Linear Regression - Project Exercise

Congratulations! You just got some contract work with an Ecommerce company based in New York City that sells clothing online but they also have in-store style and clothing advice sessions. Customers come in to the store, have sessions/meetings with a personal stylist, then they can go home and order either on a mobile app or website for the clothes they want.

The company is trying to decide whether to focus their efforts on their mobile app experience or their website. They've hired you on contract to help them figure it out! Let's get started!

Just follow the steps below to analyze the customer data (it's fake, don't worry I didn't give you real credit card numbers or emails).

Imports

Import pandas, numpy, matplotlib,and seaborn. Then set %matplotlib inline (You'll import sklearn as you need it.)

In [1]:
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
import warnings
warnings.filterwarnings('ignore')

Get the Data

We'll work with the Ecommerce Customers csv file from the company. It has Customer info, suchas Email, Address, and their color Avatar. Then it also has numerical value columns:

  • Avg. Session Length: Average session of in-store style advice sessions.
  • Time on App: Average time spent on App in minutes
  • Time on Website: Average time spent on Website in minutes
  • Length of Membership: How many years the customer has been a member.

Read in the Ecommerce Customers csv file as a DataFrame called customers.

In [3]:
customers = pd.read_csv('Ecommerce Customers')

Check the head of customers, and check out its info() and describe() methods.

In [4]:
customers.head()
Out[4]:
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 [5]:
customers.describe()
Out[5]:
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 [6]:
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

Let's explore the data!

For the rest of the exercise we'll only be using the numerical data of the csv file.

Use seaborn to create a jointplot to compare the Time on Website and Yearly Amount Spent columns. Does the correlation make sense?

In [7]:
sns.set_palette("GnBu_d")
sns.set_style('whitegrid')
In [8]:
sns.jointplot(x = 'Time on Website', y = 'Yearly Amount Spent', data = customers)
Out[8]:
<seaborn.axisgrid.JointGrid at 0x106b39160>

Do the same but with the Time on App column instead.

In [9]:
sns.jointplot(x = 'Time on App', y = 'Yearly Amount Spent', data = customers)
Out[9]:
<seaborn.axisgrid.JointGrid at 0x106b390b8>

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

In [10]:
sns.jointplot(x = 'Time on App', y = 'Length of Membership', data = customers, kind = 'hex')
Out[10]:
<seaborn.axisgrid.JointGrid at 0x106b32fd0>

Let's explore these types of relationships across the entire data set. Use pairplot to recreate the plot below.(Don't worry about the the colors)

In [11]:
sns.pairplot(customers)
Out[11]:
<seaborn.axisgrid.PairGrid at 0x10ce8f400>

Based off this plot what looks to be the most correlated feature with Yearly Amount Spent?

In [12]:
sns.heatmap(customers.corr(), cmap="Blues", annot=True)
Out[12]:
<matplotlib.axes._subplots.AxesSubplot at 0x106ae5278>

Create a linear model plot (using seaborn's lmplot) of Yearly Amount Spent vs. Length of Membership.

In [13]:
sns.lmplot(x = 'Length of Membership', y = 'Yearly Amount Spent', data = customers)
Out[13]:
<seaborn.axisgrid.FacetGrid at 0x10df7b748>

Training and Testing Data

Now that we've explored the data a bit, let's go ahead and split the data into training and testing sets. Set a variable X equal to the numerical features of the customers and a variable y equal to the "Yearly Amount Spent" column.

In [14]:
X = customers[['Avg. Session Length', 'Time on App', 'Time on Website', 'Length of Membership']]
X.head()
Out[14]:
Avg. Session Length Time on App Time on Website Length of Membership
0 34.497268 12.655651 39.577668 4.082621
1 31.926272 11.109461 37.268959 2.664034
2 33.000915 11.330278 37.110597 4.104543
3 34.305557 13.717514 36.721283 3.120179
4 33.330673 12.795189 37.536653 4.446308
In [15]:
y = customers['Yearly Amount Spent']
y.head()
Out[15]:
0    587.951054
1    392.204933
2    487.547505
3    581.852344
4    599.406092
Name: Yearly Amount Spent, dtype: float64

Use model_selection.train_test_split from sklearn to split the data into training and testing sets. Set test_size=0.3 and random_state=101

In [16]:
from sklearn.model_selection import train_test_split
In [17]:
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=101)

Training the Model

Now its time to train our model on our training data!

Import LinearRegression from sklearn.linear_model

In [18]:
from sklearn.linear_model import LinearRegression

Create an instance of a LinearRegression() model named lm.

In [19]:
lm = LinearRegression()

Train/fit lm on the training data.

In [20]:
lm.fit(X_train,y_train)
Out[20]:
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)

Print out the coefficients of the model

In [21]:
lm.coef_
Out[21]:
array([25.98154972, 38.59015875,  0.19040528, 61.27909654])

Predicting Test Data

Now that we have fit our model, let's evaluate its performance by predicting off the test values!

Use lm.predict() to predict off the X_test set of the data.

In [22]:
predictions = lm.predict(X_test)

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

In [23]:
plt.scatter(x = y_test, y = predictions)
plt.xlabel('Y Test')
plt.ylabel('Predicted Y')
Out[23]:
Text(0,0.5,'Predicted Y')

Evaluating the Model

Let's evaluate our model performance by calculating the residual sum of squares and the explained variance score (R^2).

Calculate the Mean Absolute Error, Mean Squared Error, and the Root Mean Squared Error. Refer to the lecture or to Wikipedia for the formulas

In [24]:
from sklearn import metrics
from math import sqrt

print('MAE:', 
      metrics.mean_absolute_error(y_test, predictions), ' ',
      (1./len(y_test))*(sum(abs(y_test-predictions))))
print('MSE:', 
      metrics.mean_squared_error(y_test, predictions), ' ',
      (1./len(y_test))*(sum((y_test-predictions)**2)))
print('RMSE:', 
      np.sqrt(metrics.mean_squared_error(y_test, predictions)), ' ',
      sqrt((1./len(y_test))*(sum((y_test-predictions)**2))))

MAE: 7.228148653430838   7.228148653430842
MSE: 79.81305165097457   79.81305165097456
RMSE: 8.93381506697864   8.93381506697864

Residuals

You should have gotten a very good model with a good fit. Let's quickly explore the residuals to make sure everything was okay with our data.

Plot a histogram of the residuals and make sure it looks normally distributed. Use either seaborn distplot, or just plt.hist().

In [25]:
sns.distplot((y_test-predictions), bins = 50)
Out[25]:
<matplotlib.axes._subplots.AxesSubplot at 0x10f06bcc0>

Conclusion

We still want to figure out the answer to the original question, do we focus our efforst on mobile app or website development? Or maybe that doesn't even really matter, and Membership Time is what is really important. Let's see if we can interpret the coefficients at all to get an idea.

Recreate the dataframe below.

In [26]:
df = pd.DataFrame( data = lm.coef_, columns = ['Coefficient'] ,index = X_train.columns)
df.head()
Out[26]:
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 other variables fixed, one unit of increase in:

  • Avg. Session Length increases the Yearly Amount Spent by 26 units
  • Time on App increases the Yearly Amount Spent by 39 units
  • Time on Website increases the Yearly Amount Spent by 0.2 units
  • Length of Membership increases the Yearly Amount Spent by 61 units

Do you think the company should focus more on their mobile app or on their website?

The Time on Website seems to have little influence on the Yearly Amount Spent, where as the Time on App show a stronger correlation. In that regard the revenue obtained through the App seems to be more important. However, instead of completely scraping the website, I guess the company can improve it to increase its revenue on that channel as well. Then, re-perform the analysis. Having said that, the most important variable that influence the spending is the Length of Membership.

Great Job!

Congrats on your contract work! The company loved the insights! Let's move on.