less confusing

linear_regression_class/lr_poly.py

@@ -3,7 +3,10 @@
 # notes for this course can be found at:
 # https://deeplearningcourses.com/c/data-science-linear-regression-in-python
 # https://www.udemy.com/data-science-linear-regression-in-python
-
+from __future__ import print_function, division
+from builtins import range
+# Note: you may need to update your version of future
+# sudo pip install -U future
 
 import numpy as np
 import matplotlib.pyplot as plt
@@ -16,15 +19,16 @@
     x, y = line.split(',')
     x = float(x)
     X.append([1, x, x*x]) # add the bias term x0 = 1
+    # our model is therefore y_hat = w0 + w1 * x + w2 * x**2
     Y.append(float(y))
 
 # let's turn X and Y into numpy arrays since that will be useful later
 X = np.array(X)
 Y = np.array(Y)
 
-
 # let's plot the data to see what it looks like
 plt.scatter(X[:,1], Y)
+plt.title("The data we're trying to fit")
 plt.show()
 
 
@@ -34,19 +38,22 @@
 # note: the * operator does element-by-element multiplication in numpy
 #       np.dot() does what we expect for matrix multiplication
 w = np.linalg.solve(np.dot(X.T, X), np.dot(X.T, Y))
-Yhat = np.dot(X, w)
 
 
 # let's plot everything together to make sure it worked
 plt.scatter(X[:,1], Y)
-plt.plot(sorted(X[:,1]), sorted(Yhat))
-# note: shortcut since monotonically increasing
-#       x-axis values have to be in order since the points
-#       are joined from one element to the next
+
+# to plot our quadratic model predictions, let's
+# create a line of x's and calculate the predicted y's
+x_line = np.linspace(X[:,1].min(), X[:,1].max())
+y_line = w[0] + w[1] * x_line + w[2] * x_line * x_line
+plt.plot(x_line, y_line)
+plt.title("Our fitted quadratic")
 plt.show()
 
 
 # determine how good the model is by computing the r-squared
+Yhat = X.dot(w)
 d1 = Y - Yhat
 d2 = Y - Y.mean()
 r2 = 1 - d1.dot(d1) / d2.dot(d2)