I. Menu Keys  Keys that offer choices
D. STAT
2. CALC
This menu has 13 different options. Many of these are used in statistical applications, but the regression menu selections can be very useful in algebra, trigonometry, and calculus. Several of these are the selections that will be covered on this page. Since all are essentially done in the same manner, once you have done two or three of them, the others should not present a problem.
Regression uses formulas to take data and find a curve of best fit. The curve may be a line, a power function, an exponential function, a logarithmic function, or a trigonometric function. These techniques can be quite tedious to do by hand, but the TI83 and the TI84 have several of them built in.
To find a function that best fits a given set of data points, the points must be entered in two lists. You must create the lists and then access the menu item. However, before you begin to work these examples, you must turn the diagnostics. To do this, press and then 0. This will access the CATALOG menu. Scroll down to DiagnosticOn and press ENTER and then press ENTER again.
4:LinReg(ax+b) (linear regression) uses the leastsquares formula to find an equation in the form y=ax+b that best fits a given set of data points.
Example: Create the lists L1=3,4,5,6,7,8,9 (which will represent the xvalues) and L2=4,6,7,10,12,14,16 (which will represent the yvalues). Use these points to find the line of best fit.
Before you find the line of best fit it is useful to be able to see the points plotted in what is called a scatter plot. The TI83 will plot these points. Make sure that there are no functions in the list.
Create L1 and L2.


Access the STAT PLOT
window by entering . 

Press ENTER and turn Plot1
on.
Note XList is L1 and YList is L2. 

Set a WINDOW to fit the data.


Press GRAPH you will
see the points are plotted. 

Go to STAT CALC 4.


Press ENTER and
you will see this screen. 

Now press ENTER again
to get the equation of the line. The value of r is the correlation coefficient. The closer r is to 1 the more reliable the model is. 

Go to
and clear Y1. 

Press ENTER and the
model is placed into Y1. 

Press GRAPH.

Example: Create the following lists and then use the QuadReg (quadratic regression) function to find a model equation. Follow the same steps as in the example above.
L1: 30, 35, 40, 40, 45, 50, 55, 60, 65, 65, 70
L2: 18, 20, 23, 25, 25, 28, 30, 29, 26, 25, 25
Create L1 and L2.


Set a WINDOW.


Graph the data points.


Use the QuadReg option.


Find the regression model
by pressing ENTER twice. 

Put the model into Y1
as done in the above example. 

Graph the function
and data points. 