Example 1.  Fit the curve    to the data points  .  

Solution 1.

Enter the point into a two dimensional array xys which stores points in the xy-plane.  

Look at the transpose of this "list of lists."

The two portions of this data structure are separated by  breaking off the first and second parts of the "list of lists"    and  .  

We want to use the same abscissas, and take the logarithm of the ordinates.  Notice that Mathematica uses  Log[x]  for the natural logarithm  ln(x)  this is because Mathematica has programmed the notation used in "Complex Variables" i.e. the terminology  Log[x]  is used in advanced mathematics and works both with real and complex numbers.
Caution.  None of the abscissas should be 0 because Log[0] is not defined, and all the abscissas "should" be positive, unless you are willing to "cope" with computations that might involve complex numbers.

Now "glue together" the transformed parts to form the pairs    and store them in the two dimensional array XYs which stores points in the XY-plane.  

Now use the Mathematica procedure  Fit  to get the least squares line in the XY-plane.  

Now plot the "least squares line"    in the XY-plane.

To get back to the xy-plane we could copy the coefficients from  g  or we could go looking inside Mathematica to see where they are kept.  
The data structure of  g  looks like:

So the coefficients  A  is located at and  B  is located at .  

Now we are in business, we use    and    to get the coefficients of    back in the original  xy-plane.

Now graph the function    in the xy-plane.

(c) John H. Mathews 2004