Today we examined what to do if you want to use linear regression, but the error in the data points isn't uniform. In the first example given here we look at the case where we actually know the error in the individual data points. In the second example given here we look at the more common case where the linearization transformation causes a distortion in the error in the data points, requiring the unequal weighting of linear regression to get the right answer. In the final example given here we look at the error you make if the fundamental assumption of linear regression - that you've got the correct physics incorporated into your model - isn't quite right. In all cases you need to plot (and study) your residuals!