I am performing a least squares regression as below (univariate). I would like to express the significance of the result in terms of R^2. Numpy returns a value of unscaled residual, what would be a sensible way of normalizing this.
field_clean,back_clean = rid_zeros(backscatter,field_data)
num_vals = len(field_clean)
x = field_clean[:,row:row+1]
y = 10*log10(back_clean)
A = hstack([x, ones((num_vals,1))])
soln = lstsq(A, y )
m, c = soln [0]
residues = soln [1]
print residues
See http://en.wikipedia.org/wiki/Coefficient_of_determination
Your R2 value =
1 - residual / sum((y - y.mean())**2)
which is equivalent to
1 - residual / (n * y.var())
As an example:
import numpy as np
# Make some data...
n = 10
x = np.arange(n)
y = 3 * x + 5 + np.random.random(n)
# Note that polyfit is an easier way to do this...
# It would just be "model, resid = np.polyfit(x,y,1,full=True)[:2]"
A = np.vstack((x, np.ones(n))).T
model, resid = np.linalg.lstsq(A, y)[:2]
r2 = 1 - resid / (y.size * y.var())
print r2
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