re 8 that’s interesting result. So, before Mann rescales RPCs they all have larger variance than the target PCs (calibration period). Variance matching makes the variances equal. And as Mann does not reconstruct all PCs, and RPCs are variance-matched to the target PCs, effectively the variance of reconstruction is always less than variance of target temperature. That’s why vS04 thought it is direct regression. And that’s why Mann claims that

The CPS approach thus differs from a multivariate regression approach wherein the reconstruction is guaranteed to have less variance than the target series over the calibration interval.

even though INVR itself actually amplifies.

]]>RE 15: Ok, I think I get it. Thanks

a. Why the PC1 of the instrumental temps? Why not, the value itself?

b. Why looking for a correlation with global vice local temperature? Seems non-physical to me and likely to lead to data mining/overmodeling. If there is a plausible teleconnection, then we should model to the teleconnected variable, no? But just fishing for local measures of a global trend? Seems fishy. Like throwing 20 stats into a bag and picking the one that comes up at 95% confidence level for significance! And at a minimum, hurts the claim that we have built up a global picture from multiple local sources (since they’re not really local if they are globally trained/selected/weighted).

c. What are the units for temp and proxy? Standardized and if so, how? This will influence the slope, no?

d. Question 12-2 remains. Can you explain?

e. I agree that a flat sloped line when replotted as x-y versus y-x is now steep. Why is that interesting? We all know that, no? Is there some further thing with variance or mean or something?

Please excuse my humble questions. I have no mathematical training in stats or linear algebra.

]]>where

]]>y(t) = 1/G x(t) with 1/G larger than 1.

]]>x(t) = G*y(t) with G 1.

]]>A. Are you still in the one dimensional land where Gerd was speaking to me?

B. If you say that x is “proxies”, what does that mean? Number of them in the reconstruction?

C. I can’t follow that post, Jean. ]]>

1. How are both the x and y noisy? If x is years and y is ring width, I would think that y would be noisy, but x not noisy.

2. If both are equally noisy, I would not expect any particular tendancy for flat or steep best fit lines.

3. If there is a given slope (y=kx), then adding y axis noise in general (imagine doing it multiple times), will have an overall effect of what? A tendancy to make the k value vary? Effect of (on average) of driving k down (like averaging a line with zero slope)? Is the noise, noise from the trend line or noise from “zero”? In other words, what is the average slope of the noise? Are you just averaging in stuff that has a slope of zero on average? And how are the mean of the noise and the mean of the trend line related?

4. I’m not clear what “inverting” means. If we have y=kx, does inverting mean y=(1/k)x? Or y= 1/(kx)? or just somehow “plotting” x=(1/k)y?

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