#Step 1: Import Libraries

import pandas as pd

Import numpy as np

import statsmodels.api as sm

import matplotlib.pyplot as plt

import seaborn as sns

#Step 2: Import Dataset from Web Storage (FIXED URL) url="https://stats.idre.ucla.edu/stat/data/binary.csv"

data pd.read csv(url)

print(data.head())

	admit	gre 	gpa 	rank

0	0 	380	3.61	3

1	1	660	3.67	2

2	1 	800 	4.00	1

3	1	640	3.19	4

4	0	520	2.93	4

#Step 3: Define Variables and handle 'rank' as categorical y= data['admit'] # Dependent variable

Create dummy variables for 'rank' and drop the first one to avoid multicollinearity rank_dummies pd.get_dummies(data['rank'], prefix='rank', drop_first=True)

#Combine original predictors (gre, gpa) with the new rank dummy variables

X= data[['gre', 'gpa']]

Xpd.concat(X, rank dummies), axis-1)

sm.add_constant(X) X

#Add constant (intercept) to the independent variables

#Convert boolean dummy variables to integers (e and 1) for statsmodels X[['rank 2', 'rank 3', 'rank_4']] = X[['rank_2', 'rank_3', 'rank_4']].astype(int)

#Step 4: Apply Logistic Regression (Changed from Multiple Linear Regression)

model sm. Logit(y, x).fit()

Optimization terminated successfully.

Current function value: 0.573147

Iterations 6

#Step 5: Print Model Summary

print(model.summary())Logit Regression Results

Dep. Variable:

Model:

Method:

Date:

Time:

converged:

Covariance Type:

Wed, 11 Mаг 2026

14:05:06

nonrobust

admit

No. Observations:

Logit

Df Residuals:

MLE

Df Model:

Pseudo R-squ.:

Log-Likelihood:

400

394

S

0.08292

-229.26

True

LL-Null:

-249.99

LLR p-value:

7.578e-08

coef

std err

P>[z

[0.025

0.975]

const

-3.9900

1.140

-3.500

0.000

-6.224

-1.756

gre

0.0023

0.001

2.070

0.038

0.000

0.004

gpa

0.8040

0.332

2.423

0.015

0.154

1.454

rank

2

-0.6754

0.316

-2.134

0.033

-1.296

-0.055

rank 3

-1.3402

0.345

-3.881

0.000

2.017

0.663

rank 4

-1.5515

0.418

-3.713

0.000

-2.370

-0,733

#Step 6: Predict probabilities

predictions model.predict(X)

#Step 7: Plot Actual Admission vs Predicted Probabilities

plt.figure(figsize(10, 6))

plt.scatter(y, predictions, alpha=0.5)

plt.xlabel("Actual Admission (e or 1)")

plt.ylabel("Predicted Probability of Admission")

plt.title("Actual Admission vs Predicted Probabilities from Logistic Regression")

plt.grid(True, linestyle, alpha-0.7)

plt.show()