STATISTICS
for the TI 82/83

Frequency
Histogram
Mean
Deviation
Z-Scores
Correlation
Regression
Credits
Statistics for the TI 82/83

Linear Regression

When two sets of numbers are plotted in a graph, and we feel that the points are close to being on a straight line, it is tempting to draw a straight line and say that the line describes the relationship. The question is, which line is the best one? Which straight line represents the points best? How can we find a straight line such that the difference between the line and the points is small?

If the correlation is +1 or -1, there is no problem. Then, the points really are on a straight line, and we simply draw that line. When the relationship is not perfect, and very few relationships in the real world are, the correlation is not +1 or -1, the points do not form a perfect straight line. Then, we have to decide where to draw the line.

Here, the calculator comes to our rescue. If we give the calculator the two sets of numbers, it will figure out which is the best straight line, and give us an equation that we can use to draw it. It also gives us the correlation. 

Take a look at the numbers in the table. Nine students wrote papers on the use of computers in today's homes. Two teachers graded each paper on a scale 0 to 40. The grades Mr. Watson gave are in the first column, and the grades Ms. Thurman gave are in the second column. We will call Mr. Watson's grades x, and Ms. Thurman's grades y.

Student's name Mr. Watson (x) Ms. Thurman (y)
Oscar
 37
28
Fred
 28
27
Sandy
 26
38
Jennifer
 25
29
Paul
 22
12
Norm
 17
26
Okee-Le
 15
21
Abdul
 11
24
Enrique
 9
17

Create a graph to check if there is any relationship between the grades given by the two teachers. Let the x-axis represent Mr. Watson's grading scale, and the y-axis represent Ms. Thurman's grading scale. You can use pencil and paper or your calculator.  The coordinates of the points are (37,28) , (28,27) , (26,38) , (25,29) , (22,12) , (17,26) , (15,21) , (11,24) and (9,17). Are the points close to being on a straight line?

Now, let's use the calculator to find the line that best fits the points you plotted on your graph.

Press the STAT key.  Then you get the familiar screen shown to the right.

Select ClrList by pressing 4 and press L3 followed by ENTER. Then press the STAT key again, select ClrList and press L4 followed by ENTER. This creates space for you to enter the data.
Press the STAT key and select EDIT. Now, you can enter the numbers from the table above into the calculator. Use L3 for Mr. Watson's grades and L4 for Ms. Thurman's grades.  If you are not sure how you enter the data into the calculator, you may want to review. 

When all the numbers have been entered, press the STAT key, and select CALC by pressing the right arrow key.  Choose LinReg (ax+b) by pressing 5.  Now the calculator wants to know which two lists it should use int the regression.  Press L3,L4 and then press ENTER. 

Now, the calculator gives you the equation of the line that best fits your points. The equation is on the familiar form y=ax+b and you can see that the numbers a and be are given. Which features of the line do a and b represent? 


Below the a and b you will see r=.4776. That is the correlation between the two sets of grades. As we said earlier, the correlation comes free with the regression!

Now, use the equation to draw the line in the same graph that you plotted the points on. Do you agree with the calculator that this is the line that best fits the points?

If you want the calculator to draw the line you press the Y=key. Then you get the screen shown on the right.

Press the VARS key. Then select statistics by pressing 5. 

Use the right arrow key to highlight EQ.  Select RegEQ by pressing 7.

Before you ask the calulator to plot the graph, you must select appropriate settings for the window.  Press the WINDOW key and choose the settings you think will fit your line.  If you use these settings you will be able to see the line.

    Xmin=-10
    Xmax=10
    Xscl=.01
    Ymin=-10
    Ymax=20
    Yscl=1

When the window settings are correct you can press the GRAPH key to let the calculator plot the graph. If you get an ERR:STAT message you need to make sure that the STAT PLOTS are OFF.


Finding a graph to represent points, like you did, is called regression. This type is called linear, because we are looking for a line that fits the points. In some cases, other curves would fit better than a line. We could, for example, do a quadratic regression if the points seem to lie on a parabola. Then the equation would be on the form y=ax2+bx+c. Can you think of two sets of numbers where a quadratic regression would be more appropriate than a linear regression?

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Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.

Last updated on 1/30/1999
Comments: egalindo@indiana.edu
http://www.indiana.edu/~atmat/units/statistics/stat_act7.htm