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I'm very interested in weather. I use data from weather-stations. Here are 2 examples of changing average annual temperature in Vienna and Moscow.
(I've got more, but only 2 links allowed ((
LinearModelFit method from Mathematica have been applied (blue lines).
YearTemp1
YearTemp2
Well we can see, that in model $y=a\cdot x+b$, $a$ is small, but always positive number.
Is it so called global warming, I wonder?

There is a great scatter of data, from year to year. So the question to community is:
are there additional criteria (exept just the fact that $a>0$) for someone can say:
"Yes, with probability 50% (20?...90?) we have global warming".
Mathematica has a lot of stats methods so the problem is just "what of them to use".

UPD There is similar question,
What is the best test for validating trends in time-series data? but I do not see any real answers.

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    $\begingroup$ In short: yes there are other criteria. In long, you might want to have a look at the papers cited in the footnotes of this document. That should at least help you slice you question into manageable bits $\endgroup$
    – user603
    Commented Feb 17, 2013 at 15:46
  • $\begingroup$ Good paper, thanx! Of course I try to be focused only on average annual temperature rising when talk about global warming here. $\endgroup$
    – lesobrod
    Commented Feb 17, 2013 at 16:05
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    $\begingroup$ You cannot conclude global warming from a single station, in particular not urban ones. For warming to be global you need stations from the entire world. For determining local climate change you need to correct for effects such as the urban heat island effect. You might also want to read the IPCC AR4 WG1 report. $\endgroup$
    – gerrit
    Commented Feb 17, 2013 at 22:59
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    $\begingroup$ @gerrit: Thanx I thought about it. E.g. Kiev and Moscow stations are within off-city airports. Effect of urban heat is well known, I live in 20 km from Moscow and diifference is about 5 degree. But! Now I've collected over 15 time-series all over the world. And linear regression gives positive coeff for all of them. $\endgroup$
    – lesobrod
    Commented Feb 18, 2013 at 16:07

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