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Bivariate statistics using TI-84

Bivariate statistics means statistics with two variables. Your TI-84 calculator can do the complete statistical analysis if you follow the simple steps described bellow.

1. Create two lists containing the data

Open the statistical lists:

STAT
 ► EDIT
   ► Edit...

Enter your data in lists L1 and L2 (e.g., you can enter weights in L1 and heights in L2).

Additional advice:

If the lists are not empty maybe you'll want to clear these two lists before entering new values. You can do it using:

STAT
 ► EDIT
   ► ClrList
When ClrList command appears on the screen, add the name of the list to clear: L1 or L2, and then press ENTER.
(Hint: Press 2ND  1  for L1. Press 2ND  2  for L2.)

2. Use the 2-Var Stats

To get the bivariate statistics use:

STAT
 ► CALC
   ► 2-Var Stats
When asked for additional information, enter the list labels:
X list: L1
Y list: L2
FreqList: (Leave it empty if frequencies are not given!)
Calculatepress ENTER in this line!

After pressing the ENTER button your calculator will display the results. Results include a lot of statistical parameters. The most important of them are:

x   = the mean (average) of the variable x
σx = the standard deviation of the variable x
y   = the mean (average= of the variable y
σy = the standard deviation of the variable y

3. Finding the regression line

If you want your statistical analysis to be done correctly your first step is turning on the diagnostic. To do it use the CATALOG button. Find DiagnosticOn and select it.

Then you can find the regression line (line of best fit). Use:

STAT
 ► CALC
   ► LinReg (ax+b)
When asked for additional information, enter the list labels:
X list: L1
Y list: L2
FreqList: (Leave it empty if frequencies are not given!)
StoreRegEQ: You can leave it empty – see bellow (*)
Calculatepress ENTER in this line!

After pressing the ENTER button the calculator will display the results. Results include the parameters a and b which determine the regression line y = ax + b.

Besides, you'll see the correlation coefficient r (called also Pearson product-moment correlation coefficient). If you don't see the value of r you must have forgotten to select DiagnosticOn.

Additional advice:

(*) StoreRegEQ means storing the regression line equation. If you select StoreRegEQ: Y1 then the equation will be stored as function Y1 and you can draw its graph. In order to get symbol Y1 here, press:

VARS
 ► Y-VARS
   ► Function
     ► Y1

After that you can draw the regression line – press GRAPH. However, probably you will not see the graph because it's not on the screen. Adjust the window settings (they must include all the values of your data).

4. Draw the scatter graph

For drawing the scatter graph you'll have to activate the statistical plots:

2ND STAT PLOT
 ► 1:
   ► On
GRAPH

Now the scatter graph should appear on the screen. If you don't see it you must adjust the window settings (press WINDOW and select correct values for Xmin, Xmax, Ymin, Ymax, then press GRAPH again).

If you selected StoreRegEQ: Y1 (see above (*)) you'll see the regression line, too.


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