Logistic Regression Model Application in Research

 

Logistic Regression Model for Bank loan Default Selection

A logit model (or logistic regression model) is a statistical method used to predict the probability of a binary outcome (like yes/no, success/failure) based on one or more independent variables. It transforms a linear combination of predictors into probabilities between 0 and 1 using the logistic function.

Example

Imagine a bank wants to predict whether a loan applicant will default:

• Dependent variable: Default (1 = yes, 0 = no)
• Independent variables: Income, credit score, age
• The logit model estimates how these factors influence the probability of default.

Let’s build a logit model example for predicting bank loan default using the three independent variables we mentioned: Income, Credit Score, and Age.

Example: Bank Default Prediction

Model Setup

• Dependent variable (Y): Default (1 = default, 0 = no default)
• Independent variables (X):
• (X_1): Income (in $1000s per month)
• (X_2): Credit Score (scaled 300–850)
• (X_3): Age (in years)

Example Calculation

For a borrower with:

• Income = 5 ($5000/month)
• Credit Score = 650
• Age = 40

The logit is: [ \text{logit}(p) = 2.0 + (-0.3)(5) + (-0.01)(650) + (0.05)(40) ] [ = 2.0 - 1.5 - 6.5 + 2.0 = -4.0 ]

Convert to probability: [ p = \frac{1}{1 + e^{-(-4.0)}} = \frac{1}{1 + e^{4.0}} \approx 0.018 ]

Probability of default ≈ 1.8%

Interpretation

• Income effect: Each extra $1000/month reduces odds of default by about 30%.
• Credit score effect: Each point increase reduces odds by ~1%.
• Age effect: Each year older increases odds by ~5%.

So, this borrower has a low risk of default given their decent income and moderate credit score.

simulate a small dataset (say 10 borrowers) and show how the logit model assigns different default probabilities across them?

Simulated Bank Default Probabilities

Borrower ID	Income ($1000s)	Credit Score	Age	Probability of Default
1	5.00	608	41	0.0285
2	9.61	643	63	0.0153
3	7.86	791	44	0.0023
4	6.79	713	68	0.0226
5	3.25	685	46	0.0286
6	3.25	491	61	0.3026
7	2.46	576	47	0.1045
8	8.93	460	35	0.0285
9	6.81	759	34	0.0026
10	7.66	613	66	0.0420

Insights

• Borrower 6 has the highest risk (30%) because of low income and very low credit score.
• Borrower 3 and 9 have very low risk (<0.3%) thanks to strong credit scores and decent income.
• Age effect: Older borrowers (like Borrower 10 at age 66) show slightly higher probabilities compared to younger ones with similar profiles.
• Income effect: Higher income generally reduces default risk (Borrower 2 with $9.61k/month has only 1.5% risk).
• Credit score effect: This is the strongest driver—low scores sharply increase default probability even if income is moderate.

Step‑by‑Step in SPSS GUI

1. Open your dataset
• Make sure your dependent variable (Default) is coded as 0 = No Default, 1 = Default.
• Independent variables: Income, CreditScore, Age.
2. Navigate to Logistic Regression
• Click on Analyze in the top menu.
• Go to Regression → Binary Logistic…
3. Select the Dependent Variable
• In the dialog box, move Default into the Dependent field.
4. Select the Independent Variables
• Move Income, CreditScore, and Age into the Covariates field.
5. Choose Method
• By default, SPSS uses Enter (all predictors entered at once).
• You can also choose Forward or Backward stepwise methods if you want SPSS to select variables automatically.
6. Set Options (Optional)
• Click Options… to request classification tables, Hosmer-Lemeshow test, confidence intervals, etc.
• Click Save… if you want SPSS to generate predicted probabilities or group membership for each case.
7. Run the Analysis
• Click OK to run the logistic regression.

SPSS Output

• Omnibus Test of Model Coefficients → checks if predictors improve the model.
• Model Summary → −2 Log Likelihood, Cox & Snell R², Nagelkerke R².
• Classification Table → how well the model predicts default vs no default.
• Variables in the Equation → coefficients (β), standard errors, Wald test, odds ratios (Exp(β)).

Suggestion:

Any bank can apply this model to evaluate loan applicants by defining a set of independent variables and entering the relevant data into SPSS. The analyzed results can then be reviewed to support informed decision-making on whether to approve a loan for a particular applicant.