[SciPy-User] StdErr Problem with Gary Strangman's linregress function

[totalbull at mac.com]

Thanks very much to all who have helped with this. 

I am going to go with the first-principles formulae as per below. 

Otherwise I also asked on Stack Overflow and one person answered with a scikits example:

http://stackoverflow.com/questions/2038667/scipy-linregress-function-erroneous-standard-error-return


On 11 Jan 2010, at 15:47, Nuttall, Brandon C wrote:

> For what it’s worth, using by the definition of standard error of the estimate in Crow, Davis, and Maxfield, 1960, Statistics Manual: Dover Publications (p. 156), the Excel function provides the “correct” standard error of the estimate.  Using notation from Crow, Davis, and Maxfield:
>  
> import numpy as np
> n = 4.0
> x = np.array([5.05, 6.75, 3.21, 2.66])
> y = np.array([1.65, 26.5, -5.93, 7.96])
> x2 = x*x
> y2 = y*y
> s2x = (4.0*x2.sum()-x.sum()*x.sum())/(n*(n-1.0))
> s2y = (4.0*y2.sum()-y.sum()*y.sum())/(n*(n-1.0))
> xy = x * y
> b = (4.0*xy.sum()-x.sum()*y.sum())/(4.0*x2.sum()-x.sum()*x.sum())
> a = (y.sum()-b*x.sum())/n
> s2xy = ((n-1.0)/(n-2.0))*(s2y-b*b*s2x)
> ste = np.sqrt(s2xy)
> r=b*np.sqrt(s2x)/np.sqrt(s2y)
> print "intercept: ",a
> print "gradient (slope): ",b
> print "correlation coefficient, r: ",r
> print "std err est: ",ste
>  
> Produces the output :
>  
> intercept:  -16.2811279931
> gradient (slope):  5.3935773612
> correlation coefficient, r:  0.724435142118
> std err est:  11.6964144616
>  
> This same value for the standard error of the estimate is reported with the sample x,y data at the VassarStats, Statistical Computation Web Site,http://faculty.vassar.edu/lowry/VassarStats.html.
>  
> Brandon Nuttall, KRPG-1364
> Kentucky Geological Survey
> www.uky.edu/kgs
> bnuttall at uky.edu (KGS, Mo-We)
> Brandon.nuttall at ky.gov (EEC, Th-Fr)
> 859-257-5500 ext 30544 (main)
> 859-323-0544 (direct)
> 859-684-7473 (cell)
> 859-257-1147 (FAX)
>  
> From: scipy-user-bounces at scipy.org [mailto:scipy-user-bounces at scipy.org] On Behalf Of Bruce Southey
> Sent: Sunday, January 10, 2010 8:21 PM
> To: SciPy Users List
> Subject: Re: [SciPy-User] StdErr Problem with Gary Strangman's linregress function
>  
>  
> 
> On Sun, Jan 10, 2010 at 3:35 PM, <totalbull at mac.com> wrote:
>  
> Hello, Excel and scipy.stats.linregress are disagreeing on the standard error of a regression. 
> 
> I need to find the standard errors of a bunch of regressions, and prefer to use pure Python than RPy. So I am going to scipy.stats.linregress, as advised at:
> http://www2.warwick.ac.uk/fac/sci/moac/currentstudents/peter_cock/python/lin_reg/#linregress
> 
> 
> from scipy import stats
> x = [5.05, 6.75, 3.21, 2.66]
> y = [1.65, 26.5, -5.93, 7.96]
> gradient, intercept, r_value, p_value, std_err = stats.linregress(x,y)
> gradient
> 5.3935773611970186
> 
> intercept
> -16.281127993087829
> 
> r_value
> 0.72443514211849758
> 
> r_value**2
> 0.52480627513624778
> 
> std_err
> 3.6290901222878866
> 
> 
> The problem is that the std error calculation does not agree with what is returned in Microsoft Excel's STEYX function (whereas all the other output does). From Excel:
> 
> <image001.png>
> 
> 
> Anybody knows what's going on? Any alternative way of getting the standard error without going to R?
> 
> 
> 
> 
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> 
> 
> The Excel help is rather cryptic by   :"Returns the standard error of the predicted y-value for each x in the regression. The standard error is a measure of the amount of error in the prediction of y for an individual x." But clearly this is not the same as the standard error of the 'gradient' (slope) returned by linregress. Without checking the formula, STEYX appears returns the square root what most people call the mean square error (MSE).
> 
> Bruce
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