In [2]:

    

%matplotlib inline
# pg 58 This will evaluate the prediction from section 2.1


    

In [3]:

    

from sklearn.datasets import load_boston
from sklearn.linear_model import LinearRegression


    

In [4]:

    

boston = load_boston()
lr = LinearRegression()
lr.fit(boston.data, boston.target)


    

    
Out[4]:





LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)

In [5]:

    

predictions = lr.predict(boston.data)


    

In [6]:

    

import matplotlib.pyplot as plt
import numpy as np


    

In [7]:

    

f = plt.figure(figsize=(7,5))
ax = f.add_subplot(111)
ax.hist(boston.target - predictions, bins=50)
ax.set_title('Histogram of Residuals.')


    

    
Out[7]:





<matplotlib.text.Text at 0x10c310810>






    

In [8]:

    

# look at the mean of the residuals (closer to 0 is best)
np.mean(boston.target - predictions)


    

    
Out[8]:





4.9709906810093963e-15

In [9]:

    

# Look at the Q-Q plot.


    

In [10]:

    

from scipy.stats import probplot
f = plt.figure(figsize=(7,5))
ax = f.add_subplot(111)
probplot(boston.target - predictions, plot=ax)
ax


    

    
Out[10]:





<matplotlib.axes._subplots.AxesSubplot at 0x10c291410>






    

In [11]:

    

# Created Mean Squared Error (MSE) and Mean Absolute Deviation(MAD)
# in msemad.py for this next part and later in the book.


    

In [12]:

    

from msemad import MSE, MAD


    

In [13]:

    

MSE(boston.target, predictions)


    

    
Out[13]:





21.897779217687496

In [14]:

    

MAD(boston.target, predictions)


    

    
Out[14]:





3.2729446379969334

In [40]:

    

n_bootstraps = 100
len_boston = len(boston.target)
subsample_size = np.int(0.5*len_boston)


    

In [41]:

    

subsample = lambda: np.random.choice(np.arange(0, len_boston), size=subsample_size)


    

In [42]:

    

coefs = np.ones(n_bootstraps)


    

In [43]:

    

for i in range(n_bootstraps):
    subsample_idx = subsample()
    subsample_X = boston.data[subsample_idx]
    subsample_y = boston.target[subsample_idx]
    lr.fit(subsample_X, subsample_y)
    coefs[i] = lr.coef_[0]


    

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In [ ]:

    




    

In [44]:

    

import matplotlib.pyplot as plt
f = plt.figure(figsize=(7,5))
ax = f.add_subplot(111)
ax.hist(coefs, bins=50)
ax.set_title("Histogram of the lr.coef_[0]")


    

    
Out[44]:





<matplotlib.text.Text at 0x10cdba690>






    

In [45]:

    

np.percentile(coefs, [2.5, 97.5])


    

    
Out[45]:





array([-0.18285195,  0.08042941])

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