Linear Regression by Example

In [6]:

    

%pylab inline
pylab.style.use('ggplot')
import pandas as pd


    

    




Populating the interactive namespace from numpy and matplotlib

In [7]:

    

data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)
data.head()


    

    
Out[7]:






  

    

      

      
TV
      
Radio
      
Newspaper
      
Sales
    
  
  

    

      
1
      
230.1
      
37.8
      
69.2
      
22.1
    
    

      
2
      
44.5
      
39.3
      
45.1
      
10.4
    
    

      
3
      
17.2
      
45.9
      
69.3
      
9.3
    
    

      
4
      
151.5
      
41.3
      
58.5
      
18.5
    
    

      
5
      
180.8
      
10.8
      
58.4
      
12.9
    
  

In [8]:

    

import seaborn as sns
sns.pairplot(data.drop('Sales', axis=1))


    

    
Out[8]:





<seaborn.axisgrid.PairGrid at 0x28136469208>






    

In [9]:

    

# visualize the relationship between the features and the response using scatterplots
fig, axs = plt.subplots(1, 3, sharey=True)
data.plot(kind='scatter', x='TV', y='Sales', ax=axs[0], figsize=(16, 8))
data.plot(kind='scatter', x='Radio', y='Sales', ax=axs[1])
data.plot(kind='scatter', x='Newspaper', y='Sales', ax=axs[2])


    

    
Out[9]:





<matplotlib.axes._subplots.AxesSubplot at 0x28137205f60>






    

In [13]:

    

fig, axs = pylab.subplots(1, 3, sharey=True, figsize=(16, 8))
sns.regplot(data=data, x='TV', y='Sales', ax=axs[0])
sns.regplot(data=data, x='Radio', y='Sales', ax=axs[1])
sns.regplot(data=data, x='Newspaper', y='Sales', ax=axs[2])


    

    
Out[13]:





<matplotlib.axes._subplots.AxesSubplot at 0x28137601630>






    

In [19]:

    

# this is using "formula notation" (similar to R)
import statsmodels.formula.api as smf

# create a fitted model in one line
lm1 = smf.ols(formula='Sales ~ TV', data=data).fit()

# print the coefficients
lm1.params


    

    
Out[19]:





Intercept    7.032594
TV           0.047537
dtype: float64

In [18]:

    

print('Spending $100 on TV sales results in %s unit sales.' % (round(lm1.params['TV']*100)))


    

    




Spending $100 on TV sales results in 5.0 unit sales.

In [20]:

    

lm1.rsquared


    

    
Out[20]:





0.61187505085007121

In [21]:

    

lm2 = smf.ols(formula='Sales ~ TV + Radio', data=data).fit()
lm2.params


    

    
Out[21]:





Intercept    2.921100
TV           0.045755
Radio        0.187994
dtype: float64

In [22]:

    

lm2.rsquared


    

    
Out[22]:





0.89719426108289568

In [23]:

    

lm3 = smf.ols(formula='Sales ~ TV + Radio + Newspaper', data=data).fit()
lm3.params


    

    
Out[23]:





Intercept    2.938889
TV           0.045765
Radio        0.188530
Newspaper   -0.001037
dtype: float64

In [24]:

    

lm3.rsquared


    

    
Out[24]:





0.89721063817895208

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