Case Study-1 Advertising Sales
Predict Sales Using Linear Regression: Advertising – Sales Problem
In this problem statement, the manager of a sales team wants to predict sales based on the monthly spending in different media such as TV, newspapers, and Radio. The data set contains monthly spent on TV, Radio, newspapers, and sales. By using multiple linear regression, you can build models using different features. We dive in and see how to predict sales using Linear Regression
Step1: Importing and Understanding Data.
import pandas as pd
# Importing advertising.csv
advertising_multi = pd.read_csv('advertising.csv')
# Looking at the first five rows
advertising_multi.head()
Output:
TV Radio Newspaper Sales
0 230.1 37.8 69.2 22.1
1 44.5 39.3 45.1 10.4
2 17.2 45.9 69.3 9.3
3 151.5 41.3 58.5 18.5
4 180.8 10.8 58.4 12.9Step2: Verify values and type of data. This method provides information about dataframe, dtype, and columns.
advertising_multi.info()
Output:
RangeIndex: 200 entries, 0 to 199
Data columns (total 4 columns):
TV 200 non-null float64
Radio 200 non-null float64
Newspaper 200 non-null float64
Sales 200 non-null float64
dtypes: float64(4)
memory usage: 6.3 KBStep3: Let’s look at some statistical information about the dataframe.
This is the way, a user can get some sense about the data if it is completely new to data.
advertising_multi.describe()
Output:
TV Radio Newspaper Sales
count 200.000000 200.000000 200.000000 200.000000
mean 147.042500 23.264000 30.554000 14.022500
std 85.854236 14.846809 21.778621 5.217457
min 0.700000 0.000000 0.300000 1.600000
25% 74.375000 9.975000 12.750000 10.375000
50% 149.750000 22.900000 25.750000 12.900000
75% 218.825000 36.525000 45.100000 17.400000
max 296.400000 49.600000 114.000000 27.000000 Step4: Visualising Data.
import matplotlib.pyplot as plt import seaborn as sns %matplotlib inline sns.pairplot(advertising_multi, x_vars=['TV','Radio','Newspaper'], y_vars='Sales',size=7, aspect=0.7, kind='scatter')
Output:
Step5: Splitting the Data for dependent and independent attributes.
# Putting feature variable to X X = advertising_multi[['TV','Radio','Newspaper']] # Putting response variable to y y = advertising_multi['Sales']
Step6 : Split X and y into X_train, X_test, y_train,y_test.
from sklearn.cross_validation import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.7, random_state=100)
Step7: Performing Linear Regression. Fit the model to the training data.
Here we have used the ‘Scikit’ library to predict sales using linear regression.
from sklearn.linear_model import LinearRegression lm = LinearRegression() # fit the model to the training data lm.fit(X_train,y_train)
Step8: Model Evaluation.
# print the intercept print(lm.intercept_)
Output:
2.65278966888Step9: Let’s see the coefficient.
coeff_df = pd.DataFrame(lm.coef_, X_test.columns, columns=['Coefficient']) coeff_df
Output:
Coefficient
TV 0.045426
Radio 0.189758
Newspaper 0.004603Step10: Predict using the model. Test your model with the test dataset.
# Making predictions using the model y_pred = lm.predict(X_test)
Step11: Calculating Error Terms.
from sklearn.metrics import mean_squared_error, r2_score
mse = mean_squared_error(y_test, y_pred)
r_squared = r2_score(y_test, y_pred)
print('Mean_Squared_Error :' ,mse)
print('r_square_value :',r_squared)
Output:
Mean_Squared_Error : 1.85068199416
r_square_value : 0.905862210753Training using Statsmodels Package:
Statsmodels is a python library that allows performing statistical analysis of data. You can use this to perform linear regression similar to the Scikit-learn library.
import statsmodels.api as sm X_train_sm = X_train #Unlike Sklearn, statsmodels don't automatically fit a constant, #so you need to use the method sm.add_constant(X) in order to add a constant. X_train_sm = sm.add_constant(X_train_sm) # Fit the data in one line lm_1 = sm.OLS(y_train,X_train_sm).fit() # print the coefficients lm_1.params
Output:
const 2.652790
TV 0.045426
Radio 0.189758
Newspaper 0.004603
dtype: float64Verify the details of the model.
print(lm_1.summary())
Output:
OLS Regression Results
==============================================================================
Dep. Variable: Sales R-squared: 0.893
Model: OLS Adj. R-squared: 0.890
Method: Least Squares F-statistic: 377.6
Date: Wed, 28 Feb 2018 Prob (F-statistic): 9.97e-66
Time: 18:17:05 Log-Likelihood: -280.83
No. Observations: 140 AIC: 569.7
Df Residuals: 136 BIC: 581.4
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 2.6528 0.384 6.906 0.000 1.893 3.412
TV 0.0454 0.002 27.093 0.000 0.042 0.049
Radio 0.1898 0.011 17.009 0.000 0.168 0.212
Newspaper 0.0046 0.008 0.613 0.541 -0.010 0.019
==============================================================================
Omnibus: 40.095 Durbin-Watson: 1.862
Prob(Omnibus): 0.000 Jarque-Bera (JB): 83.622
Skew: -1.233 Prob(JB): 6.94e-19
Kurtosis: 5.873 Cond. No. 443.
==============================================================================
If you notice at P-value, you can find the P-value of the Newspaper is very high which means the Newspaper attribute is insignificant.
Re-run the model :
Step12: Remove the Newspaper attribute from the dataframe.
# Removing Newspaper from our dataframe X_train_new = X_train[['TV','Radio']] X_test_new = X_test[['TV','Radio']] # Model building lm.fit(X_train_new,y_train) # Making predictions y_pred_new = lm.predict(X_test_new)
Step13: Now check the R-sq error and RMSE.
from sklearn.metrics import mean_squared_error, r2_score
mse = mean_squared_error(y_test, y_pred_new)
r_squared = r2_score(y_test, y_pred_new)
print('Mean_Squared_Error :' ,mse)
print('r_square_value :',r_squared)
Output:
Mean_Squared_Error : 1.78474005209
r_square_value : 0.909216449172Step14: Compare actual value vs predicted value.
#Actual vs Predicted
c = [i for i in range(1,61,1)]
fig = plt.figure()
plt.plot(c,y_test, color="blue", linewidth=2.5, linestyle="-")
plt.plot(c,y_pred, color="red", linewidth=2.5, linestyle="-")
fig.suptitle('Actual and Predicted', fontsize=20) # Plot heading
plt.xlabel('Index', fontsize=18) # X-label
plt.ylabel('Sales', fontsize=16) # Y-label
Output:
In this blog, you learned about how to predict sales using Linear Regression and follow this link to learn more about Linear Regression.
#Predict Sales Using Linear Regression
