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CI_Workshop_Teplitskiy_Regression.py
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CI_Workshop_Teplitskiy_Regression.py
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# -*- coding: utf-8 -*-
# <nbformat>3.0</nbformat>
# <markdowncell>
# #Regression Example
#
# - Regression = continuous outcome variable (e.g. "price")
# - Classification = discrete outcome variable (e.g. "class")
#
# ###Goal: Find "best" line
#
# Example with only one predictor, "Year"
#
# <img src=http://www.sigmazone.com/images/Pit91_Scatter_Error.gif>
#
# ###Solution:
# - Minimize squared distances ("errors")
#
# ###Evaluation
# - model fit: R^2
# <img src=http://www.rapidinsightinc.com/wordpress/wp-content/uploads/r-squared-710x400.png>
#
# ###Coefficients
#
# size? statistical significance?
# - Usually calculate: **If** the actual coefficient was 0, how often would we see a coefficient *estimate* this large or larger?
# - *"How consistent is the evidence with the null hypothesis?"*
# - Not exactly what we want
# - In practice, good enough if p < 0.05
# <codecell>
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import statsmodels.formula.api as smf
# <markdowncell>
# ##Data: Boston Housing Prices
# <markdowncell>
# <img src=http://25.media.tumblr.com/d51ffb3725335088ab12fa34bf4c134c/tumblr_mle1snD31n1qe5ugfo6_250.gif>
# <markdowncell>
# ###How much do people care about pollution?
# <codecell>
from sklearn.datasets import load_boston
boston = load_boston()
# <codecell>
print boston.DESCR
# <markdowncell>
# ###Set up our df
# <codecell>
column_names = [
'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
df = pd.DataFrame(boston.data, columns=column_names)
df['MEDV'] = boston.target
# <codecell>
df.columns
# <markdowncell>
# ### Let's look at value and crime
# <codecell>
plt.scatter(df.CRIM, df.MEDV)
# <codecell>
results = smf.ols(formula='standardize(MEDV) ~ C(CRIM)', data=df).fit()
results.summary()
# <codecell>
results.params
# <codecell>
plt.scatter(df.CRIM, df.MEDV)
xs = np.linspace(0, df.CRIM.max(), 100)
plt.plot(xs, xs*results.params[0], 'r--')
# <markdowncell>
# <img src=http://img1.wikia.nocookie.net/__cb20121212025209/glee/images/4/4c/PaulaWut.gif>
# <markdowncell>
# ###Let's add an intercept
# <codecell>
results = smf.ols(formula='MEDV ~ CRIM', data=df).fit()
results.summary()
# <codecell>
plt.scatter(df.CRIM, df.MEDV)
xs = np.linspace(0, df.CRIM.max(), 100)
plt.plot(xs, results.params[0] + xs*results.params[1], 'r--')
# <markdowncell>
# ##Handling categorical variables, standardizing
# <markdowncell>
# ###by using the R-style formula
# - C(var_name)
# - standardize(var_name)
# <markdowncell>
# #Exercise:
# Predict house prices as well as you can!