import scipy.stats
import numpy.linalg as la
import numpy
def regress(X,y):
"""
Perform a multiple linear regression of y onto X. X is a num
observations by (num variables +1) array. X should contain a
column of ones to generate the intercept. y is a num observations
array of independent variables
return value B, residuals, stats
B: the regression coeffients; Ypred = B.T * X.T
residuals: array( y - Ypred.T)
stats = Rsquared, F, p
"""
# regression coeffs are given by (Xt*X)-1*Xt*y
N = X.shape[0]
origshape = y.shape
y.shape = N, 1
X = numpy.matrix(X)
Y = numpy.matrix(y)
Xt = X.T
Xt_X_i = la.inv(Xt*X)
B = Xt_X_i*Xt*Y
Ypred = B.T * Xt
residuals = numpy.array(Y-Ypred.T)
CF = N*numpy.mean(y)**2 # correction factor
SStotal = float(Y.T*Y-CF)
SSregress = float(B.T * Xt * Y - CF)
SSerror = SStotal - SSregress
Rsquared = SSregress/SStotal
dfTotal = N-1
dfRegress = len(B)-1
dfError = dfTotal - dfRegress
F = SSregress/dfRegress / (SSerror/dfError)
prob = 1-scipy.stats.f.cdf(F, dfRegress, dfError)
stats = Rsquared, F, prob
y.shape = origshape
B = numpy.asarray(B)
#print 'B', B
#print 'B[:,0]', B[:,0]
#print 'B[0,:]', B[0,:]
return B[:,0], residuals, stats
