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Logistic Regression Pro

Advanced binary classification with comprehensive features

Model Hyperparameters

Add Data Point

Data Points (5)

#XYClassActions
11.00000Negative
22.00000Negative
33.00001Positive
44.00001Positive
55.00001Positive

Model Results

Model Equation

P(y=1|x) = σ(2.2205x + -5.2553)

Weight (w)

2.2205

Bias (b)

-5.2553

Accuracy

100.00%

Precision

100.00%

Recall

100.00%

F1 Score

100.00%

Make Prediction

Batch Predictions

Step-by-Step Solution

1
Step 1: Given n=5n = 5 data points: (1,0)(1, 0), (2,0)(2, 0), (3,1)(3, 1), (4,1)(4, 1), (5,1)(5, 1)
2
Step 2: Initialize parameters:
w=0,b=0w = 0, \quad b = 0
3
Step 3: Set hyperparameters:
Learning Rate=0.1,Iterations=1000\text{Learning Rate} = 0.1, \quad \text{Iterations} = 1000
4
Step 4: The sigmoid function is defined as:
σ(z)=11+e−z\sigma(z) = \frac{1}{1 + e^{-z}}
5
Step 5: For each iteration, calculate the prediction:
z(i)=wx(i)+bz^{(i)} = wx^{(i)} + b
y^(i)=σ(z(i))\hat{y}^{(i)} = \sigma(z^{(i)})
6
Step 6: Calculate gradients:
∂L∂w=1n∑i=1n(y^(i)−y(i))x(i)\frac{\partial L}{\partial w} = \frac{1}{n}\sum_{i=1}^{n}(\hat{y}^{(i)} - y^{(i)})x^{(i)}
∂L∂b=1n∑i=1n(y^(i)−y(i))\frac{\partial L}{\partial b} = \frac{1}{n}\sum_{i=1}^{n}(\hat{y}^{(i)} - y^{(i)})
7
Step 7: Update parameters using gradient descent:
w:=w−α∂L∂ww := w - \alpha \frac{\partial L}{\partial w}
b:=b−α∂L∂bb := b - \alpha \frac{\partial L}{\partial b}
8
Step 8: After 1000 iterations, the final parameters are:
w=2.2205,b=−5.2553w = 2.2205, \quad b = -5.2553
9
Step 9: The logistic regression model is:
P(y=1∣x)=σ(2.2205x+−5.2553)\boxed{P(y=1|x) = \sigma(2.2205x + -5.2553)}
10
Step 10: Model Performance Metrics: - Accuracy = 100.00%100.00\% - Precision = 100.00%100.00\% - Recall = 100.00%100.00\% - F1 Score = 100.00%100.00\%

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Model Evaluation

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