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 [275]:

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 [276]:

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



In [277]:









    Out[277]:






  
    
      
      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 [278]:









    Out[278]:






  
    
      
      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 [279]:









    



<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 [280]:



In [281]:









    Out[281]:





<seaborn.axisgrid.JointGrid at 0x120bfcc88>

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



In [282]:









    Out[282]:





<seaborn.axisgrid.JointGrid at 0x132db5908>

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



In [283]:









    Out[283]:





<seaborn.axisgrid.JointGrid at 0x130edac88>

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 [284]:









    Out[284]:





<seaborn.axisgrid.PairGrid at 0x132fb3da0>

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



In [285]:

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



In [286]:









    Out[286]:





<seaborn.axisgrid.FacetGrid at 0x13538d0b8>

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 [287]:



In [288]:

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 [289]:



In [290]:

Training the Model

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

Import LinearRegression from sklearn.linear_model



In [291]:

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



In [292]:

Train/fit lm on the training data.



In [293]:









    Out[293]:





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

Print out the coefficients of the model



In [294]:









    



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 [295]:

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



In [296]:









    Out[296]:





<matplotlib.text.Text at 0x135546320>

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 [303]:









    



MAE: 7.22814865343
MSE: 79.813051651
RMSE: 8.93381506698

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 [317]:

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 [298]:









    Out[298]:






  
    
      
      Coeffecient
    
  
  
    
      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?

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

Answer here

Great Job!

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

	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

	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

	Coeffecient
Avg. Session Length	25.981550
Time on App	38.590159
Time on Website	0.190405
Length of Membership	61.279097