Chapter 5: Predicting Customer Revenue Using Linear Regression

Activity 8: Examining Relationships between Storefront Locations and Features about their Area

1. Load the data from location_rev.csv and then take a look at it:

   import pandas as pd
   
   df = pd.read_csv('location_rev.csv')
   df.head()

2. Use seaborn's pairplot function to visualize the data and its relationships:

   import seaborn as sns
   %matplotlib inline
   
   sns.pairplot(df)

3. Use correlations to investigate the relationship between the different variables and the location revenue:

   df.corr()

The resulting correlations should make sense. The more competitors in the area, the lower the revenue of a location, while the median income, loyalty members, and population density are all positively related. A location's age is also positively correlated with revenue, indicating that the longer a location is open, the better known it is and the more customers it attracts (or perhaps, only locations that do well last a long time).

Activity 9: Building a Regression Model to Predict Storefront Location Revenue

1. Import the data from location_rev.csv and view the first few rows:

   import pandas as pd
   df = pd.read_csv('location_rev.csv')
   df.head()

2. Create a variable, X, with the predictors in it, and store the outcome (revenue) in a separate variable, y:

   X = df[['num_competitors',
          'median_income',
          'num_loyalty_members',
          'population_density',
          'location_age'
          ]]
   y = df['revenue']

3. Split the data into training and test sets. Use random_state = 100:

   from sklearn.model_selection import train_test_split
   
   X_train, X_test, y_train, y_test = train_test_split(X, y, random_state = 100)

4. Create a linear regression model and fit it on the training data:

   from sklearn.linear_model import LinearRegression
   
   model = LinearRegression()
   model.fit(X_train,y_train)

5. Print out the model coefficients:

   model.coef_

6. Print out the model intercept:

   model.intercept_

7. Produce a prediction for a location that has 3 competitors; a median income of 30,000; 1,200 loyalty members; a population density of 2,000; and a location age of 10:

   single_location = pd.DataFrame({
       'num_competitors': [3],
       'median_income': [30000],
       'num_loyalty_members': [1200],
       'population_density': [2000],
       'location_age': [10]
   })
   
   model.predict(single_location)

8. Plot the model predictions versus the true values on the test data:

   import matplotlib.pyplot as plt
   %matplotlib inline
   
   plt.scatter(model.predict(X_test),y_test)
   plt.xlabel('Model Predictions')
   plt.ylabel('True Value')
   plt.plot([0, 100000], [0, 100000], 'k-', color = 'r')
   plt.show()

9. Calculate the correlation between the model predictions and the true values of the test data:

   from scipy.stats.stats import pearsonr
   
   pearsonr(model.predict(X_test),y_test)

The first number shows an extremely high correlation value (just over 0.9, where 1.0 would be a perfect correlation). The second number shows an extremely small p-value, indicating that it's very unlikely that this correlation is due to chance. Taken together, this indicates that our model is working very well on the test data.