# How to interpret a regression coefficient for the reciprocal of an independent variable?

Does anyone know how to interpret a coefficient when the variable in the model is the reciprocal of the original variable? I have an inverse equation, where $\text{time} = \beta_0 + \beta_1(1/\text{horsepower})$, where $\text{time}$ is how long it takes to accelerate a car. I need to hypothesize the sign of the variable $\text{horsepower}$. But to do that, I need to understand what it means.

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I assume you want to know how long it takes to accelerate to a given speed? – gung Dec 25 '12 at 14:32

The interpretation of a beta is the same whether the variable is in its original form or a reciprocal. Specifically, holding all else equal, a one unit change in the variable (in whatever form it has been entered into the model), will correspond to $\beta_1$ units change in the response.
What you need to understand is the meaning of $1/\text{horsepower}$. I'm not sure what the substantive meaning of this is for the potential acceleration of a car, but to the extent that more horsepower enables a car to accelerate faster, more horsepower means a smaller reciprocal horsepower, so the sign of $\beta_1$ would be negative.