Standard Practice for Regression Analysis with a Single Predictor Variable

Importancia y uso:

4.1 Regression analysis is a procedure that uses data to study the statistical relationships between two or more variables (1, 2).3 This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.

4.2 A regression model consists of: (1) a regression function that relates the mean values of the response variable distribution to fixed values of the predictor variable, and (2) a statistical distribution that describes the variability in the response variable values at a fixed value of the predictor variable.

4.2.1 The regression analysis utilizes either 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.

4.3 The information in this practice is arranged as follows.

4.3.1 Section 5 gives a general outline of the steps in the regression analysis procedure. The subsequent sections cover procedures for estimation of specific regression models.

4.3.2 Section 6 assumes a straight line relationship between the two variables. This is also known as the simple linear regression model or a first order model. This model should be used as a starting point for understanding the XY relationship and ultimately defining the best fitting model to the data.

4.3.3 Section 7 considers a proportional relationship between the variables, where the ratio of one variable to the other is constant. The intercept is constrained to be zero. This model is useful for single point calibration, where a reference material is run periodically as a standard during routine testing to correct for drift in instrument performance over a given range of test results.

4.3.4 Section 8 discusses a regression function that considers curvature in the XY relationship, the second order polynomial model.

4.3.5 Annex A1 provides supplemental information of a more mathematical nature in regression.

4.3.6 Appendix X1 lists calculations for the curvature model estimates and exhibits a worksheet for these calculations.

Subcomité:

E11.10

Referida por:

E0456-13AR22E01, D8405-21, E3297-21, D8406-22, E2862-23, E3323-22, E3023-21, E2935-21, E2935-21, D8272-19, E2586-19E01

Volúmen:

14.01

Número ICS:

03.120.30 (Application of statistical methods)

Palabras clave:

correlation; least squares; predictor variable; regression; response variable;