AbstractA pollution rose consists of selective averages of concentrations of an air pollutant for all sectors of the wind rose. Generally the sectors are 10 or 20 degrees wide and one‐hour averages of concentrations and wind directions are used. Complications arise when daily averages of concentrations have to be used. The number of data is much smaller and the variability of the wind direction over 24 hours is large. In this paper, a linear regression model is presented and applied to a real set of data. The standard solution of the regression problem is shown to give useless results; this is a consequence of the ill‐conditioning (multicollinearity) of the data. Large improvements are achieved with ridge regression and other forms of penalized least squares estimation. Cross‐validation is used for obtaining good values of the penalty parameter automati