Logistic regression and linear regression serve different purposes and are used for different types of problems:
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Output Type:
- Linear Regression: Predicts a continuous output (e.g., prices, temperatures).
- Logistic Regression: Predicts a categorical output (e.g., binary outcomes like yes/no, or multi-class outcomes).
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Model Equation:
- Linear Regression: The relationship is modeled as a linear equation: ( y = mx + b ).
- Logistic Regression: Uses the logistic function to model the probability of a binary outcome: ( P(y=1|x) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x)}} ).
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Loss Function:
- Linear Regression: Typically uses Mean Squared Error (MSE) as the loss function.
- Logistic Regression: Uses Log Loss (or Cross-Entropy Loss) to measure the performance of the model.
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Assumptions:
- Linear Regression: Assumes a linear relationship between the independent and dependent variables.
- Logistic Regression: Does not assume a linear relationship; instead, it models the log-odds of the probability of the outcome.
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Interpretability:
- Linear Regression: Coefficients represent the change in the output for a one-unit change in the predictor.
- Logistic Regression: Coefficients represent the change in the log-odds of the outcome for a one-unit change in the predictor.
These differences make logistic regression suitable for classification tasks, while linear regression is used for regression tasks.
