The following are looking at Calculator usage, not the mathematics. Therefore there will be no explanation of the mathematics, just finding stuff on the calculator. This is all done on a TI-83 Plus Silver Edition but the same screens should be seen (without a couple minor exceptions that won't affect what we're doing) on the TI-82, TI-83, and TI-83 Plus.

Data Into A List
Press <STAT>		Choose Edit
Enter the data into L1 or L1 and L2 depending on the kind of problem. Enter a number and press <▼> or <ENTER>		Use <►> in order to enter data in another list using the same method as we did for L1.
Clearing Data From A List
Press <STAT>		Choose Edit
Use the arrow keys to put the cursor on the name of L2		On the key pad, press <CLEAR> and then <▼>
Drawing A Scatter Plot
Put the data into two lists. Usually you want to use L1 and L2 but that is not required		Press <2nd> and <STAT PLOT> (above the <y=> key
Choose a plot to define. I'll choose Plot 1		Put the cursor on "On" and press <ENTER>
For all that we'll do, we want "Type" to be the one highlighted		Be sure "Xlist" and "Ylist" have the lists in which you put the data
"Mark" shows which symbol will be used to show points. The square is best.		Press <WINDOW>
Change Xmin so it is a little lower than the smallest x value in your data. Change Xmax so it is a little higher than the largest x value in your data. Change Ymin so it is a little lower than the smallest y value in your data. Change Ymax so it is a little higher than the largest y value in your data.
For most of what we'll do, Xscl and Yscl will be ignored. They can be changed, however, so the tick marks representing units on the x and y axes will be something other than 1. For example, if the difference between Xmin and Xmax is 100, you might want to put Xscl to be 5. Generally, having Xscl as about (Xmax-Xmin)/20 is good. The same works for Yscl.
Press <GRAPH>

Linear Regression
As above, put data in lists. When possible you should use L1 and L2 since those are the defaults for the regression commands. I'll do this example using L1 and L2 and the next using L3 and L4.
Here is the data.		Here is the scatter plot. (I changed the window)
To do the linear regression, press <STAT>		Choose "CALC"
Choose "LinReg(ax+b). Our data is in L1 and L2 so we enter those separated by a comma. We want the equation for the line put in y1 so put another comma.		Press <VARS>
Choose "Y-VARS"		Choose "Function"
Choose Y1		Press <ENTER>
Thus, the linear regression line is y = -1.8x + 63.33333333333. If you have a TI-83 and do not see r and r^2, press <2nd><CATALOG> (that's above the <0> key). Scroll down until you find "DiagnosticOn" and choose it. Then it <ENTER> and repeat the linear regression.
Press Y= to see the function inserted in y1		Now press <GRAPH>
Exponential Regression
As above, put data in lists. I'll do this example using L3 and L4.
Here is the data.		Change the window to fit the data
Redefine Plot1 to use L3 for Xlist and L4 for Ylist		Here is the scatter plot. (I changed the window)
To do the exponential regression, press <STAT>		Choose "CALC"
Scroll down		Choose "ExpReg"
Before pressing <ENTER>, add L3, L4 and another comma		Press <VARS>
Choose "Y-VARS"		Choose "Function"
Choose Y1		Press <ENTER>
Thus, the exponential regression equation is y = 6.73872325*1.218777843^x		Look at Y1 to see that the function is there
Now press <GRAPH>