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In [61]:

    
import numpy as np
import pandas as pd



In [2]:

    
# dataset from Chapter 3 of An Introduction to Statistical Learning ()
data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)



In [6]:

    
# check the shape of the dataframe (rows, columns)
data.shape
data.head()



In [4]:

    
import seaborn as sns

%matplotlib inline



In [11]:

    
# visualize the relationship between the features and the response using scatterplots
sns.pairplot(data, x_vars=['TV','radio','newspaper'], y_vars=['sales'], height=5, aspect=0.8, kind='reg')









    



/Users/g4brielvs/.pyenv/versions/3.7.0/envs/or/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval






    Out[11]:





<seaborn.axisgrid.PairGrid at 0x112a4a668>



In [38]:

    
# create a list of feature names
feature_cols = ['TV','radio','newspaper']

# select a subset of the original dataframe
X = data[feature_cols]

# create a list of response
response_cols = ['sales']

# select a subset of the original dataframe
y = data[response_cols]



In [19]:

    
#from sklearn.cross_validation import train_test_split
from sklearn.model_selection import train_test_split



In [26]:

    
# default split is 75% for training and 25% for testing
X_train, X_test, y_train, y_test = train_test_split(X, y)



In [31]:

    
from sklearn.linear_model import LinearRegression

# instantiate
linreg = LinearRegression()

# fit the model to the training dataset
linreg.fit(X_train, y_train)









    Out[31]:





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



In [64]:

    
# print the intercept and coefficients
print(linreg.intercept_)
print(linreg.coef_)









    



[2.79946036]
[[0.04688543 0.18260704 0.00184359]]

Model evaluation metrics for regression

Evalution matrics for classification problems, such as accuracy, are not useful for regression.

Let's create some example numeric predictions, and calculate three common evalution metrics for regression.



In [46]:

    
#define numerical examples
true = [100, 50, 30, 20]
pred = [90, 50, 50, 30]

Mean Absolute Error (MAE) is the mean of the absolute value of the errors:

$$\frac{1}{n} \sum_{i=1}^{n} | y_i - \hat{y}_i| $$



In [60]:

    
# calculate MAE using scikit-learn
from sklearn import metrics
print metrics.median_absolute_error(true, pred)

Mean Squared Error (MSE) is the mean of the squared errors:

$$\frac{1}{n} \sum_{i=1}^{n} ( y_i - \hat{y}_i)^2 $$



In [61]:

    
# calculate MSE using scikit-learn
print metrics.mean_squared_error(true, pred)

Root Mean Squared Error (RMSE) is the square root of the mean of the squared errors:

$$\sqrt{\frac{1}{n} \sum_{i=1}^{n} ( y_i - \hat{y}_i)^2}$$



In [68]:

    
# calculate RMSE using scikit-learn
import numpy as np
print np.sqrt(metrics.mean_squared_error(true, pred))









    



12.2474487139

Comparing these metrics:

MAE is the easiest to understand, because it's the average error.
MSE is more popular than MAE, because MSE "punishes" larger errors.
RMSE is even more popular than MSE, because RMSE is interpretable in the "y" units.

RMSE for our sales predictions:



In [73]:

    
# make predictions on the testing subset
y_pred = linreg.predict(X_test)

# RMSE
print np.sqrt(metrics.mean_squared_error(y_test, y_pred))









    



1.56799801941

Feature Selection



In [84]:

    
# select first two features
feature_cols = ['TV', 'Radio']

# select subset
X = data[feature_cols]

#y = data.Sales
y = data[response_cols]

# split into training and testing
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)

# fit the model
linreg.fit(X_train, y_train)

# make predictions
y_pred = linreg.predict(X_test)

# compute RMSE
print np.sqrt(metrics.mean_squared_error(y_test, y_pred))









    



1.38790346994



In [ ]:

	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