The basis of a multiple linear regression is to assess whether one continuous dependent variable can be predicted from a set of independent (or predictor) variables. Or in other words, how much variance in a continuous dependent variable is explained by a set of predictors. Certain regression selection approaches are helpful in testing predictors, thereby increasing the efficiency of analysis.
The standard method of entry is simultaneous (a.k.a. the enter method); all independent variables are entered into the equation at the same time. This is an appropriate analysis when dealing with a small set of predictors and when the researcher does not know which independent variables will create the best prediction equation. Each predictor is assessed as though it were entered after all the other independent variables were entered, and assessed by what it offers to the prediction of the dependent variable that is different from the predictions offered by the other variables entered into the model.
Selection, on the other hand, allows for the construction of an optimal regression equation along with investigation into specific predictor variables. The aim of selection is to reduce the set of predictor variables to those that are necessary and account for nearly as much of the variance as is accounted for by the total set. In essence, selection helps to determine the level of importance of each predictor variable. It also assists in assessing the effects once the other predictor variables are statistically eliminated. The circumstances of the study, along with the nature of the research questions guide the selection of predictor variables.
Four selection procedures are used to yield the most appropriate regression equation: forward selection, backward elimination, stepwise selection, and block-wise selection. The first three of these four procedures are considered statistical regression methods. Many times researchers use sequential regression (hierarchical or block-wise) entry methods that do not rely upon statistical results for selecting predictors. Sequential entry allows the researcher greater control of the regression process. Items are entered in a given order based on theory, logic or practicality, and are appropriate when the researcher has an idea as to which predictors may impact the dependent variable.
Statistical Regression Methods of Entry:
Sequential Regression Method of Entry:
Essentially, the multiple regression selection process enables the researcher to obtain a reduced set of variables from a larger set of predictors, eliminating unnecessary predictors, simplifying data, and enhancing predictive accuracy. Two criterion are used to achieve the best set of predictors; these include meaningfulness to the situation and statistical significance. By entering variables into the equation in a given order, confounding variables can be investigated and variables that are highly correlated can be combined into blocks.
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