x | 5 | 8 | 9 | 11 | 15 |
---|---|---|---|---|---|
y | 11 | 18 | 18 | 20 | 28 |
![]() | 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 ![]() ![]() |
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If the screen is not blank, press the ![]() 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. |
![]() | 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. | ||||||||||||
![]() | 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
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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 | ||||||||||||
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There are two methods to removing the lines from the screen.
The first is to just press the ![]() | ||||||||||||
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Figure 4 shows the effect of pressing the ![]() ![]() ![]() ![]() | ||||||||||||
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Now that we have the cursor on the second equation, we implement the alternative method by
pressing the ![]() | ||||||||||||
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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 ![]() | ||||||||||||
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Now we have a blank graph with appropriate axes. Press the ![]()
| ||||||||||||
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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 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||||||||||||
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Then, to finish the process, press
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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
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||||||||||||
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Let us take a look at out points. We press the ![]() | ||||||||||||
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In order to be sure that the calculator is set to display or plot our points.
press ![]() ![]() ![]() | ||||||||||||
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It is hard to show the blinking light in Figure 12, but it is on the On
option. Use the ![]() | ||||||||||||
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We are ready to see the plot of the points. To do this
press the ![]() | ||||||||||||
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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. | ||||||||||||
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To open the Figure 15 screen, press the ![]() | ||||||||||||
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Press ![]() ![]() | ||||||||||||
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The TI-83 merely pastes the selected command from Figure 16 onto the main screen. To
perform that command, press the ![]() | ||||||||||||
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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 ![]() | ||||||||||||
![]() |
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 | ||||||||||||
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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 ![]() | ||||||||||||
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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. | ||||||||||||
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Press ![]() | ||||||||||||
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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,
![]() ![]() | ||||||||||||
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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 ![]() | ||||||||||||
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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 | ||||||||||||
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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 .
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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 ![]() |
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Now that we are closer to our goal,
repeat pressing the ![]() |
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Press ![]() |
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The command has been pasted onto the main screen. Press ![]() |
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The caculator responses with DONE. |
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We now return to the STAT window by pressing the ![]() ![]() ![]() ![]() |
![]() |
Press ![]() |
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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 | 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 |
x | 5 | 8 | 9 | 11 | 15 |
---|---|---|---|---|---|
y | 11 | 10 | 18 | 20 | 28 |
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Press ![]() ![]() |
![]() |
The calculator displays the lists that are defined. Use the ![]() ![]() |
![]() |
Press
![]() ![]() |
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Now press ![]() |
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The list has been changed and all of the correct values are here. |
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Pressing
![]() |
![]() |
Press the ![]() |
![]() |
Press ![]() |
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New results appear on the screen represented in Figure 41. Note that all of the values have changed. |
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We might think that we can look at the new regression line, so we press ![]() |
![]() |
Returning to the Y= screen via the
![]() |
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Instead we will move the highlight down to the Y3= line. |
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Then use the ![]() |
![]() |
Use the cursor right key to highlight the EQ sub-menu. |
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Press the
![]() |
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Now press ![]() |
©Roger M. Palay
Saline, MI 48176
August, 2010