Model of Colour Value and Substance Concentration Based on Ridge Regression

Abstract

Based on the data of colour value and substance concentration, the quantitative relationship between colour reading and substance concentration in digital photos is studied in this paper. Correlation coefficient, variance inflation factor (VIF) and condition indices are used to analyse the collinearity of variables, and the regression model of colour value and material concentration of digital photos is established by ridge regression method. The ridge trace shows that the least square regression coefficient is very unstable at high collinearity. As the bias parameter increases from 0 to 0.0477, the ridge regression coefficient becomes stabilized and the model’s coefficient of determination does not decrease significantly. The maximum VIF (k) is 3.5161 (less than 10), which indicates that the coefficients of the model constructed by the ridge regression method is more robust, and the prediction effect of the model is better than that estimated by the least square method.