In [1]:

    

import pandas as pd
import numpy as np
from random import randint
from pandas import Series,DataFrame
import seaborn as sns
import matplotlib.pyplot as plt
import matplotlib
%matplotlib inline
plt.rcParams['figure.figsize'] = (12, 10)
plt.rcParams['font.size'] = 14


    

In [8]:

    

%%html
<style>
table {float:left}
</style>


    

In [2]:

    

from sklearn.datasets import load_boston
boston = load_boston()
type(boston)


    

    
Out[2]:





sklearn.datasets.base.Bunch

In [13]:

    

type(boston.data)


    

    
Out[13]:





numpy.ndarray

In [57]:

    

print boston.target.shape
plt.figure()
sns.distplot(boston.target)


    

    




(506L,)






    
Out[57]:





<matplotlib.axes._subplots.AxesSubplot at 0x16522f98>






    

In [22]:

    

# least square estimation (based on setting 1st derivation equation to zero)
# Betas = [1/(X_tr*X)]*X_tr*Y
Y = boston.target
X = boston.data
X_tr = X.transpose()
inv = np.linalg.inv(X_tr.dot(X))
b = (inv.dot(X_tr)).dot(Y)


    

In [25]:

    

y_pred = X.dot(b)


    

In [35]:

    

# Computer R Squared
ssreg = np.sum((y_pred-Y.mean())**2)
sstot = np.sum((Y-Y.mean())**2)
R_sq = ssreg/sstot
print 'R Squared  = {:.2f}'.format(R_sq)


    

    




R Squared  = 0.75

In [55]:

    

#standardized residual plot
res = Y-y_pred
res_d = ((1.0/(len(res)-1))*np.sum(res**2))**0.5
res_stu = res/res_d

plt.figure()
grid = sns.JointGrid(x=Y, y=res_stu, space=0, size=6, ratio=50)
grid.plot_joint(plt.scatter, color="g")
grid.plot_marginals(sns.rugplot, height=1, color="g")
grid.set_axis_labels(xlabel="Boston house price",ylabel="studentized residues")


    

    
Out[55]:





<seaborn.axisgrid.JointGrid at 0x129d2828>






    






<matplotlib.figure.Figure at 0x129d2860>






    

In [47]:

    

res_d


    

    
Out[47]:





4.9214055276647812

In [48]:

    

res_stu[0:10]


    

    
Out[48]:





array([-1.03680849, -0.59059747,  0.70472156,  0.74969103,  1.34784177,
        0.69130444,  0.27808008,  1.62532507,  1.10028356,  0.13043357])

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