The standard deviation of the slope

In a previous post, http://evilreductionist.blogspot.com/2010/01/climate-sensitivity.html, I calculated the observed climate sensitivity of the earth over the past 130 years.

In this post, I will provide an estimate of the 95 per cent confidence interval for that climate sensitivity.

The data is autocorrelated. This means that I cannot use the normal method for calculating the standard deviation of a slope, which is given here:

http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/ErrRegr.html

What I need to do is make an estimate of the autoregression coefficient and then use this to substitute a new effective N into the standard deviation equation.

The effective N will equal N*(1-ARC)/(1+ARC), with ARC being the autoregression coefficient.

I examined the autocorrelation of the data and found the ARC to be .882. However, I do not think that it justifies that level of accuracy, as it might even be as high as .95, although that is unlikely.

An ARC of .882 yielded a 95 per cent confidence interval for the observed climate sensitivity over the past 130 years of 2.02 +/- .76 in degrees celsius. If it is as high as .95, then the 95 per cent confidence interval would be 2.02 +/- 1.64 in degrees celsius. This is a big range.


new:

I have now re-examined the ARC and determined a 95 per cent confidence interval for it. This interval is from .84 to .99, with a middle value of close to .92. This middle value gives a range for the observed climate sensitivity of two plus or minus one degrees celsius.