# Linear Regression

Linear regression attempts to explain the variation present in one variable (for example Height) in terms in terms of a linear relationship to variation in one or more predictor variables (for example Age). The variable you are attempting to predict is assumed to be dependent upon the predictor variables in some way i.e. there is a cause effect relationship, and this variable is termed the dependent variable. In the above example, height may be expected to depend on age whereas the reverse is not true (i.e. your age isn’t determined by your height). Linear regression can be performed with a single predictor variable, this is called Simple Linear Regression, or with 2 or more predictor variables, a process called Multiple Linear Regression. Stepwise Multiple Regression attempts to select a subset of predictor variables that best describe any existing relationship with the dependant variable, excluding those variables that add little to the predictive power.

statistiXL provides two regression modules. The first, the Linear Regression module, provides comprehensive Model I regression analysis. The module allows the selection of one or more predictor variables for each single dependent variable with or without weighting. Options include forward or backwards stepwise regression (with P level to enter or remove), forcing of the relationship through the origin, and graphical output (normal probability plot, residuals plot, scatterplots). The second module allows you to compare several simple regressions with each other, providing tests for differences in slope and intercept.

Results from regression analysis are presented in tabular form and graphical form. Summary statistics are provided, if this option is selected. Statistics include the R², the correlation coefficient, the adjusted R², and the standard error of the estimate. An ANOVA table is given, to summarise the significance of the regression relationship. The regression coefficients, including intercept and regression slope, are given with standard errors, confidence limits, t and P values. Optionally, Residuals, Standardised Residuals and Studentised Residuals can be output and for multiple regression Partials can also be produced.

The help file included with statistiXL provides an introduction to linear regression analysis, and a number of examples including simple regression, regression forced through the origin, multiple regression, stepwise multiple regression and polynomial regression.