Prerequisite: Understanding Logistic Regression
Logistic regression is the type of regression analysis used to find the probability of a certain event occurring. It is the best suited type of regression for cases where we have a categorical dependent variable which can take only discrete values.
The dataset :
In this article, we will predict whether a student will be admitted to a particular college, based on their gmat, gpa scores and work experience. The dependent variable here is a Binary Logistic variable, which is expected to take strictly one of two forms i.e., admitted or not admitted.
Building the Logistic Regression model :
Statsmodels is a Python module that provides various functions for estimating different statistical models and performing statistical tests
- First, we define the set of dependent(y) and independent(X) variables. If the dependent variable is in non-numeric form, it is first converted to numeric using dummies. The file used in the example for training the model, can be downloaded here.
- Statsmodels provides a Logit() function for performing logistic regression. The Logit() function accepts y and X as parameters and returns the Logit object. The model is then fitted to the data.
Python3
# importing librariesimport statsmodels.api as smimport pandas as pd # loading the training dataset df = pd.read_csv('logit_train1.csv', index_col = 0) # defining the dependent and independent variablesXtrain = df[['gmat', 'gpa', 'work_experience']]ytrain = df[['admitted']] # building the model and fitting the datalog_reg = sm.Logit(ytrain, Xtrain).fit() |
Output :
Optimization terminated successfully.
Current function value: 0.352707
Iterations 8
In the output, ‘Iterations‘ refer to the number of times the model iterates over the data, trying to optimize the model. By default, the maximum number of iterations performed is 35, after which the optimization fails.
The summary table :
The summary table below gives us a descriptive summary about the regression results.
Python3
# printing the summary tableprint(log_reg.summary()) |
Output :
Logit Regression Results
==============================================================================
Dep. Variable: admitted No. Observations: 30
Model: Logit Df Residuals: 27
Method: MLE Df Model: 2
Date: Wed, 15 Jul 2020 Pseudo R-squ.: 0.4912
Time: 16:09:17 Log-Likelihood: -10.581
converged: True LL-Null: -20.794
Covariance Type: nonrobust LLR p-value: 3.668e-05
===================================================================================
coef std err z P>|z| [0.025 0.975]
-----------------------------------------------------------------------------------
gmat -0.0262 0.011 -2.383 0.017 -0.048 -0.005
gpa 3.9422 1.964 2.007 0.045 0.092 7.792
work_experience 1.1983 0.482 2.487 0.013 0.254 2.143
===================================================================================
Explanation of some of the terms in the summary table:
- coef : the coefficients of the independent variables in the regression equation.
- Log-Likelihood : the natural logarithm of the Maximum Likelihood Estimation(MLE) function. MLE is the optimization process of finding the set of parameters that result in the best fit.
- LL-Null : the value of log-likelihood of the model when no independent variable is included(only an intercept is included).
- Pseudo R-squ. : a substitute for the R-squared value in Least Squares linear regression. It is the ratio of the log-likelihood of the null model to that of the full model.
Predicting on New Data :
Now we shall test our model on new test data. The test data is loaded from this csv file.
The predict() function is useful for performing predictions. The predictions obtained are fractional values(between 0 and 1) which denote the probability of getting admitted. These values are hence rounded, to obtain the discrete values of 1 or 0.
Python3
# loading the testing dataset df = pd.read_csv('logit_test1.csv', index_col = 0) # defining the dependent and independent variablesXtest = df[['gmat', 'gpa', 'work_experience']]ytest = df['admitted'] # performing predictions on the test datasetyhat = log_reg.predict(Xtest)prediction = list(map(round, yhat)) # comparing original and predicted values of yprint('Actual values', list(ytest.values))print('Predictions :', prediction) |
Output :
Optimization terminated successfully.
Current function value: 0.352707
Iterations 8
Actual values [0, 0, 0, 0, 0, 1, 1, 0, 1, 1]
Predictions : [0, 0, 0, 0, 0, 0, 0, 0, 1, 1]
Testing the accuracy of the model :
Python3
from sklearn.metrics import (confusion_matrix, accuracy_score) # confusion matrixcm = confusion_matrix(ytest, prediction) print ("Confusion Matrix : \n", cm) # accuracy score of the modelprint('Test accuracy = ', accuracy_score(ytest, prediction)) |
Output :
Confusion Matrix : [[6 0] [2 2]] Test accuracy = 0.8
