Link to the previous post : https://statinfer.com/204-1-2-regression-in-python/

In the last post we went through concept of Regression. In this post we will try to implement and practice Linear regression.

Practice : Regression Line Fitting

Dataset: AirPassengers\AirPassengers.csv
Find the correlation between Promotion_Budget and Passengers
Draw a scatter plot between Promotion_Budget and Passengers. Is there any any pattern between Promotion_Budget and Passengers?
Build a linear regression model on Promotion_Budget and Passengers.
Build a regression line to predict the passengers using Inter_metro_flight_ratio

In [6]:

import pandas as pd
air = pd.read_csv("datasets\\AirPassengers\\AirPassengers.csv")
air.shape

Out[6]:

(80, 9)

In [7]:

air.columns.values

Out[7]:

array(['Week_num', 'Passengers', 'Promotion_Budget',
       'Service_Quality_Score', 'Holiday_week',
       'Delayed_Cancelled_flight_ind', 'Inter_metro_flight_ratio',
       'Bad_Weather_Ind', 'Technical_issues_ind'], dtype=object)

In [8]:

air.head(5)

Out[8]:

	Week_num	Passengers	Promotion_Budget	Service_Quality_Score	Holiday_week	Delayed_Cancelled_flight_ind	Inter_metro_flight_ratio	Bad_Weather_Ind	Technical_issues_ind
0	1	37824	517356	4.00000	NO	NO	0.70	YES	YES
1	2	43936	646086	2.67466	NO	YES	0.80	YES	YES
2	3	42896	638330	3.29473	NO	NO	0.90	NO	NO
3	4	35792	506492	3.85684	NO	NO	0.40	NO	NO
4	5	38624	609658	3.90757	NO	NO	0.87	NO	YES

In [9]:

# Find the correlation between Promotion_Budget and Passengers
import numpy as np
np.corrcoef(air.Passengers,air.Promotion_Budget)

Out[9]:

array([[ 1.        ,  0.96585103],
       [ 0.96585103,  1.        ]])

In [10]:

# Draw a scatter plot between   Promotion_Budget and Passengers. Is there any any pattern between Promotion_Budget and Passengers?

import matplotlib.pyplot as plt
%matplotlib inline 

plt.scatter(air.Passengers, air.Promotion_Budget)

Out[10]:

<matplotlib.collections.PathCollection at 0x90bda20>

In [11]:

#Build a linear regression model and estimate the expected passengers for a Promotion_Budget is 650,000
##Regression Model  promotion and passengers count

from sklearn.linear_model import LinearRegression
lr = LinearRegression()
lr.fit(air[["Promotion_Budget"]], air[["Passengers"]])
predictions = lr.predict(air[["Promotion_Budget"]])

In [12]:

import statsmodels.formula.api as sm
model = sm.ols(formula='Passengers ~ Promotion_Budget', data=air)
fitted1 = model.fit()

In [13]:

fitted1.summary()

Out[13]:

OLS Regression Results
Dep. Variable:	Passengers	R-squared:	0.933
Model:	OLS	Adj. R-squared:	0.932
Method:	Least Squares	F-statistic:	1084.
Date:	Wed, 27 Jul 2016	Prob (F-statistic):	1.66e-47
Time:	11:48:26	Log-Likelihood:	-751.34
No. Observations:	80	AIC:	1507.
Df Residuals:	78	BIC:	1511.
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[95.0% Conf. Int.]
Intercept	1259.6058	1361.071	0.925	0.358	-1450.078 3969.290
Promotion_Budget	0.0695	0.002	32.923	0.000	0.065 0.074

Omnibus:	26.624	Durbin-Watson:	1.831
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5.188
Skew:	-0.128	Prob(JB):	0.0747
Kurtosis:	1.779	Cond. No.	2.67e+06

In [14]:

# Build a regression line to predict the passengers using Inter_metro_flight_ratio

plt.scatter(air.Inter_metro_flight_ratio,air.Passengers)

Out[14]:

<matplotlib.collections.PathCollection at 0xb13f2b0>

In [15]:

import sklearn as sk

from sklearn.linear_model import LinearRegression
lr = LinearRegression()
lr.fit(air[["Inter_metro_flight_ratio"]], air[["Passengers"]])

Out[15]:

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

In [16]:

predictions = lr.predict(air[["Inter_metro_flight_ratio"]])

In [17]:

import statsmodels.formula.api as sm
model = sm.ols(formula='Passengers ~ Inter_metro_flight_ratio', data=air)
fitted2 = model.fit()

In [18]:

fitted2.summary()

Out[18]:

OLS Regression Results
Dep. Variable:	Passengers	R-squared:	0.242
Model:	OLS	Adj. R-squared:	0.232
Method:	Least Squares	F-statistic:	24.90
Date:	Wed, 27 Jul 2016	Prob (F-statistic):	3.58e-06
Time:	11:48:27	Log-Likelihood:	-848.30
No. Observations:	80	AIC:	1701.
Df Residuals:	78	BIC:	1705.
Df Model:	1
Covariance Type:	nonrobust

coef	std err	t	P>\|t\|	[95.0% Conf. Int.]
Intercept	2.044e+04	4993.747	4.093	0.000	1.05e+04 3.04e+04
Inter_metro_flight_ratio	3.507e+04	7027.768	4.990	0.000	2.11e+04 4.91e+04

Omnibus:	10.172	Durbin-Watson:	1.385
Prob(Omnibus):	0.006	Jarque-Bera (JB):	10.098
Skew:	0.822	Prob(JB):	0.00641
Kurtosis:	3.573	Cond. No.	9.48

The next post is on how good is my regression line.

Link to the next post : https://statinfer.com/204-1-4-how-good-is-my-regression-line/

204.1.3 Practice : Regression Line Fitting

Practice : Regression Line Fitting

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204.1.3 Practice : Regression Line Fitting

Practice : Regression Line Fitting

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