## Multiple regression
## DescriptionMultiple regression is a statistical method used to examine the relationship between one dependent variable b in the regression equation_{i}are estimated using the method of least squares. In this method, the sum of squared residuals between the regression plane and the observed values of the dependent variable are minimized. The regression equation represents a (hyper)plane in a X, _{2}X, ... _{3}X, plus one dimension for the dependent variable _{k}Y.## Required inputThe following need to be entered in the ## Dependent variableThe variable whose values you want to predict. ## Independent variablesSelect at least one variable you expect to influence or predict the value of the dependent variable. Also called predictor variables or explanatory variables. ## WeightsOptionally select a variable containing relative weights that should be given to each observation (for weighted multiple least-squares regression). Select the dummy variable "*** AutoWeight 1/SD^2 ***" for an automatic weighted regression procedure to correct for heteroscedasticity (Neter et al., 1996). This dummy variable appears as the first item in the drop-down list for Weights. ## FilterOptionally enter a data filter in order to include only a selected subgroup of cases in the analysis. ## Options- Method: select the way independent variables are entered into the model.
- Enter: enter all variables in the model in one single step, without checking
- Forward: enter significant variables sequentially
- Backward: first enter all variables into the model and next remove the non-significant variables sequentially
- Stepwise: enter significant variables sequentially; after entering a variable in the model, check and possibly remove variables that became non-significant.
- Enter variable if P< A variable is entered into the model if its associated significance level is less than this P-value.
- Remove variable if P> A variable is removed from the model if its associated significance level is greater than this P-value.
- Report Variance Inflation Factor (VIF): option to show the Variance Inflation Factor in the report. A high Variance Inflation Factor is an indicator of multicollinearity of the independent variables. Multicollinearity refers to a situation in which two or more explanatory variables in a multiple regression model are highly linearly related.
- Zero-order and simple correlation coefficients: option to create a table with correlation coefficients between the dependent variable and all independent variables separately, and between all independent variables.
## ResultsAfter clicking the OK button, the following results are displayed in the results window: In the
where
^{2}-adjusted may decrease if variables are entered in the model that do not add significantly to the model fit.or
When discussing multiple regression analysis results, generally the coefficient of multiple determination is used rather than the multiple correlation coefficient.
s, r_{bi}_{partial}, t-value and P-value.
- The partial correlation coefficient r
_{partial}is the coefficient of correlation of the variable with the dependent variable, adjusted for the effect of the other variables in the model. - If P is less than the conventional 0.05, the regression coefficient can be considered to be significantly different from 0, and the corresponding variable contributes significantly to the prediction of the dependent variable.
- Optionally the table includes the Variance Inflation Factor (VIF). A high Variance Inflation Factor is an indicator of multicollinearity of the independent variables. Multicollinearity refers to a situation in which two or more explanatory variables in a multiple regression model are highly linearly related.
- You have selected a stepwise model and the variable was removed because the P-value of its regression coefficient was above the threshold value.
- The tolerance of the variable was very low (less than 0.0001). The tolerance is the inverse of the Variance Inflation Factor (VIF) and equals 1 minus the squared multiple correlation of this variable with all other independent variables in the regression equation. If the tolerance of a variable in the regression equation is very small then the regression equation cannot be evaluated.
## Repeat procedureIf you want to repeat the ## Literature- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
- Armitage P, Berry G, Matthews JNS (2002) Statistical methods in medical research. 4th ed. Blackwell Science.
- Neter J, Kutner MH, Nachtsheim CJ, Wasserman W (1996) Applied linear statistical models. 4
^{th}ed. Boston: McGraw-Hill.
## See also |