added linear regression example

code/linear_regression.py

@@ -0,0 +1,53 @@
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+def estimate_coef(x, y):
+    # number of observations/points
+    n = np.size(x)
+
+    # mean of x and y vector
+    m_x, m_y = np.mean(x), np.mean(y)
+
+    # calculating cross-deviation and deviation about x
+    SS_xy = np.sum(y*x - n*m_y*m_x)
+    SS_xx = np.sum(x*x - n*m_x*m_x)
+
+    # calculating regression coefficients
+    b_1 = SS_xy / SS_xx
+    b_0 = m_y - b_1*m_x
+
+    return(b_0, b_1)
+
+def plot_regression_line(x, y, b):
+    # plotting the actual points as scatter plot
+    plt.scatter(x, y, color = "m",
+               marker = "o", s = 30)
+
+    # predicted response vector
+    y_pred = b[0] + b[1]*x
+
+    # plotting the regression line
+    plt.plot(x, y_pred, color = "g")
+
+    # putting labels
+    plt.xlabel('x')
+    plt.ylabel('y')
+
+    # function to show plot
+    plt.show()
+
+def main():
+    # observations
+    x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    y = np.array([1, 3, 2, 5, 7, 8, 8, 9, 10, 12])
+
+    # estimating coefficients
+    b = estimate_coef(x, y)
+    print("Estimated coefficients:\nb_0 = {}  \\nb_1 = {}".format(b[0], b[1])) 
+
+    # plotting regression line
+    plot_regression_line(x, y, b)
+
+if __name__ == "__main__":
+    main()