numpy/scipy: correlation

Robert Kern robert.kern at
Mon Nov 13 00:03:36 CET 2006

sturlamolden wrote:
> Robert Kern wrote:
>> The difference between the two models is that the first places no restrictions
>> on the distribution of x. The second does; both the x and y marginal
>> distributions need to be normal. Under the first model, the correlation
>> coefficient has no meaning.
> That is not correct. The correlation coefficient is meaningful in both
> models, but must be interpreted differently. However, in both cases a
> correlation coefficient of 1 or -1 indicates an exact linear
> relationship between x and y.
> Under the first model ("linear regression"), the squared correlation
> coefficient is the "explained variance", i.e. the the proportion of y's
> variance accounted for by the model y = m*x  + o.


Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
 that is made terrible by our own mad attempt to interpret it as though it had
 an underlying truth."
  -- Umberto Eco

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