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If I have predictor variables which are a mixture of continuous and categorical, and a response variable that is continuous.

What approach should I apply? Linear regression, logistic regression or k means clustering.

For example,

Response variable: Probability of developing a disease (continuous) Predictor variable: Food Class Intake (categorical), Age (continuous), freq of exercise (continuous)

Hence, what would be the best approach based on the 3 machine learning models?

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Usually you should develop multiple models simultaneously. As the No Free Lunch Theorem states there is no way to know which model will perform better, before modeling. In practice you can make some educated guesses, but there is no need to rush them.

If your output is continuous you shouldn't use a classification model like logistic regression. Although the name can be confusing logistic regression is just linear regression with a sigmoid function applied to the output, so it can put out class probabilities and is used for classification.

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