# [Numpy-discussion] Question on lstsq and correlation coeff

Anthony Kong Anthony.Kong@macquarie....
Wed Feb 25 18:31:37 CST 2009

``` Hi, Josef,

Thanks very much for the quick and helpful response.

Could you also comment on the use of lstsq(): Why it leads to inconsistent result?

Cheers, Anthony

-----Original Message-----
From: numpy-discussion-bounces@scipy.org [mailto:numpy-discussion-bounces@scipy.org] On Behalf Of josef.pktd@gmail.com
Sent: Thursday, 26 February 2009 11:09 AM
To: Discussion of Numerical Python
Subject: Re: [Numpy-discussion] Question on lstsq and correlation coeff

On Wed, Feb 25, 2009 at 6:21 PM, Anthony Kong <Anthony.Kong@macquarie.com> wrote:
> Hi, all,
>
> It is probably a newbie question.
>
> I trying to use scipy/numpy in a finanical context. I want to compute
> the correlation coeff of two series (returns vs index returns). I
> tried two appoarches
>
> Firstly,
>
> from scipy.linalg import lstsq
> coeffs,a,b,c = lstsq(matrix, returns) # matrix contains index returns
>
> then I tried,
>
> import numpy as np
> cov = np.cov(idx1, returns)
> print cov.tolist()
> stddev_x = np.std(returns, ddof=1)
> stddev_y = np.std(idx1, ddof=1)
> print "cor = %s" % (cov.tolist()[:-1] /(stddev_x * stddev_y)) They
> differ from each other.
>
> As you can see from the numpy example, I am trying to find cor coeff
> for a sample. (ddof=1)
>
> So, my question is: is the discrepency caused by the fact that I am
> trying to use lstsq() on a 'sample popluation' (i.e. I am not
> regressing a full return series)? Is it correct to use lstsq() this way?
>

the most direct way to calculate the correlation matrix, use index [0,1] to get coefficient.

numpy.corrcoef(x, y=None, rowvar=1, bias=0)

np.cov, that you used, uses biased estimator, denominator = N by default, but for std you used N-1

Josef
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