Jackknife resampling to estimate errors in fitted parameters
Jackknife resampling is a method to estimate the errors of parameters fitted with the FitLine(), FitPoly(), FitExp()... etc commands. In the SciPy module in Python you can calculate the covariance matrix and the standard errors of the parameters are then the square roots of the diagonal elements. However, since GeoGebra does not calculate the covariance matrix, we have to resort to other means. In Jackknife resampling we remove one data point at a time, refitting our function each time. Eg. Assume we have 8 datapoints and we want to measure the slope of a fitted line. Removing one point at a time and refitting the line to the 7 remaining points, we end up with 8 different fitted lines, one for each point we removed. So we also have 8 different values for the slope. We can now calculate the standard deviation of these 8 values. The standard error in this method is the standard deviation multiplied by the square root of the number of data points, here 8. From the standard error, we can find the 95 % confidence intervals in the usual way, see the powerpoint for formulas.