# Continuous dependent variable with upper and lower bounds: logit transformation appropriate?

I'm analyzing the relationship between a (log-transformed) continuous independent variable and a continuous dependent variable that has a lower and upper bound. If I scale the dependent variable to values between 0 and 1, then take the logit, the relationship becomes linear, with seemingly homogenous variance.

Is it appropriate to then use ordinary least squares regression? Can I judge the model fit by R-square, or can I use a goodness-of-fit test based on deviance? Is it meaningful to look at deviance residuals to judge individual data points?

• I would have thought beta regression would be slightly more appealing than logistic. Perhaps you need to explain a little bit more about the nature of your variables by editing into your question? Nov 14, 2016 at 18:35
• This concerns a typical bioanalytical experiment: a range of known concentrations of a chemical (independent variable) are determined by a certain analytical method, in this case colorimetric (the dependent variable: absorption of light). The objective is to derive a calibration curve, and use this to infer concentrations in measured experimental samples. The colorimetric method is bound between a background absorption as concentrations approach 0, and a maximum absorption at ever increasing concentrations. - simonderijck Nov 14, 2016 at 20:15
• Use fractional logit. Beta regression doesn’t allow zeros or ones in the dependent variable. Aug 31, 2018 at 20:17

• Logit is for categorical variable? Not necessarily so. What we now call logit was used to transform continuous proportions over several decades long before it was introduced as (in more recent terms) a link function for binary responses. The main thing to worry about with log$[p/(1-p)]$ is that it is not defined for $p$ of 0 or 1. Jan 9, 2018 at 14:26