Knew this cold but still fumbled the output layer explanation a bit.
Start by defining both models and their core purpose: linear regression predicts continuous values, while logistic regression predicts probabilities for classification. Then contrast them across key dimensions such as output type, underlying function, loss function, and evaluation metrics. Finally, tie the differences to practical implications for model selection and trade-offs in real-world ML systems.
Pro tip: Emphasize that logistic regression is a linear model for classification, not regression, and highlight how the choice impacts interpretability, assumptions, and deployment. Mention that at Amazon, understanding these trade-offs is crucial for scalable, cost-effective solutions.
Clarify that linear regression is used for regression tasks (predicting continuous outcomes), while logistic regression is used for binary classification tasks (predicting probabilities).
Describe how linear regression models the output as a linear combination of inputs, whereas logistic regression applies a sigmoid function to a linear combination to output probabilities between 0 and 1.
Contrast mean squared error (MSE) for linear regression with cross-entropy (log loss) for logistic regression, and note that both can be optimized via gradient descent but logistic regression uses maximum likelihood estimation.
Mention that linear regression is evaluated with R-squared, MSE, etc., while logistic regression uses accuracy, precision, recall, AUC-ROC. Also note assumptions: linearity, independence, homoscedasticity for linear; linearity between log-odds and features for logistic.
Explain how these differences affect model selection, interpretability, and deployment, such as logistic regression providing probabilities and being robust for classification, while linear regression is unsuitable for binary outcomes.
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