Data Analysis:  Regression Formulas

In linear graphing, one skill learned is to find an equation of a line passing through two given point.  There are mathematical techniques which will find the "best" approximation of a graph that passes through a larger set of points.  These techniques are called Regression formulas.  By hand, they are very tedious.  With the calculator, they are a snap.

1. To start the procedure, enter some data into the lists  as is done in the plotting points routine   go to plotting points
   
2. Press the STAT key, then the Right arrow key to see the screen at the right.   The regression formulas begin at option 4, which is a linear equation, and continues with quadratic (5), cubic (6) etc.  Scrolling down reveals more options, most of which will not be used in college algebra.  Select the one you think will give the best approximation, ie, the one that will touch the most points.
   
   
   
   
3. If we choose (5), this screen appears:
4. Enter the x- and y- value list names with a comma between them.  The L1 and L2 lists are the default lists.  If your data is in these two lists, just press ENTER.
             
   
   
   
   
   
   
   
5. The next screen reveals the results of the regression calculation.  The calculated approximation is y = -.75x² +2.05x + 4.25
   And here is the data from which the equation was found:

How good a fit is it?  Could we do better with a different regression formula?

To answer these questions, continue to the next data analysis topic,  graphing regression equations.