A Simple Linear Regression Example

Based on the historical data, a company is trying to decide between developping their Website or their mobile App to make the user experience more enjoyable and profitable.

For this purpose, we can perform a machine learning method called linear regression in order to find the answer.

Getting to know the Data

In [1]:
# Import of library
import pandas as pd
In [2]:
# Reading the historical data
data = pd.read_csv("data.csv")
In [3]:
# finding out how many rows and columns are in the dataframe
data.shape
Out[3]:
(500, 6)
In [4]:
# Looking at the first rows of our dataframe
data.head()
Out[4]:
ID Avg. Session Length Time on App Time on Website Length of Membership Yearly Amount Spent
0 1 34.497268 12.655651 39.577668 4.082621 587.951054
1 2 31.926272 11.109461 37.268959 2.664034 392.204933
2 3 33.000915 11.330278 37.110597 4.104543 487.547505
3 4 34.305557 13.717514 36.721283 3.120179 581.852344
4 5 33.330673 12.795189 37.536653 4.446308 599.406092

As we can see data of the company, each row representing a single client with the following information:

  • Avg. Session Length: The average session of in-store style advice sessions
  • Time on App: The average time that was spent on the App in minutes
  • Time on Website: Average time spent on the Website in minutes
  • Length of Membership: How many years the client has been a member
  • Yearly Amount Spent: The amount spent per year
In [5]:
# Looking at the last lines of our dataframe
data.tail()
Out[5]:
ID Avg. Session Length Time on App Time on Website Length of Membership Yearly Amount Spent
495 496 33.237660 13.566160 36.417985 3.746573 573.847438
496 497 34.702529 11.695736 37.190268 3.576526 529.049004
497 498 32.646777 11.499409 38.332576 4.958264 551.620145
498 499 33.322501 12.391423 36.840086 2.336485 456.469510
499 500 33.715981 12.418808 35.771016 2.735160 497.778642
In [6]:
# Droping the ID column since it is irrelevant for the anlysis
data.drop('ID', 1,inplace=True)
In [7]:
# Getting an overview of our data
data.describe()
Out[7]:
Avg. Session Length Time on App Time on Website Length of Membership Yearly Amount Spent
count 500.000000 500.000000 500.000000 500.000000 500.000000
mean 33.053194 12.052488 37.060445 3.533462 499.314038
std 0.992563 0.994216 1.010489 0.999278 79.314782
min 29.532429 8.508152 33.913847 0.269901 256.670582
25% 32.341822 11.388153 36.349257 2.930450 445.038277
50% 33.082008 11.983231 37.069367 3.533975 498.887875
75% 33.711985 12.753850 37.716432 4.126502 549.313828
max 36.139662 15.126994 40.005182 6.922689 765.518462
In [8]:
# Making sure there is no NaN
data.isnull().values.any()
Out[8]:
False

Exploring the Data

We will take a close look at the time spent on both the App and the Website keeping in mind that: a large amount of spent time on one will hint to more business, meaning a wise choice of development and investement on the platform.

For the exploratory process we will use Plotly and Cufflinks which will allow us to create interactive plots.

The libraries can be installed by typing into your command line/terminal:

pip install plotly
pip install cufflinks
In [24]:
import plotly.plotly as py
import plotly.figure_factory as ff
import cufflinks as cf
from plotly import __version__
from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot
init_notebook_mode(connected=True)
cf.go_offline()
print(__version__)

IOPub data rate exceeded.
The notebook server will temporarily stop sending output
to the client in order to avoid crashing it.
To change this limit, set the config variable
`--NotebookApp.iopub_data_rate_limit`.

2.4.1
In [12]:
# Plotting "Time on App" against "Yearly Amount Spent"
data.iplot(kind='scatter',x='Time on App',y='Yearly Amount Spent',mode='markers',size=10,color="green")
In [13]:
# Plotting "Time on Website" against "Yearly Amount Spent"
data.iplot(kind='scatter',x='Time on Website',y='Yearly Amount Spent',mode='markers',size=10,color="green")
In [14]:
fig = ff.create_scatterplotmatrix(data, height=1000, width=900)
iplot(fig, filename='Scatterplot Matrix')

From the previous plot, we can clearly notice a correlation between the "Yearly Amount Spent" and "Length of Membership".

Training and Testing the Data

Now, we can move on to linear regression, but first, we should define our dependent variable Y, and then split our data into training and testing to perfom the machine learning.

In [15]:
# Y variable
Y = data['Yearly Amount Spent']
In [16]:
# X : The remaining features 
X = data[['Avg. Session Length', 'Time on App','Time on Website', 'Length of Membership']]
In [17]:
# Splitting data into training set and testing set using sklearn
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.33)
In [18]:
# Training the model
from sklearn.linear_model import LinearRegression
lm = LinearRegression()
lm.fit(X_train,y_train)
Out[18]:
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)
In [19]:
# Testing the model
predictions = lm.predict(X_test)
In [20]:
# Ploting Test against Predicted
import matplotlib.pyplot as plt
%matplotlib inline
plt.scatter(y_test,predictions, color="green")
plt.xlabel('Y Test')
plt.ylabel('Predictions')
Out[20]:
Text(0,0.5,'Predictions')

Evaluating the Model

The model can be evaluated using sklearn metrics, by calculating the following:

MAE : Mean Absolute Error

MSE : Mean Squared Error

RMSE : Root Mean Squared Error

In [21]:
# Calculating Metrics
import numpy as np
from sklearn import metrics

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)))

MAE: 7.3404264542
MSE: 81.5723932569
RMSE: 9.03174364433

Final Thoughts

We will take a look at the coefficients and see what we can learn from them.

In [22]:
# Calculating Coeffecients
coeffecients = pd.DataFrame(lm.coef_,X.columns)
coeffecients.columns = ['Coeffecient']
coeffecients
Out[22]:
Coeffecient
Avg. Session Length 25.491100
Time on App 38.857608
Time on Website 0.385880
Length of Membership 61.773266

If we compare App vs. Website, we can clearly see that the easy way is investing on developping the App. This choice will be more reasonable to bring more success to the company. In the other hand, the Website can use some attention in order to make it more profitable, and ideas from the accumulated App experience can be used to have a strong user experience from the Website.