Linear Regression - Project Exercise

In this project, we are going to analyze customer data from an online store and decide whether or not this company should invest more on their website or mobile app, based on the customer behavior.

Imports


In [ ]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

Get the Data


In [2]:
customers =  pd.read_csv('Ecommerce Customers')

Checking the head of customers, and checking out its info() and describe() methods


In [3]:
customers.head()


Out[3]:
Email Address Avatar Avg. Session Length Time on App Time on Website Length of Membership Yearly Amount Spent
0 mstephenson@fernandez.com 835 Frank Tunnel\nWrightmouth, MI 82180-9605 Violet 34.497268 12.655651 39.577668 4.082621 587.951054
1 hduke@hotmail.com 4547 Archer Common\nDiazchester, CA 06566-8576 DarkGreen 31.926272 11.109461 37.268959 2.664034 392.204933
2 pallen@yahoo.com 24645 Valerie Unions Suite 582\nCobbborough, D... Bisque 33.000915 11.330278 37.110597 4.104543 487.547505
3 riverarebecca@gmail.com 1414 David Throughway\nPort Jason, OH 22070-1220 SaddleBrown 34.305557 13.717514 36.721283 3.120179 581.852344
4 mstephens@davidson-herman.com 14023 Rodriguez Passage\nPort Jacobville, PR 3... MediumAquaMarine 33.330673 12.795189 37.536653 4.446308 599.406092

In [4]:
customers.describe()


Out[4]:
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 [5]:
customers.info()


<class 'pandas.core.frame.DataFrame'>
RangeIndex: 500 entries, 0 to 499
Data columns (total 8 columns):
Email                   500 non-null object
Address                 500 non-null object
Avatar                  500 non-null object
Avg. Session Length     500 non-null float64
Time on App             500 non-null float64
Time on Website         500 non-null float64
Length of Membership    500 non-null float64
Yearly Amount Spent     500 non-null float64
dtypes: float64(5), object(3)
memory usage: 31.3+ KB

Exploratory Data Analysis

Creating a jointpolot with seaborn to compare user time on website and yearly amount spent. Is there any correlation?


In [6]:
sns.jointplot(x='Time on Website', y='Yearly Amount Spent', data=customers, color='green')


Out[6]:
<seaborn.axisgrid.JointGrid at 0xaff9358>

The same for time on app


In [7]:
sns.jointplot(x='Time on App', y='Yearly Amount Spent', data=customers, color='green')


Out[7]:
<seaborn.axisgrid.JointGrid at 0xaff9630>

Using jointplot to create a 2D hex bin plot comparing Time on App and Length of Membership


In [8]:
sns.jointplot(x='Time on App', y='Length of Membership', data=customers, kind='hex')


Out[8]:
<seaborn.axisgrid.JointGrid at 0xaff9518>

Using a pairplot to explore patterns in the entire dataset


In [9]:
sns.pairplot(customers)


Out[9]:
<seaborn.axisgrid.PairGrid at 0xc1c5eb8>

Length of membership seems to be the most correlated feature with Yearly Amount Spent

Creating a linear model plot of Yearly Amount Spent vs. Length of Membership


In [10]:
sns.lmplot(x='Length of Membership', y='Yearly Amount Spent', data=customers)


Out[10]:
<seaborn.axisgrid.FacetGrid at 0xc1fc1d0>

Training and Testing Data


In [ ]:
customers.columns

In [24]:
X = customers[['Avg. Session Length', 'Time on App', 'Time on Website', 'Length of Membership']]

In [25]:
y = customers['Yearly Amount Spent']

In [26]:
from sklearn.cross_validation import train_test_split

In [27]:
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=101)

Training the Model

Time to train our model on our training data!


In [28]:
from sklearn.linear_model import LinearRegression

In [29]:
lm = LinearRegression()

In [30]:
lm.fit(X_train, y_train)


Out[30]:
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)

Print out the coefficients of the model


In [31]:
print(lm.coef_)


[ 25.98154972  38.59015875   0.19040528  61.27909654]

Predicting Test Data


In [34]:
predictions = lm.predict(X_test)

In [35]:
predictions


Out[35]:
array([ 456.44186104,  402.72005312,  409.2531539 ,  591.4310343 ,
        590.01437275,  548.82396607,  577.59737969,  715.44428115,
        473.7893446 ,  545.9211364 ,  337.8580314 ,  500.38506697,
        552.93478041,  409.6038964 ,  765.52590754,  545.83973731,
        693.25969124,  507.32416226,  573.10533175,  573.2076631 ,
        397.44989709,  555.0985107 ,  458.19868141,  482.66899911,
        559.2655959 ,  413.00946082,  532.25727408,  377.65464817,
        535.0209653 ,  447.80070905,  595.54339577,  667.14347072,
        511.96042791,  573.30433971,  505.02260887,  565.30254655,
        460.38785393,  449.74727868,  422.87193429,  456.55615271,
        598.10493696,  449.64517443,  615.34948995,  511.88078685,
        504.37568058,  515.95249276,  568.64597718,  551.61444684,
        356.5552241 ,  464.9759817 ,  481.66007708,  534.2220025 ,
        256.28674001,  505.30810714,  520.01844434,  315.0298707 ,
        501.98080155,  387.03842642,  472.97419543,  432.8704675 ,
        539.79082198,  590.03070739,  752.86997652,  558.27858232,
        523.71988382,  431.77690078,  425.38411902,  518.75571466,
        641.9667215 ,  481.84855126,  549.69830187,  380.93738919,
        555.18178277,  403.43054276,  472.52458887,  501.82927633,
        473.5561656 ,  456.76720365,  554.74980563,  702.96835044,
        534.68884588,  619.18843136,  500.11974127,  559.43899225,
        574.8730604 ,  505.09183544,  529.9537559 ,  479.20749452,
        424.78407899,  452.20986599,  525.74178343,  556.60674724,
        425.7142882 ,  588.8473985 ,  490.77053065,  562.56866231,
        495.75782933,  445.17937217,  456.64011682,  537.98437395,
        367.06451757,  421.12767301,  551.59651363,  528.26019754,
        493.47639211,  495.28105313,  519.81827269,  461.15666582,
        528.8711677 ,  442.89818166,  543.20201646,  350.07871481,
        401.49148567,  606.87291134,  577.04816561,  524.50431281,
        554.11225704,  507.93347015,  505.35674292,  371.65146821,
        342.37232987,  634.43998975,  523.46931378,  532.7831345 ,
        574.59948331,  435.57455636,  599.92586678,  487.24017405,
        457.66383406,  425.25959495,  331.81731213,  443.70458331,
        563.47279005,  466.14764208,  463.51837671,  381.29445432,
        411.88795623,  473.48087683,  573.31745784,  417.55430913,
        543.50149858,  547.81091537,  547.62977348,  450.99057409,
        561.50896321,  478.30076589,  484.41029555,  457.59099941,
        411.52657592,  375.47900638])

Create a scatterplot of the real test values versus the predicted values.


In [39]:
plt.scatter(predictions, y_test)
plt.xlabel('Y test')
plt.ylabel('Predicted Y')


Out[39]:
<matplotlib.text.Text at 0xfac0f28>

Evaluating the Model


In [40]:
from sklearn import metrics

In [41]:
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:  7.22814865343
MSE:  79.813051651
RMSE:  8.93381506698

Residuals


In [46]:
sns.distplot((y_test - predictions), bins=50)


D:\Usuarios\westerley.reis\AppData\Local\Continuum\Anaconda3\lib\site-packages\statsmodels\nonparametric\kdetools.py:20: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  y = X[:m/2+1] + np.r_[0,X[m/2+1:],0]*1j
Out[46]:
<matplotlib.axes._subplots.AxesSubplot at 0x10dc84a8>

Conclusion

Do we focus our efforts on the app or on the development of the website?


In [47]:
df = pd.DataFrame(lm.coef_, X.columns, columns=['Coefficient'])

In [48]:
df


Out[48]:
Coefficient
Avg. Session Length 25.981550
Time on App 38.590159
Time on Website 0.190405
Length of Membership 61.279097

How can you interpret these coefficients?

  • Holding all the other features fixed, 1 unit increase in Avg. Session Length is associated with an increase of 25.98 total dollars spent.
  • Holding all the other features fixed, 1 unit increase in Time on App is associated with an increase of 38.59 total dollars spent.
  • Holding all the other features fixed, 1 unit increase in Time on Website is associated with an increase of 0.19 total dollars spent.
  • Holding all the other features fixed, 1 unit increase in Length of Membership is associated with an increase of 61.27 total dollars spent.

Should the company focus more on their mobile app or on their website?

There are 2 ways to think about this: Develop the website to catch up to the performance of the mobile app, or just develop the app more since that's what is working better. The answer to this question really depends on the company. As a Data Scientist, it's great to explore the relationship between the Length of Membership and Mobile App (or Website) before draw a conclusion.