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Linear Regression Project

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 pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

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

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

In [3]:
customers.head()
Out[3]:
In [4]:
customers.describe()
Out[4]:
In [5]:
customers.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 500 entries, 0 to 499 Data columns (total 8 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 Email 500 non-null object 1 Address 500 non-null object 2 Avatar 500 non-null object 3 Avg. Session Length 500 non-null float64 4 Time on App 500 non-null float64 5 Time on Website 500 non-null float64 6 Length of Membership 500 non-null float64 7 Yearly Amount Spent 500 non-null float64 dtypes: float64(5), object(3) memory usage: 31.4+ 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 [6]:
sns.set_palette("GnBu_d")
sns.set_style('whitegrid')
In [7]:
sns.jointplot(x='Time on Website',y='Yearly Amount Spent',data=customers)
Out[7]:
<seaborn.axisgrid.JointGrid at 0x1dffe4d7430>
Notebook Image

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

In [8]:
sns.jointplot(x='Time on App',y='Yearly Amount Spent',data=customers)
Out[8]:
<seaborn.axisgrid.JointGrid at 0x1dffe676ee0>
Notebook Image

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

In [9]:
sns.jointplot(x="Time on App", y="Length of Membership", kind="hex", data=customers)
Out[9]:
<seaborn.axisgrid.JointGrid at 0x1dffe7ec610>
Notebook Image
In [27]:
sns.jointplot(x="Time on Website", y="Length of Membership", kind="hex", data=customers)
Out[27]:
<seaborn.axisgrid.JointGrid at 0x1dfff4fc2e0>
Notebook Image

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 [10]:
sns.pairplot(customers)
Out[10]:
<seaborn.axisgrid.PairGrid at 0x1dffe9335b0>
Notebook Image

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

In [11]:
#Length of Membership

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

In [12]:
sns.lmplot(x='Length of Membership',y='Yearly Amount Spent',data=customers)
Out[12]:
<seaborn.axisgrid.FacetGrid at 0x1dfff490040>
Notebook Image

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 [13]:
customers.columns
Out[13]:
Index(['Email', 'Address', 'Avatar', 'Avg. Session Length', 'Time on App',
       'Time on Website', 'Length of Membership', 'Yearly Amount Spent'],
      dtype='object')
In [14]:
X = customers[['Avg. Session Length', 'Time on App','Time on Website', 'Length of Membership']]
In [15]:
y = customers['Yearly Amount Spent']

** 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()

Print out the coefficients of the model

In [21]:
# The coefficients
print('Coefficients: \n', lm.coef_)
Coefficients: [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(y_test, predictions)
Out[23]:
<matplotlib.collections.PathCollection at 0x1dfa102bb50>
Notebook Image

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
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: 7.228148653430837 MSE: 79.81305165097459 RMSE: 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 0x1dfa1082130>
Notebook Image

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]:
cdf = pd.DataFrame(lm.coef_,X.columns,columns=['Coeff'])
cdf.head()
Out[26]:

** How can you interpret these coefficients? **

Interpreting the coefficients:

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

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

This is tricky, there are two ways to think about this: Develop the Website to catch up to the performance of the mobile app, or develop the app more since that is what is working better. This sort of answer really depends on the other factors going on at the company, you would probably want to explore the relationship between Length of Membership and the App or the Website before coming to a conclusion!

Great Job!

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