# Odds ratio for continuous variable

I have a question

How would you interpret the odds ratios for a continuous variable?

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1
– Macro Feb 1 '12 at 2:27

## 1 Answer

It's not completely clear from your question, but I'm assuming you're talking about the situation where you have a single binary response $Y$ and a continuous predictor $X$ and fit a logistic regression model:

$$\log \left( \frac{ P(Y_{i}=1|X_{i}) }{P(Y_{i}=0|X_{i})} \right) = \beta_{0} + \beta_{1} X_{i}$$

Then the odds ratio, $e^{\beta_{1}}$, is the odds ratio associated with a one unit increase in $X$.

Essentially you can think of it as the odds ratio between $Y$ and the dummy variable $B$ defined such that $B=1$ if $X=x+1$ and $B=0$ if $X=x$.

Note: The assumption underlying the logistic model is that this odds ratio does not depend on $x$.

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