known_ys: known y-values
known_xs: known x-values
LOGFIT function applies the “least squares” method to fit the logarithmic equation y = a + b * ln(sign * (x - c)) , sign = +1 or -1 to your data. The graph of the equation is a logarithmic curve moved horizontally by c and possibly mirrored across the y-axis (if sign = -1).
LOGFIT returns an array having five columns and one row. `Sign' is given in the first column, `a', `b', and `c' are given in columns 2 to 4. Column 5 holds the sum of squared residuals.
An error is returned when there are less than 3 different x's or y's, or when the shape of the point cloud is too different from a ``logarithmic'' one. You can use the above formula = a + b * ln(sign * (x - c)) or rearrange it to = (exp((y - a) / b)) / sign + c to compute unknown y's or x's, respectively. This is non-linear fitting by trial-and-error. The accuracy of `c' is: width of x-range -> rounded to the next smaller (10^integer), times 0.000001. There might be cases in which the returned fit is not the best possible.