Remark.  The least squares line is often times called the line of regression.

Mathematica Subroutine (Least Squares Line).

Philosophy.  What comes first the chicken or the egg ?  Which coordinate is more sacred, the abscissas or the ordinates.  We are always free to choose which variable is independent when we graph a line;    or   .  When you realize that two different "least squares lines" can be produced we are amazed.  What should we do ?  Which line should we use ?  You must decide a priori which variable is independent and which is dependent and then proceed. Exercise 3 asked you to think about the mathematics that is involved with this "paradox."

Another "Fit"

Theorem (Power Fit). Given the    data points  ,  the power curve    that fits the points has coefficients a given by:

    .

Remark.  The case m = 1 is a line that passes through the origin.

Mathematica Subroutine (Power Curve).