# Selection Process for Multiple Regression

### Entry Method Overview

The standard way to enter variables in a regression analysis is all at once, known as the simultaneous or enter method. This approach works well with a small number of predictors, especially when it’s unclear which variables will best predict the outcome. It treats each predictor as if it were added last, evaluating its unique contribution to predicting the dependent variable, beyond what’s already predicted by other variables in the model.

### Selection Methods for Refining Predictions

Selection methods refine the regression equation by narrowing down the predictor variables to those most essential, aiming to explain almost as much variance as the full set. This process highlights the significance of each predictor and its effect after accounting for other variables. The choice of predictors is guided by the study’s context and research questions.

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### Four Key Selection Procedures:

1. Forward Selection: Starts with no variables and adds them one by one, beginning with the one most correlated with the outcome. Variables considered more important are added first and remain in the model.
2. Backward Elimination: Begins with all variables in the model, removing them one at a time if they don’t enhance the regression equation.
3. Stepwise Selection: A mix of the first two methods, evaluating the contribution of each variable at every step. This method decides whether to keep or remove variables based on their statistical significance.
4. Block-wise Selection: Similar to forward selection but adds variables in groups based on theoretical or practical reasons. This method allows for a focused analysis of each block, disregarding other variables temporarily. Variables that don’t contribute are removed, and the order of entry influences which variables are retained.

### Sequential Regression Method:

• Block-wise Selection: Organizes predictors into blocks for theoretical or practical reasons, applying a stepwise method within each block. This approach gives the researcher more control over which variables are considered and in what order, based on their theoretical impact on the dependent variable.

### Simplifying the Selection Process:

The goal of multiple regression selection is to streamline the set of predictor variables, removing those that aren’t necessary, to simplify the data and improve prediction accuracy. The selection is based on two criteria: relevance to the research context and statistical significance. This methodical entry of variables allows for a detailed examination of confounding factors and the grouping of highly correlated variables, enhancing the clarity and effectiveness of the regression analysis.

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References:

Cohen, J. & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates. View

Cramer, D. (1998). Fundamental statistics for social research: Step by step calculations and computer techniques using SPSS for Windows. New York, NY: Routledge. View

Halinski, R. S. & Feldt, L. S. (1970). The selection of variables in multiple regression analysis. Journal of Educational Measurement, 7 (3). 151-157.

Leech, N. L., Barrett, K. C., & Morgan, G.A. (2008). SPSS for intermediate statistics: Use and interpretation (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers. View

Pedhazur, E. (1997). Multiple regression in behavioral research: Explanation and prediction (3rd ed.). Orlando, FL: Holt, Rinehart & Winston, Inc.

Stevens, J. P. (2002). Applied multivariate statistics for the social sciences (4th ed.). Mahwah, NJ: Lawrence Erlbaum Associates. View

Tabachnick, B. G. & Fidell, L. S. (2001). Using multivariate statistics (4th ed.). Boston, MA: Allyn and Bacon. View

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