Calculates the confidence band of a linear regression model at the desired confidence level, using analytical methods

confband.py

def confband(xd,yd,a,b,conf=0.95,x=None):
	"""
Calculates the confidence band of the linear regression model at the desired confidence
level, using analytical methods. The 2sigma confidence interval is 95% sure to contain 
the best-fit regression line. This is not the same as saying it will contain 95% of 
the data points.

Arguments:
- conf: desired confidence level, by default 0.95 (2 sigma)
- xd,yd: data arrays
- a,b: linear fit parameters as in y=ax+b
- x: (optional) array with x values to calculate the confidence band. If none is provided, will
  by default generate 100 points in the original x-range of the data.
  
Returns:
Sequence (lcb,ucb,x) with the arrays holding the lower and upper confidence bands 
corresponding to the [input] x array.

Usage:
>>> lcb,ucb,x=nemmen.confband(all.kp,all.lg,a,b,conf=0.95)
calculates the confidence bands for the given input arrays

>>> pylab.fill_between(x, lcb, ucb, alpha=0.3, facecolor='gray')
plots a shaded area containing the confidence band

References:
1. http://en.wikipedia.org/wiki/Simple_linear_regression, see Section Confidence intervals
2. http://www.weibull.com/DOEWeb/confidence_intervals_in_simple_linear_regression.htm

Author: Rodrigo Nemmen
v1 Dec. 2011
v2 Jun. 2012: corrected bug in computing dy
	"""
	alpha=1.-conf	# significance
	n=xd.size	# data sample size

	if x==None: x=numpy.linspace(xd.min(),xd.max(),100)

	# Predicted values (best-fit model)
	y=a*x+b

	# Auxiliary definitions
	sd=scatterfit(xd,yd,a,b)	# Scatter of data about the model
	sxd=numpy.sum((xd-xd.mean())**2)
	sx=(x-xd.mean())**2	# array

	# Quantile of Student's t distribution for p=1-alpha/2
	q=scipy.stats.t.ppf(1.-alpha/2.,n-2)

	# Confidence band
	dy=q*sd*numpy.sqrt( 1./n + sx/sxd )
	ucb=y+dy	# Upper confidence band
	lcb=y-dy	# Lower confidence band

	return lcb,ucb,x

For those who are wondering, scatterfit would appear to be from this gist: https://gist.github.com/rsnemmen/0eb32832c657c19e4d39