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w2p3.py
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# coding: utf-8
# # Week 2 Problem 3
#
# If you are not using the `Assignments` tab on the course JupyterHub server to read this notebook, read [Activating the assignments tab](https://github.com/lcdm-uiuc/info490-sp17/blob/master/help/act_assign_tab.md).
#
# A few things you should keep in mind when working on assignments:
#
# 1. Make sure you fill in any place that says `YOUR CODE HERE`. Do **not** write your answer in anywhere else other than where it says `YOUR CODE HERE`. Anything you write anywhere else will be removed or overwritten by the autograder.
#
# 2. Before you submit your assignment, make sure everything runs as expected. Go to menubar, select _Kernel_, and restart the kernel and run all cells (_Restart & Run all_).
#
# 3. Do not change the title (i.e. file name) of this notebook.
#
# 4. Make sure that you save your work (in the menubar, select _File_ → _Save and CheckPoint_)
#
# 5. You are allowed to submit an assignment multiple times, but only the most recent submission will be graded.
# ----
#
# ## Problem 2.3. Logistic Regression
#
# In this problem, we will fit a logistic regression model on day of the week and air carriers to predict whether a flight is delayed or not.
# In[1]:
get_ipython().magic('matplotlib inline')
import numpy as np
import pandas as pd
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns
import statsmodels
import statsmodels.api as sm
from nose.tools import assert_equal
from numpy.testing import assert_array_equal, assert_array_almost_equal
from pandas.util.testing import assert_frame_equal
sns.set(style="white", font_scale=2.0)
# We will use the columns `DayOfWeek` and `UniqueCarrier` as attributes and `DepDelay` as the target prediction. For simplicity, we will only use the flights that departed from O'Hare.
# In[2]:
filename = '/home/data_scientist/data/2001.csv'
usecols = (3, 8, 15, 17)
columns = ['DayOfWeek', 'UniqueCarrier', 'DepDelay', 'Origin']
all_data = pd.read_csv(filename, header=0, na_values=['NA'], usecols=usecols, names=columns).dropna()
local = all_data.loc[all_data['Origin'] == 'ORD'].dropna()
# Let's print print out the first few columns.
#
# ```python
# >>> print(local.head())
# ```
#
# ```
# DayOfWeek UniqueCarrier DepDelay Origin
# 1855 2 US -1 ORD
# 1856 3 US -4 ORD
# 1857 4 US -3 ORD
# 1858 5 US -3 ORD
# 1859 6 US -4 ORD
# ```
# In[3]:
print(local.head())
# We will using logistic regression on the `DayOfWeek` and `UniqueCarrier` columns to predict whether a flight is delayed or not. However, logistic regression is for predicting **binary** outcomes and `DepDelay` is not binary. So our first task will be to convert this column into binary numbers.
#
# ## Convert DepDelay to binary
#
# - Write a function named `convert_to_binary()` that converts a specific column of a DataFrame into 0's or 1's using the `cutoff` parameter. See the function doctsring for more.
# - It actually does not matter whether 0's or 1's are integers or floats, but to pass assertion tests, make sure that your 0's and 1's are **integers** for all parts of this notebook unless otherwise required.
# In[4]:
def convert_to_binary(df, column, cutoff):
'''
Converts one column in Pandas.DataFrame "df" into binary
as a new column, and returns the new DataFrame ("df" plus new binary column).
Note that "df" should NOT be altered.
The returned DataFrame has one more column than "df".
The name of this column is in the form "column_binary".
For example, if "column" is "DepDelay", the name of the extra column
in the returned DataFrame is "DepDelay_binary".
We assume that df[column] contains only ints or floats.
If df[column] < cutoff, df[column_binary] is 0.
If df[column] >= cutoff, df[column_binary] is 1.
Parameters
----------
df: A Pandas.DataFrame.
column: A string.
cutoff: An int.
Returns
-------
A Pandas.DataFrame.
'''
#Creates a copy of df so it doesn't get altered
result=df.copy()
#Changes type of column to int
result[column]=result[column].astype(int)
#If entry is less than cutoff, then the entry in the new column is 0. Else, it is 1.
result[column+'_binary']=(result[column]>=cutoff).astype(int)
return result
# We will define a flight to be late if its departure delay is more than or equal to 5 minutes, and on-time if its departure delay is less than 5 minutes.
#
# ```python
# >>> local = convert_to_binary(local, 'DepDelay', 5)
# >>> print(local.tail(10))
# ```
#
# ```
# DayOfWeek UniqueCarrier DepDelay Origin DepDelay_binary
# 5960735 6 DL 4 ORD 0
# 5960736 7 DL 7 ORD 1
# 5960737 1 DL -2 ORD 0
# 5960738 2 DL -3 ORD 0
# 5960739 3 DL 0 ORD 0
# 5960740 4 DL 58 ORD 1
# 5960741 5 DL 1 ORD 0
# 5960742 6 DL 0 ORD 0
# 5960743 7 DL -8 ORD 0
# 5960744 1 DL -3 ORD 0
# ```
# In[5]:
local = convert_to_binary(local, 'DepDelay', 5)
print(local.tail(10))
# Let's use some simple unit tests to see if the function works as expected.
# In[6]:
df0 = pd.DataFrame({
'a': list(range(-5, 5)),
'b': list(range(10))
})
test1 = convert_to_binary(df0, 'a', 0)
answer1 = df0.join(pd.DataFrame({'a_binary': [0] * 5 + [1] * 5}))
assert_frame_equal(test1, answer1)
test2 = convert_to_binary(df0, 'b', 4)
answer2 = df0.join(pd.DataFrame({'b_binary': [0] * 4 + [1] * 6}))
assert_frame_equal(test2, answer2)
# ## Convert categorical variables to dummy indicator variables
#
# `DayOfWeek` and `UniqueCarrier` are categorical variables, while we need binary indicator variables to perform logistic regression.
#
# - Use [pandas.get_dummies()](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.get_dummies.html) to write a function named `convert_to_dummy()` that transforms categorical variables into binary indicator variables.
# In[7]:
def convert_to_dummy(df, dummy_columns, keep_columns):
'''
Transforms categorical variables of dummy_columns into binary indicator variables.
Parameters
----------
df: A pandas.DataFrame
dummy_columns: A list of strings. Columns of df that are converted to dummies.
keep_columns: A list of strings. Columns of df that are kept in the result.
Returns
-------
A pandas.DataFrame
'''
#Dummifies the dummy columns and converts its type to int
result=pd.get_dummies(df[dummy_columns],columns=dummy_columns).astype(int)
#Joins the keep columns from the old dataframe
result=df[keep_columns].join(result)
return result
# Now we should have only binary indicators in all columns.
#
# ```python
# >>> data = add_dummy(local, add_columns=['DayOfWeek', 'UniqueCarrier'], keep_columns=['DepDelay_binary'])
# >>> print(data.head())
# ```
#
# ```
# DepDelay_binary DayOfWeek_1 DayOfWeek_2 DayOfWeek_3 DayOfWeek_4 \
# 1855 0 0 1 0 0
# 1856 0 0 0 1 0
# 1857 0 0 0 0 1
# 1858 0 0 0 0 0
# 1859 0 0 0 0 0
#
# DayOfWeek_5 DayOfWeek_6 DayOfWeek_7 UniqueCarrier_AA \
# 1855 0 0 0 0
# 1856 0 0 0 0
# 1857 0 0 0 0
# 1858 1 0 0 0
# 1859 0 1 0 0
#
# UniqueCarrier_AS UniqueCarrier_CO UniqueCarrier_DL UniqueCarrier_HP \
# 1855 0 0 0 0
# 1856 0 0 0 0
# 1857 0 0 0 0
# 1858 0 0 0 0
# 1859 0 0 0 0
#
# UniqueCarrier_MQ UniqueCarrier_NW UniqueCarrier_TW UniqueCarrier_UA \
# 1855 0 0 0 0
# 1856 0 0 0 0
# 1857 0 0 0 0
# 1858 0 0 0 0
# 1859 0 0 0 0
#
# UniqueCarrier_US
# 1855 1
# 1856 1
# 1857 1
# 1858 1
# 1859 1
# ```
# In[8]:
data = convert_to_dummy(local, dummy_columns=['DayOfWeek', 'UniqueCarrier'], keep_columns=['DepDelay_binary'])
print(data.head())
# In[9]:
df0 = pd.DataFrame({
'a': ['a'] * 3,
'b': [1] * 3,
'c': [c for c in 'abc'],
'd': list(range(3))
})
test1 = convert_to_dummy(df0, dummy_columns=['c'], keep_columns=['a'])
answer1 = pd.DataFrame({
'a': ['a'] * 3,
'c_a': [1, 0, 0], 'c_b': [0, 1, 0], 'c_c': [0, 0, 1]
})
assert_frame_equal(test1, answer1)
test2 = convert_to_dummy(df0, dummy_columns=['c', 'd'], keep_columns=['b'])
answer2 = pd.DataFrame({
'b': [1] * 3,
'c_a': [1, 0, 0], 'c_b': [0, 1, 0], 'c_c': [0, 0, 1],
'd_0': [1, 0, 0], 'd_1': [0, 1, 0], 'd_2': [0, 0, 1]
})
assert_frame_equal(test2, answer2)
# ## Add intercept
#
# The [Logit()](http://statsmodels.sourceforge.net/0.6.0/generated/statsmodels.discrete.discrete_model.Logit.html) function doesn't include intercept by default and we have to manualy add the intercept.
#
# - Write a function named `add_intercept()` that adds an extra column named `Intercept` with all 1's.
# In[10]:
def add_intercept(df):
'''
Appends to "df" an "Intercept" column whose values are all 1.0.
Note that "df" should NOT be altered.
Parameters
----------
df: A pandas.DataFrame
Returns
-------
A pandas.DataFrame
'''
#Creates a copy of df so it doesn't get altered
result=df.copy()
#Sets the intercept to 1
result['Intercept']=1
return result
# Let's check if there is now an `Intercept` column.
#
# ```python
# >>> data = add_intercept(data)
# >>> print(data['Intercept'].head())
# ```
#
# ```
# 1855 1
# 1856 1
# 1857 1
# 1858 1
# 1859 1
# Name: Intercept, dtype: int64
# ```
# In[11]:
data = add_intercept(data)
print(data['Intercept'].head())
# In[12]:
df0 = pd.DataFrame({'a': [c for c in 'abcde']})
test1 = add_intercept(df0)
answer1 = df0.join(pd.DataFrame({'Intercept': [1] * 5}))
assert_frame_equal(test1, answer1)
# ## Function: fit\_logistic()
#
# - Use statsmodels [Logit()](http://blog.yhat.com/posts/logistic-regression-and-python.html) to fit a logistic regression model to the columns in `train_columns`. Use (non-regularized) maximum likelihood with the default parameters (no optional parameters).
# In[13]:
def fit_logitistic(df, train_columns, test_column):
'''
Fits a logistic regression model on "train_columns" to predict "test_column".
The function returns a tuple of (model ,result).
"model" is an instance of Logit(). "result" is the result of Logit.fit() method.
Parameters
----------
train_columns: A list of strings
test_column: A string
Returns
-------
A tuple of (model, result)
model: An object of type statsmodels.discrete.discrete_model.Logit
result: An object of type statsmodels.discrete.discrete_model.BinaryResultsWrapper
'''
#Creates a logistical model
model=sm.Logit(df[test_column], df[train_columns])
#Creates the fit for the model
result=model.fit()
return model, result
# Note that we exclude `DayOfWeek_1` and `UniqueCarrier_AA` from our fit to prevent [multicollinearity](https://en.wikipedia.org/wiki/Multicollinearity#Remedies_for_multicollinearity).
#
# ```python
# >>> model, result = fit_logitistic(data, train_columns=train_columns, test_column='DepDelay_binary')
# ```
#
# ```
# Optimization terminated successfully.
# Current function value: 0.589094
# Iterations 5
# ```
#
# ```python
# >>> print(result.summary())
# ```
#
# ```
# Logit Regression Results
# ==============================================================================
# Dep. Variable: DepDelay_binary No. Observations: 321227
# Model: Logit Df Residuals: 321211
# Method: MLE Df Model: 15
# Date: Thu, 21 Jan 2016 Pseudo R-squ.: 0.005735
# Time: 22:05:38 Log-Likelihood: -1.8923e+05
# converged: True LL-Null: -1.9032e+05
# LLR p-value: 0.000
# ====================================================================================
# coef std err z P>|z| [95.0% Conf. Int.]
# ------------------------------------------------------------------------------------
# DayOfWeek_2 -0.1574 0.015 -10.479 0.000 -0.187 -0.128
# DayOfWeek_3 0.0164 0.015 1.113 0.266 -0.012 0.045
# DayOfWeek_4 0.2148 0.014 14.911 0.000 0.187 0.243
# DayOfWeek_5 0.2059 0.014 14.274 0.000 0.178 0.234
# DayOfWeek_6 0.0229 0.015 1.514 0.130 -0.007 0.053
# DayOfWeek_7 0.1085 0.015 7.397 0.000 0.080 0.137
# UniqueCarrier_AS -0.3596 0.134 -2.679 0.007 -0.623 -0.096
# UniqueCarrier_CO -0.0101 0.030 -0.339 0.735 -0.069 0.048
# UniqueCarrier_DL 0.5507 0.024 22.889 0.000 0.504 0.598
# UniqueCarrier_HP 0.8619 0.039 22.121 0.000 0.786 0.938
# UniqueCarrier_MQ 0.0906 0.012 7.502 0.000 0.067 0.114
# UniqueCarrier_NW 0.2597 0.025 10.572 0.000 0.212 0.308
# UniqueCarrier_TW 0.3749 0.036 10.343 0.000 0.304 0.446
# UniqueCarrier_UA 0.1901 0.010 19.987 0.000 0.172 0.209
# UniqueCarrier_US 0.2573 0.027 9.632 0.000 0.205 0.310
# Intercept -1.1426 0.012 -94.960 0.000 -1.166 -1.119
# ====================================================================================
# ```
# In[14]:
train_columns = [ ### 'DayofWeek_1' # do not include this
'DayOfWeek_2', 'DayOfWeek_3', 'DayOfWeek_4',
'DayOfWeek_5', 'DayOfWeek_6', 'DayOfWeek_7',
### 'UniqueCarrierAA' # do not include this
'UniqueCarrier_AS', 'UniqueCarrier_CO', 'UniqueCarrier_DL',
'UniqueCarrier_HP', 'UniqueCarrier_MQ', 'UniqueCarrier_NW',
'UniqueCarrier_TW', 'UniqueCarrier_UA', 'UniqueCarrier_US',
'Intercept'
]
model, result = fit_logitistic(data, train_columns=train_columns, test_column='DepDelay_binary')
# In[15]:
print(result.summary())
# In[16]:
assert_equal(isinstance(model, statsmodels.discrete.discrete_model.Logit), True)
assert_equal(isinstance(result, statsmodels.discrete.discrete_model.BinaryResultsWrapper), True)
assert_equal(model.exog_names, train_columns)
assert_equal(model.endog_names, 'DepDelay_binary')
assert_array_equal(model.exog, data[train_columns].values)
assert_array_equal(model.endog, data['DepDelay_binary'].values)
test_conf_int = result.conf_int()
answer_conf_int = pd.DataFrame(
index=train_columns,
data={
0: np.array([
-0.18681953, -0.01247828, 0.18652782, 0.17760447, -0.00675086,
0.07974488, -0.6227236 , -0.06873794, 0.50352299, 0.78551841,
0.06694527, 0.21153022, 0.30383117, 0.17150234, 0.20497387,
-1.166157 ]),
1: np.array([
-0.12794527, 0.04524193, 0.24298324, 0.23413964, 0.05254801,
0.13724129, -0.09649653, 0.04848345, 0.59783265, 0.93824414,
0.11429806, 0.30780938, 0.44591082, 0.20879553, 0.30969833,
-1.11899193])
}
)
assert_frame_equal(test_conf_int, answer_conf_int)
# We see that the probability of flights being delayed is higher on Thursdays (`DayOfWeek_4`) and Fridays(`DayOfWeek_5`). In terms of carriers, `HP` an `MQ` airlines are more likely to be delayed than others.
#
# Does this result make sense? Let calculate the mean of `DepDelay` for each day of the week. We see that Thursday and Friday have the highest mean values.
#
# ```python
# >>> print(local.groupby('DayOfWeek').mean().sort_values(by='DepDelay', ascending=False))
# ```
#
# ```
# DepDelay DepDelay_binary
# DayOfWeek
# 4 11.419251 0.311135
# 5 11.306297 0.309324
# 7 10.244282 0.288786
# ```
# In[17]:
print(local.groupby('DayOfWeek').mean().sort_values(by='DepDelay', ascending=False))
# We can do the same for `UniqueCarrier`, and HP and DL airline indeed have the highest mean departure delay.
#
# ```python
# >>> print(local.groupby('UniqueCarrier').mean().sort_values(by='DepDelay', ascending=False))
# ```
#
# ```
# DayOfWeek DepDelay DepDelay_binary
# UniqueCarrier
# HP 3.973684 18.245494 0.444845
# DL 3.972141 11.719453 0.370235
# UA 3.953615 11.027225 0.291036
# ```
# In[18]:
print(local.groupby('UniqueCarrier').mean().sort_values(by='DepDelay', ascending=False))
# In[ ]: