Polyfit is a great tool to fit a line to a set of points. However my data has varying levels of statistical significance.
For example, for one point (x1,y2) I might only have 10 observations, while for another point (x2,y2) I might have 10,000 observations. I usually have at least 10 points and I'd like to weight each according to statistical significance when using polyfit. Is there any way (or a similar function) that allows for that?
One possibility is to use weighted least squares in statsmodels
roughly:
y is response or endogenous variable (endog)
x is your 1 dimensional explanatory variable
w your weight array, the higher the more weight on that observation
to get the polynomial matrix, and fit
import numpy as np
import statsmodels.api as sm
exog = np.vander(x, degree+1)
result = sm.WLS(y, exog, weight=w).fit()
the parameters are in result.params. The fitted values are in result.fittedvalues
Prediction has changed between versions. With version 0.4 you can use
result.predict(np.vander(x_new, degree+1))
more straightforward:
import numpy as np
result = np.polynomial.polynomial.polyfit(x,y,deg,w=weight of each observation)
I do not know about numpy but you can write your own polyfit function. Polyfit is just solving of linear equation.
http://en.wikipedia.org/wiki/Polynomial_regression#Matrix_form_and_calculation_of_estimates
(in your case epsilon is probably 0)
You can see that all you have to do is multipling each line in y and each line in x whit your coeficient.
This shoul be like 10 lines of code (i remeber that it took me like 4h to reinvent minsquare equation on my own, but only 2 lines of code in MATLAB)
