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.

1.1 This practice covers regression analysis methodology for estimating, evaluating, and using the simple linear regression model to define the statistical relationship between two numerical variables.

1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.

1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.

1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.