Alberto

Alberto

Experience is not what
happens to a man;
it is what a man does
with what happens to him.
-Aldous Huxley

Python: Linear Regression

Utilizzo l’environment conda py3

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~$ conda activate py3

Versione modulo installato

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~$ pip show scikit-learn
Name: scikit-learn
Version: 0.23.1
Summary: A set of python modules for machine learning and data mining
Home-page: http://scikit-learn.org
Author: None
Author-email: None
License: new BSD
Location: /home/user/miniconda3/envs/py3/lib/python3.7/site-packages
Requires: scipy, joblib, threadpoolctl, numpy
Required-by:

USA Housing

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import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

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# data
USAhousing = pd.read_csv('USA_Housing.csv')
USAhousing.head()
Avg. Area Income Avg. Area House Age Avg. Area Number of Rooms Avg. Area Number of Bedrooms Area Population Price Address
0 79545.458574 5.682861 7.009188 4.09 23086.800503 1.059034e+06 208 Michael Ferry Apt. 674\nLaurabury, NE 3701...
1 79248.642455 6.002900 6.730821 3.09 40173.072174 1.505891e+06 188 Johnson Views Suite 079\nLake Kathleen, CA...
2 61287.067179 5.865890 8.512727 5.13 36882.159400 1.058988e+06 9127 Elizabeth Stravenue\nDanieltown, WI 06482...
3 63345.240046 7.188236 5.586729 3.26 34310.242831 1.260617e+06 USS Barnett\nFPO AP 44820
4 59982.197226 5.040555 7.839388 4.23 26354.109472 6.309435e+05 USNS Raymond\nFPO AE 09386

EDA

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USAhousing.info()

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<class 'pandas.core.frame.DataFrame'>
RangeIndex: 5000 entries, 0 to 4999
Data columns (total 7 columns):
 #   Column                        Non-Null Count  Dtype  
---  ------                        --------------  -----  
 0   Avg. Area Income              5000 non-null   float64
 1   Avg. Area House Age           5000 non-null   float64
 2   Avg. Area Number of Rooms     5000 non-null   float64
 3   Avg. Area Number of Bedrooms  5000 non-null   float64
 4   Area Population               5000 non-null   float64
 5   Price                         5000 non-null   float64
 6   Address                       5000 non-null   object 
dtypes: float64(6), object(1)
memory usage: 273.6+ KB

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# statistiche
USAhousing.describe()
Avg. Area Income Avg. Area House Age Avg. Area Number of Rooms Avg. Area Number of Bedrooms Area Population Price
count 5000.000000 5000.000000 5000.000000 5000.000000 5000.000000 5.000000e+03
mean 68583.108984 5.977222 6.987792 3.981330 36163.516039 1.232073e+06
std 10657.991214 0.991456 1.005833 1.234137 9925.650114 3.531176e+05
min 17796.631190 2.644304 3.236194 2.000000 172.610686 1.593866e+04
25% 61480.562388 5.322283 6.299250 3.140000 29403.928702 9.975771e+05
50% 68804.286404 5.970429 7.002902 4.050000 36199.406689 1.232669e+06
75% 75783.338666 6.650808 7.665871 4.490000 42861.290769 1.471210e+06
max 107701.748378 9.519088 10.759588 6.500000 69621.713378 2.469066e+06 
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# nomi colonne
USAhousing.columns

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Index(['Avg. Area Income', 'Avg. Area House Age', 'Avg. Area Number of Rooms',
       'Avg. Area Number of Bedrooms', 'Area Population', 'Price', 'Address'],
      dtype='object')

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# pairplot
sns.pairplot(USAhousing)

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<seaborn.axisgrid.PairGrid at 0x7ffba0e6db50>

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# price distribution
sns.distplot(USAhousing['Price'])

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<matplotlib.axes._subplots.AxesSubplot at 0x7ffb7646ef10>

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# heatmap
sns.heatmap(USAhousing.corr(), cmap='magma_r', annot=True)

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<matplotlib.axes._subplots.AxesSubplot at 0x7ffb7645cb50>

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Training Model

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# sklearn
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn import metrics

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# X e y
X = USAhousing[['Avg. Area Income', 'Avg. Area House Age', 'Avg. Area Number of Rooms','Avg. Area Number of Bedrooms', 'Area Population']]
y = USAhousing['Price']

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# train e test set
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=101)

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# train model
lm = LinearRegression()
lm.fit(X_train,y_train)

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LinearRegression()

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# intercept
print(lm.intercept_)

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-2640159.7968526687

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# coefficients
coeff_df = pd.DataFrame(data=lm.coef_,index=X.columns,columns=['Coefficient'])
coeff_df
Coefficient
Avg. Area Income 21.528276
Avg. Area House Age 164883.282027
Avg. Area Number of Rooms 122368.678027
Avg. Area Number of Bedrooms 2233.801864
Area Population 15.150420

Predictions

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predictions = lm.predict(X_test)

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# scatterplot predictions
plt.scatter(y_test,predictions,marker='o',edgecolors='black',alpha=0.1,s=20)

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<matplotlib.collections.PathCollection at 0x7ffb572f8f50>

png

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# distplot residuals
sns.distplot(y_test-predictions,bins=30, hist_kws=dict(edgecolor="black", linewidth=1))

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<matplotlib.axes._subplots.AxesSubplot at 0x7ffb56de2a10>

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Metrics

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print('MAE:', metrics.mean_absolute_error(y_test, predictions))
print('MSE:', metrics.mean_squared_error(y_test, predictions))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, predictions)))

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MAE: 82288.22251914944
MSE: 10460958907.208954
RMSE: 102278.82922290885

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# Explained Variance Score (R^2)
metrics.explained_variance_score(y_test,predictions)

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0.9178179926151842

Boston dataset

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# df su cui giocare
from sklearn.datasets import load_boston
boston = load_boston()
print(boston.DESCR)
boston_df = boston.data

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.. _boston_dataset:

Boston house prices dataset
---------------------------

**Data Set Characteristics:**  

    :Number of Instances: 506 

    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.

    :Attribute Information (in order):
        - CRIM     per capita crime rate by town
        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.
        - INDUS    proportion of non-retail business acres per town
        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)
        - NOX      nitric oxides concentration (parts per 10 million)
        - RM       average number of rooms per dwelling
        - AGE      proportion of owner-occupied units built prior to 1940
        - DIS      weighted distances to five Boston employment centres
        - RAD      index of accessibility to radial highways
        - TAX      full-value property-tax rate per $10,000
        - PTRATIO  pupil-teacher ratio by town
        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town
        - LSTAT    % lower status of the population
        - MEDV     Median value of owner-occupied homes in $1000's

    :Missing Attribute Values: None

    :Creator: Harrison, D. and Rubinfeld, D.L.

This is a copy of UCI ML housing dataset.
https://archive.ics.uci.edu/ml/machine-learning-databases/housing/


This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.

The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic
prices and the demand for clean air', J. Environ. Economics & Management,
vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics
...', Wiley, 1980.   N.B. Various transformations are used in the table on
pages 244-261 of the latter.

The Boston house-price data has been used in many machine learning papers that address regression
problems.   
     
.. topic:: References

   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.
   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.

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