[likelihood] regression slope equals correlation coefficient

statistics/material/varianceexplained.py

@@ -0,0 +1,40 @@
+import numpy as np
+import scipy.stats as st
+import matplotlib.pyplot as plt
+
+x = np.arange(0.0, 10.0, 0.5)
+ytrue = 2.0*x
+y = ytrue + 5.0*np.random.randn(len(x))
+z = np.polyfit(x, y, 1)
+p = np.poly1d(z)
+
+r, _ = st.pearsonr(x, y)
+
+print('total variance: %g' % np.var(y))
+print('residual variance: %g' % np.var(y-p(x)))
+print('variance explained: %g' % (1.0-np.var(y-p(x))/np.var(y)))
+print('r: %g' % r)
+print('variance explained: %g' % (r*r))
+print('slope: %g' % z[0])
+
+fig, axs = plt.subplots(1, 2, sharex=True, sharey=True)
+axs[0].plot(x, ytrue, 'r')
+axs[0].scatter(x, y, c='b')
+axs[0].plot(x, p(x), 'b')
+axs[1].scatter(x, y-p(x), c='b')
+#plt.show()
+
+xn = (x - np.mean(x))/np.std(x)
+yn = (y - np.mean(y))/np.std(y)
+z = np.polyfit(xn, yn, 1)
+p = np.poly1d(z)
+r, _ = st.pearsonr(xn, yn)
+
+print('r: %g' % r)
+print('slope: %g' % z[0])
+
+fig, ax = plt.subplots()
+ax.scatter(xn, yn, c='b')
+ax.plot(xn, p(xn), 'b')
+plt.show()
+