Merge pull request #1284 from AmrutaJayanti/MD

Create Logistic-Regression.md

Author: ajay-dhangar

docs/Machine Learning/Logistic-Regression.md

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+# Logistic Regression
+
+
+``` python
+from sklearn.datasets import make_classification
+
+X, y = make_classification(n_samples=100, n_features=2, n_informative=2, n_redundant=0, n_clusters_per_class=1, random_state=42)
+```
+Above, is the custom dataset made using `make_classification` from
+`sklearn.datasets` .
+
+``` python
+import matplotlib.pyplot as plt
+plt.scatter(X[:,0],X[:,1])
+plt.show()
+```
+![55558f59d1b98e9a3cc68d08daae54b9b065d057](https://github.com/AmrutaJayanti/codeharborhub/assets/142327526/84578011-0887-43da-b972-9e6f04ae505e)
+
+
+
+Logistic Regression is a statistical method used for binary
+classification problems. It models the probability that a given input
+belongs to a particular category.
+
+Logistic Function (Sigmoid Function): The core of logistic regression is
+the logistic function, which is an S-shaped curve that can take any
+real-valued number and map it into a value between 0 and 1. The function
+is defined as:
+
+$$\sigma(x) = \frac{1}{1 + e^{-x}}$$
+
+where $x$ is the input to the function
+
+Logistic Regression is generally used for linearly separated data.
+
+Logistic Regression cost function :
+
+$J(\beta) = - \frac{1}{m} \sum_{i=1}^{m} \left[ y_i \log(h_\beta(x_i)) + (1 - y_i) \log(1 - h_\beta(x_i)) \right]$
+
+### Applications
+
+-   **Medical Diagnosis**: Predicting whether a patient has a certain
+    disease (e.g., diabetes, cancer) based on diagnostic features.
+-   **Spam Detection**: Classifying emails as spam or not spam.
+-   **Customer Churn**: Predicting whether a customer will leave a
+    service.
+-   **Credit Scoring**: Assessing whether a loan applicant is likely to
+    default on a loan.
+
+
+``` python
+from sklearn.model_selection import train_test_split
+x_train,x_test,y_train,y_test = train_test_split(X,y,test_size=0.2,random_state=42)
+```
+
+`X`,`y` are split into training and testing data using `train_test_split`
+
+``` python
+from sklearn.linear_model import LogisticRegression
+
+model = LogisticRegression()
+model.fit(x_train,y_train)
+y_pred = model.predict(x_test)
+
+from sklearn.metrics import accuracy_score
+accuracy_score(y_test,y_pred)
+
+```
+Output:
+    
+    1.0
+
+Our model predicts data accurately. Hence the accuracy score is 1 .
+
+``` python
+import numpy as np
+x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
+y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
+xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.01),
+                     np.arange(y_min, y_max, 0.01))
+
+# Predict the class for each grid point
+Z = model.predict(np.c_[xx.ravel(), yy.ravel()])
+Z = Z.reshape(xx.shape)
+
+# Plot decision boundary and data points
+plt.figure(figsize=(8, 6))
+plt.contourf(xx, yy, Z, alpha=0.8, cmap='viridis')
+plt.scatter(X[:, 0], X[:, 1], c=y, cmap='viridis', marker='o', edgecolors='k')
+plt.xlabel('Feature 1')
+plt.ylabel('Feature 2')
+plt.title('Logistic Regression Decision Boundary')
+plt.show()
+```
+
+![3709358d7ef950353a7f26d9dfbb2f5f16fc962e](https://github.com/AmrutaJayanti/codeharborhub/assets/142327526/bd7361ac-b710-4975-8fb2-1ad4bf0ebe99)
+
+
+
+