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.)

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In [1]:

import pandas as pd
import numpy, matplotlib.pyplot as plt
import seaborn as sns

%matplotlib inline

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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.

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In [2]:

customers = pd.read_csv('Ecommerce Customers')

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

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In [3]:

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Out[3]:

.dataframe thead tr:only-child th {
text-align: right;
}

.dataframe thead th {
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}

.dataframe tbody tr th {
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}

Email
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
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

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In [4]:

customers.describe()

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Out[4]:

.dataframe thead tr:only-child th {
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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

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In [5]:

customers.info()

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<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

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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?

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In [7]:

sns.jointplot(customers['Time on Website'], customers['Yearly Amount Spent'])

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Out[7]:

<seaborn.axisgrid.JointGrid at 0x111172390>

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

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In [8]:

sns.jointplot(customers['Time on App'], customers['Yearly Amount Spent'])

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Out[8]:

<seaborn.axisgrid.JointGrid at 0x10f46df98>

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

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In [9]:

sns.jointplot(customers['Time on App'], customers['Length of Membership'], kind='hex')

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Out[9]:

<seaborn.axisgrid.JointGrid at 0x107575ba8>

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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)

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In [10]:

sns.pairplot(data=customers)

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Out[10]:

<seaborn.axisgrid.PairGrid at 0x113bb9320>

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Atma: Inference from pairplot

• longer memberships - spend more. important to keep your regular memebers happy
• correlation bw time on app and purchases. Focus on app more. Keep website functional
• session length - not a strong correlation

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

Length of membership followed by time on app

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

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In [12]:

sns.lmplot('Length of Membership', 'Yearly Amount Spent', data=customers)

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Out[12]:

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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.

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In [13]:

customers.columns

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Out[13]:

Index(['Email', 'Address', 'Avatar', 'Avg. Session Length', 'Time on App',
'Time on Website', 'Length of Membership', 'Yearly Amount Spent'],
dtype='object')

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In [14]:

x = customers[['Avg. Session Length', 'Time on App',
'Time on Website', 'Length of Membership']]
y = customers['Yearly Amount Spent']

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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

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In [15]:

from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(x,y, test_size=0.3, random_state=101)

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In [17]:

x_train.shape

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Out[17]:

(350, 4)

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In [19]:

y_test.shape

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Out[19]:

(150,)

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Training the Model

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

Import LinearRegression from sklearn.linear_model

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In [3]:

from sklearn.linear_model import LinearRegression

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

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In [21]:

lm = LinearRegression()

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Train/fit lm on the training data.

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In [22]:

lm.fit(x_train, y_train)

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Out[22]:

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

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Print out the coefficients of the model

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In [23]:

lm.coef_

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Out[23]:

array([ 25.98154972,  38.59015875,   0.19040528,  61.27909654])

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In [24]:

pd.DataFrame(lm.coef_, index=x_train.columns, columns=['Coefficients'])

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Out[24]:

.dataframe thead tr:only-child th {
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Coefficients

Avg. Session Length
25.981550

Time on App
38.590159

Time on Website
0.190405

Length of Membership
61.279097

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In [25]:

lm.intercept_

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Out[25]:

-1047.9327822502385

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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.

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In [26]:

y_predicted = lm.predict(x_test)

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

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In [36]:

plt.scatter(y_test, y_predicted)
# plt.title='Fitted vs predicted'
plt.xlabel ='Fitted - yearly purchases'
plt.ylabel ='Predicted - yearly purchases'

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In [296]:

plt.scatter()

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Out[296]:

<matplotlib.text.Text at 0x135546320>

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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

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In [32]:

from sklearn.metrics import mean_absolute_error, mean_squared_error
import numpy as np

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In [33]:

print("MAE: " + str(mean_absolute_error(y_test, y_predicted)))
print("MSE: " + str(mean_squared_error(y_test, y_predicted)))
print("RMSE: " + str(np.sqrt(mean_squared_error(y_test, y_predicted))))

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MAE: 7.22814865343
MSE: 79.813051651
RMSE: 8.93381506698

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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().

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In [35]:

sns.distplot((y_test - y_predicted), bins=50)

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Out[35]:

<matplotlib.axes._subplots.AxesSubplot at 0x1169e7e80>

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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.

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In [298]:

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Out[298]:

Coeffecient

Avg. Session Length
25.981550

Time on App
38.590159

Time on Website
0.190405

Length of Membership
61.279097

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How can you interpret these coefficients?

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