```
# creating a class LogisticRegression
import numpy as np
# Creating a sigmoid function as we'll be using it
def sigmoid(x):
return 1 / (1 + np.exp(-x))
class LogisticRegression:
def __init__(self, lr=0.001, n_iters=1000):
self.lr = lr
self.n_iters = n_iters
self.weights = None
self.bias = None
# always start by adding fit and predict funciton
def fit(self, X, y):
# Initializing weights and bias
= X.shape
n_samples, n_features self.weights = np.zeros(n_features) # assigning zeros as weights
self.bias = 0
# Gradient Descent
for _ in range(self.n_iters):
= np.dot(X, self.weights) + self.bias
linear_pred = sigmoid(linear_pred)
predictions
# Gradient calculation
= (1 / n_samples) * np.dot(X.T, (predictions - y))
dw = (1 / n_samples) * np.sum(predictions - y)
db
# Update weights and bias
self.weights -= self.lr * dw
self.bias -= self.lr * db
def predict(self, X):
= np.dot(X, self.weights) + self.bias
linear_pred = sigmoid(linear_pred)
y_pred = [0 if i <= 0.5 else 1 for i in y_pred]
class_pred return class_pred
```

# Explanation and steps for logistic regression

Probabilities are utilized instead of specific values in this approach which is not the case for linear regression. Instead of mean square error, cross-entropy is employed.

The Gradient Descent method is applied for LogisticRegression as well.

Weight calculation involves subtracting the gradient from the current weight.

Steps: (i) Training - Initialize weight and bias as zero. (ii) Given a data point - predict result, calculate error, use gradient descent to determine new weight and bias, repeat n times. (iii) Testing - input values into the equation, select label based on probability.

The same equation as in linear regression is utilized, integrated into the sigmoid function.

## model building

## testing

```
# testing how accurate it is with breast_cancer dataset from scikit_learn
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt
# Load data
= datasets.load_breast_cancer()
bc = bc.data, bc.target
X, y
# Split data
= train_test_split(X, y, test_size=0.2, random_state=1234)
X_train, X_test, y_train, y_test
# Normalize features
= StandardScaler()
scaler = scaler.fit_transform(X_train)
X_train = scaler.transform(X_test)
X_test
# Initialize and fit the logistic regression model
= LogisticRegression(lr=0.01, n_iters=1000)
clf
clf.fit(X_train, y_train)
# Predict on test data
= clf.predict(X_test)
y_pred
# Accuracy function
def accuracy(y_pred, y_test):
= np.sum(y_pred == y_test) / len(y_test)
accuracy return accuracy
# Calculate accuracy
= accuracy(y_pred, y_test)
acc print(f'Accuracy: {acc:.2f}')
```

`Accuracy: 0.94`