Example 2.  Find the other "Least Squares Lines"    for the data points
.  
Use the subroutine Regression to find the line.
2 (a).  Use the computer to find the least squares lines  .   
2 (b).  Is it the same as the line we found in Example 1 ?   Why?

Solution 2.

First, enter the data points.

Reverse the order of the coordinates of the points from    to  .

Use Mathematica to find the "Least Squares Line"  .  

Plot the "Least Squares Line"    using the  ParametricPlot  procedure.

Compare the two "Least Squares Lines"  .  

Are the two lines the same ? Solve the second formula for x in terms of y.

The two formulas are not the same.

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

Which can be compared with example 1.

Which "least squares fit" do you think is best ?

Question.  Are we comparing the "same thing" or is it apple's verses oranges?

(c) John H. Mathews 2004