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In this paper, we present a general framework for estimating regression models subject to a user-defined level of fairness. We enforce fairness as a model selection step in which we choose the value of a ridge penalty to control the effect of sensitive attributes. We then estimate the parameters of the model conditional on the chosen penalty value. Our proposal is mathematically simple, with a solution that is partly in closed form and produces estimates of the regression coefficients that are intuitive to interpret as a function of the level of fairness. Furthermore, it is easily extended to generalised linear models, kernelised regression models and other penalties, and it can accommodate multiple definitions of fairness. We compare our approach with the regression model from Komiyama et al. (in: Proceedings of machine learning research. 35th international conference on machine learning (ICML), vol 80, pp 2737–2746 …