The Linear, Polynomial, Exponential, Logarithmic, and Power curve fits in KaleidaGraph are calculated using the Least Squared Error method. Least Squares computes a set of coefficients to the specified function, that minimize the square of the difference between the original data and the predicting function. In other words, it minimizes the square of the error between the original data and the values predicted by the equation.
On a log-log or semi-log plot, a Linear curve fit may not appear as a straight line. This is because the divisions along a log scale are not equally spaced. However, it is possible to get the appearance of a straight line using one of the following curve fits:
On a log-log plot (both axes are logarithmic), use a Power curve fit.
On a semi-log plot with a linear Y axis (X axis is log), use a Logarithmic curve fit.
On a semi-log plot with a linear X axis (Y axis is log), use an Exponential curve fit.
When you apply a Power curve fit, the equation is first converted into a Linear equation (log y = log a + b * log x). This Linear fit is applied to the data. After the fit, the intercept is converted back (10^a) for display in the Power equation.
The correlation coefficient for the Power fit shows the correlation between the Power curve fit and the original data. Some other programs show the correlation between the Linear curve fit and the log of the data. That is why when you apply a linear fit to the logged data in KG, you get the same R value as some other programs report for their Power fits.
During the calculation of the Power curve fit, the error is minimized on a log scale, not a linear scale.