4.1 Regression analysis is a statistical procedure that studies the statistical relationships between two or more variables Ref. (1, 2).3 In general, one of these variables is designated as a response variable and the rest of the variables are designated as predictor variables. Then the objective of the model is to predict the response from the predictor variables.

4.1.1 This standard considers a numerical response variable and only a single numerical predictor variable.

4.1.2 The regression model consists of: (1) a mathematical function that relates the mean values of the response variable distribution to fixed values of the predictor variable, and (2) a description of statistical distribution that describes the variability in the response variable at fixed levels of the predictor variable.

4.1.3 The regression procedure utilizes experimental or observational data to estimate the parameters defining a regression model and their precision. Diagnostic procedures are utilized to assess the resulting model fit and can suggest other models for improved prediction performance.

4.1.4 The regression model can be useful for developing process knowledge through description of the variable relationship, in making predictions of future values, and in developing control methods for the process generating values of the variables.

4.2 Section 5 in this standard deals with the simple linear regression model using a straight line mathematical relationship between the two variables where variability of the response variable over the range of values of the predictor variable is described by a normal distribution with constant variance. Appendix X1 provides supplemental information.