Example 1.  Find the standard "least squares line"    for the data points
.  
Use the subroutine Regression to find the line.  Compare with the line obtained with Mathematica's Fit procedure.

Solution 1.

First, enter the data points.  This can be done as a list of lists or by using the Input menu and the Create Table submenu.

Using the Create Table submenu, we can get the following display to fill in the numbers.

When we fill in the numbers it will look like

After the data has been entered, compute the formulas for the least squares line.

Let's see how the subroutine Regression  works.  The command for determining the abscissas is

The command for determining the ordinates is

We can add them up by using the selection operation    and the summation found in the "BasisInput Palette" .

If you want to add up their squares then be careful using the power.  Sometimes extra parenthesis helps.

Let's peek at the linear system that was solved.

Of course we want a graph.

The sum of the residual's squared for this example is:

(c) John H. Mathews 2004