Example  3.  Often times a  scientist must decide which formula "fits" the data best.
3 (a).  Find both the "exponential fit" and "power fit" for the data points  .  
3 (b).  Discuss how this was accomplished and what transformations were used in the process.
3 (c).  Determine which curve fits the data best.

Solution 3.

3 (a).  Fit the curve    to the data points  .  

Find the logarithm of the ordinates and form list of transformed points.

Compute the coefficients of the linear system and get the coefficients  A  and  B, and compute the coefficients  a and  c  and the exponential fit.

3 (b).  Fit the curve    to the data points  .  

Find the logarithm of both the abscissas and ordinates and form lists of transformed points.

Compute the coefficients of the linear system and get the coefficients  A  and  B, and compute the coefficients  a and  c  and the power fit.

3  (c).  Determine which curve    or    is the better fit to the data points.

First, consider   and the sum of the squares of the residuals  

Second, consider   and the sum of the squares of the residuals  

Since  ,  it appears that the fit    is best.

(c) John H. Mathews 2004