I agree that Nature should have peer-reviewed this Corrigendum given all the controversy and Mann’s defensiveness. And they should have published MM’s comment in some form. But MM still had a big effect and should not get discouraged. And they did the right thing by going to another peer-reviewed journal (GRL).

]]>Allow me to explain somewhat. Most of statistics does **linear** regression (the workhorse is OLS – Ordinary Linear Regression). Some tricks can be done to ensure that this regression is correct even for non-linear functional forms. For example, taking logs of the data is one such trick Y=XY can be transformed into the linear regression log(Y)=log(X)+log(Y) (you can have exponents on the X and Y but I didn’t want to unnecessarily complicate this example).

Another trick/assumption is that you can linearise any non-linear function by taking a first order Taylor expansion. The point with this is that the approximation is ‘locally’ correct. However, depending on how important the other terms in the Taylor expansion are ‘local’ may be a very small area. Thus, in the present context, the question is whether the true temperature/proxy function is near enough to linear over the relevant range. Relevant is a rather vague term but at one level if you are talking about observations within the bounds of the data set then you are on safer ground than if you are extrapolating to values outside the bounds of your data set.

Hope this helps in some small way…

]]>Now I know that non-linear data points can be plotted on a chart to reveal a linear line if the number of such points is sufficiently small, and that adding more data points makes the line disappear revealing the true non-linear nature of the data. My question is: is there anything in the nature of statistics whereby a nonlinear system has a linear explanation and still be valid/

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