How do you calculate a best fit line in python, and then plot it on a scatterplot in matplotlib?
I was I calculate the linear best-fit line using Ordinary Least Squares Regression as follows:
from sklearn import linear_model
clf = linear_model.LinearRegression()
x = [[t.x1,t.x2,t.x3,t.x4,t.x5] for t in self.trainingTexts]
y = [t.human_rating for t in self.trainingTexts]
regress_coefs = clf.coef_
regress_intercept = clf.intercept_
This is multivariate (there are many x-values for each case). So, X is a list of lists, and y is a single list. For example:
x = [[1,2,3,4,5], [2,2,4,4,5], [2,2,4,4,1]]
y = [1,2,3,4,5]
But how do I do this with higher order polynomial functions. For example, not just linear (x to the power of M=1), but binomial (x to the power of M=2), quadratics (x to the power of M=4), and so on. For example, how to I get the best fit curves from the following?
Extracted from Christopher Bishops's "Pattern Recognition and Machine Learning", p.7: