Linear Regression

Let's fabricate some data that shows a roughly linear relationship between page speed and amount purchased:



In [5]:

    
%matplotlib inline
import numpy as np
from pylab import *

pageSpeeds = np.random.normal(3.0, 1.0, 1000)
purchaseAmount = 100 - (pageSpeeds + np.random.normal(0, 0.1, 1000)) * 3

scatter(pageSpeeds, purchaseAmount)









    Out[5]:





<matplotlib.collections.PathCollection at 0x8956c50>

As we only have two features, we can keep it simple and just use scipy.state.linregress:



In [6]:

    
from scipy import stats

slope, intercept, r_value, p_value, std_err = stats.linregress(pageSpeeds, purchaseAmount)

Not surprisngly, our R-squared value shows a really good fit:



In [7]:

    
r_value ** 2









    Out[7]:





0.9909426264422585

Let's use the slope and intercept we got from the regression to plot predicted values vs. observed:



In [8]:

    
import matplotlib.pyplot as plt

def predict(x):
    return slope * x + intercept

fitLine = predict(pageSpeeds)

plt.scatter(pageSpeeds, purchaseAmount)
plt.plot(pageSpeeds, fitLine, c='r')
plt.show()

Activity

Try increasing the random variation in the test data, and see what effect it has on the r-squared error value.



In [ ]: