window. We press to Save these values, to close the window, and to perform the computation.

Figure 17 Figure 17 shows the window that pops up to give us the results of the computation. This STAT VARS window is identical to that produced in Figure 13 of the other web page, Steps to a Linear Regression on the TI-89, which used a different approach to doing this same problem.
We can close the STAT VARS window and return to the List Editor by pressing the key.

Figure 17a Leaving Figure 17 would return us to the image captured in Figure 9. Now we do want to set up a plot. Again, we do this by pressing .

Figure 18 We will define Plot1 by pressing .

Figure 19 The window shown in Figure 19 allows us to define Plot 1. The default is a Scatter plot, and that is what we want. We will be happy to use a small Box as a marker of the location of the data points on the plot. We need to specify the x list and the y list. We use the key to move down to those items.

Figure 20 In Figure 20 we have identified the x list as the valuse in column c1, and the y list as the values in column c2. We can press to accept that last input value. and again, but this time to SAVE the settings. This will take us to Figure 21.

Figure 21 Here we can see that the definition of Plot1 has changed to indicate that we want a Scatter plot, using the small Box as a marker, with the x list as c1 and the y list as c2.

Figure 22 We can move to view the plot and the graph of the Regression Equation by pressing .
The result shown in Figure 22 depends upon the calculator WINDOW settings being the standard settings, ^–10 to 10 for both x and y. With those settings we can see the regression equation, but only two of the data points. The third point has an x value of 9 which could be graphed, but the y value is 13 which is off the window.

Figure 23 It is pretty clear that we want to see more of the data points. We can press to open the Zoom window. Then, by using the key, we can move the highlight down to item number 9, ZoomData. We will select that action by pressing the key.

Figure 24 The resulting new graph, shown in Figure 24, has had its WINDOW settings changes to accommodate all of the data points. Unfortunately, that means that the y-axis is no longer visible, and, the x-axis, which seems to be on the image, is not really the x-axis. We can press to open the WINDOW screen, shown in Figure 25.

Figure 25 The values displayed in Figure 25 are those set by the calculator when we used the ZoomData command. We will want to change those values so that they conform to the values used inthe text.

Figure 26 Once the new values are set, we can press to draw a new graph, shown in Figure 27.

Figure 27 Finally, we have a graph similar to the one generated for the text.
The beauty of using the built-in special functions of the TI-89 is that we can change data values and produce new results with relative ease. For example, if we want to change the final data pair from (25,31) to (25,39), we can perform the follwoing steps.

Figure 28 Open the APPS menu via . Select the Data/Matrix Editor, via . Then choose to open the Current item via the key.

Figure 29 In the List Editor, move to row 8 column 2 and change the value there from 31 to 39. Press the to accept that new value.
Then, press to move to the Calc tab.

Figure 30 The calculator presents the Calculate window.

Figure 31 Fill in the Calculate window as before. Press to save the values and open the STAT VARS window.

Figure 32 Read the values from the STAT VARS window. Press to indicate OK. Then press to generate a new plot, shown in Figure 33.

Figure 33 The data points have been plotted again. Because there has been a change in a data point, the regression equation has changed.

Figure 1	We will start by entering the data into the calculator. To do this we will use the List Editor. We open the List Editor by first pressing the key. This brings up the window shown in Figure 1. Of the options presented, we are interested in #6, Data/Matrix Editor. We can press the key to select that option and move to Figure 2.
Figure 2	The TI-89 responds by asking if we want to edit the current item, open an existing item, or create a new item. This is a new problem. Therefore, we press to indicate that we want a new item.
Figure 3	To define a new item, the TI-89 needs more information. Figure 3 shows the screen that the calculator uses to obtain that information. The default is to have the new item be of type Data. This is not what we want. Therefore we press the cursor control key to move to Figure 4.
Figure 4	In Figure 4 we see a new window, one that allows us to choose the type of data that we want. In our case we want a list of values. We press to select the List option.
Figure 5	The calculator returns to the previous screen, having changed Data to List in the Type line. Because we will create the new list in the main folder, we will leave the second line as it is. We use the key to move down to the third line where we need to specify a name for our list. In Figure 5 we have supplied the name miles for the new item. We did that by pressing to shift into a locked alphabetic mode, and then to produce the letters. Finally, we press to accept our name, and then again to indicate that the information on the window is OK.
Figure 6	In Figure 6 we finally see the List Editor. We are ready to start entering the data from our two lists. Note that the calculator is still in alphabetic mode. We will have to press the key to get out of that mode. Then we can start entering the values from the first list.
Figure 7	Figure 7 captures the screen after we have entered the first 3 values from our miles list, and in the middle of the entry of the fourth value, 11, which is in the data and command entry line.
Figure 8	In Figure 8 we have finished entering the eight values for the first list, miles, and we have used the key to move over to the next column, the c2 column, where we have started to enter the corresponding values of the times list. Note that we happen to be entering the values from the end of the list toward the top of the list. Figure 8 illustrates the screen after we have entered two values and as we are about to enter the value into row 6 column 2, namely 21. The calculator has prefilled the as yet unspecified values at the top of the list with the "undef" designation.
Figure 9	As of Figure 9 we have entered all of the values into our two columns. The List Editor makes it easy for us to enter the data, to check the data, and to verify that corresponding values from the two lists are on the same row of data. At this point we are ready to set up the plot area. To do this we press .
Figure 10	The result is the window shown in Figure 10. Actually, we do not want to be here. Rather thn set up the plot, we want to specify the kind of data analysis that is to be performed. We really want to return to the previous window, shown in Figure 9, and from there select the Calc tab. To do this we press .
Figure 11	Figrue 11 shows the "Calculate" screen. The default "Calculation Type" is TwoVar. We want to alter that selection. Therefore, we press to move to Figure 12.
Figure 12	Now we have some choices for the Calculation Type. In particular, item 5 is the LinReg or Linear Regression option. We select taht option by pressing .
Figure 13	In Figure 13 we can verify that the Calculation Type has been changed to LinReg. In addition, we have specified that the x list is in c1 and the y list is in c2. Those were the column names that we saw back in Figures 6 through 9.
Figure 14	We use the key to move down to the next option, "Store RegEQ to". The default is none. We want to change that setting. Therefore, we press to see the alternate values.
Figure 15	The new window in Figure 15 gives the alternate values for the Store RegEQ to setting. We want to select y1(x). Press to move the highlight down to that item. Then press to select it.
Figure 16	Again, the change is reflected in the Calculate window. We press to Save these values, to close the window, and to perform the computation.
Figure 17	Figure 17 shows the window that pops up to give us the results of the computation. This STAT VARS window is identical to that produced in Figure 13 of the other web page, Steps to a Linear Regression on the TI-89, which used a different approach to doing this same problem. We can close the STAT VARS window and return to the List Editor by pressing the key.
Figure 17a	Leaving Figure 17 would return us to the image captured in Figure 9. Now we do want to set up a plot. Again, we do this by pressing .
Figure 18	We will define Plot1 by pressing .
Figure 19	The window shown in Figure 19 allows us to define Plot 1. The default is a Scatter plot, and that is what we want. We will be happy to use a small Box as a marker of the location of the data points on the plot. We need to specify the x list and the y list. We use the key to move down to those items.
Figure 20	In Figure 20 we have identified the x list as the valuse in column c1, and the y list as the values in column c2. We can press to accept that last input value. and again, but this time to SAVE the settings. This will take us to Figure 21.
Figure 21	Here we can see that the definition of Plot1 has changed to indicate that we want a Scatter plot, using the small Box as a marker, with the x list as c1 and the y list as c2.
Figure 22	We can move to view the plot and the graph of the Regression Equation by pressing . The result shown in Figure 22 depends upon the calculator WINDOW settings being the standard settings, ^–10 to 10 for both x and y. With those settings we can see the regression equation, but only two of the data points. The third point has an x value of 9 which could be graphed, but the y value is 13 which is off the window.
Figure 23	It is pretty clear that we want to see more of the data points. We can press to open the Zoom window. Then, by using the key, we can move the highlight down to item number 9, ZoomData. We will select that action by pressing the key.
Figure 24	The resulting new graph, shown in Figure 24, has had its WINDOW settings changes to accommodate all of the data points. Unfortunately, that means that the y-axis is no longer visible, and, the x-axis, which seems to be on the image, is not really the x-axis. We can press to open the WINDOW screen, shown in Figure 25.
Figure 25	The values displayed in Figure 25 are those set by the calculator when we used the ZoomData command. We will want to change those values so that they conform to the values used inthe text.
Figure 26	Once the new values are set, we can press to draw a new graph, shown in Figure 27.
Figure 27	Finally, we have a graph similar to the one generated for the text. The beauty of using the built-in special functions of the TI-89 is that we can change data values and produce new results with relative ease. For example, if we want to change the final data pair from (25,31) to (25,39), we can perform the follwoing steps.
Figure 28	Open the APPS menu via . Select the Data/Matrix Editor, via . Then choose to open the Current item via the key.
Figure 29	In the List Editor, move to row 8 column 2 and change the value there from 31 to 39. Press the to accept that new value. Then, press to move to the Calc tab.
Figure 30	The calculator presents the Calculate window.
Figure 31	Fill in the Calculate window as before. Press to save the values and open the STAT VARS window.
Figure 32	Read the values from the STAT VARS window. Press to indicate OK. Then press to generate a new plot, shown in Figure 33.
Figure 33	The data points have been plotted again. Because there has been a change in a data point, the regression equation has changed.