Multiple Regression Analysis & Its Implication in Research

Abstract

This paper seeks to explore the concept of multiple regression analysis and its implication in research. The research also analyzes many aspects of multiple linear regression and its major purposes. The research describes types of research question that can be answered through MLR, identifying the types of variables serve as independent and dependent variables. The advantages gained from a logistic regression when compared to other multivariate tests are also discussed.

Multiple Regression Analysis & Its Implication in Research

Multiple regression, closely interconnected to linear regression and correlation, is a statistical technique in which, on more than a few continuous independent variables, a single continuous dependent variable is regressed. (Draper & Smith, 1982) We will first consider in some detail linear regression, and will then examine how multiple regression is generalized through it.

In simple linear regression, y = ß0 + ß1x + e is the model applied to illustrate the association involving a single independent variable x and a dependent variable y, where ß0 and ß1 are the model parameters, and probabilistic error term is e that describes the variability in y that cannot be explicated by the linear relationship with x. The model would be deterministic in the absence of error term; and knowledge of the value of x in that case, would be adequate to find out the value of y. (Statistics, 2012)

The model for simple linear regression is broadened in multiple regression analysis, to make up the association between the p independent variables x1, x2, . . . , xp and dependent variable y. y = ß0 + ß1x1 + ß2x2 + . . . + ßpxp + e is the generalized form of the multiple regression model. ß0, ß1, . . . , ßp are the parameters of the model and e is the error term.

In multiple regression, analysis and interpretation is determined by two conditions. All independent variables are not dependent on one another statistically, in the first condition. As this does not happen very often logically therefore it can be acquired at times from theory or from careful choice of IV's. Each IV is linked to the DV in this case, in extent equivalent to Pearson's correlation.

Purposes of Multiple Regression

Typical purposes of multiple regression are prediction of scores of dependent variable from the independent variables, model relationships of real world variable, and explain variation of dependent variable succinctly. Applications of multiple regression in prediction are generally to take decisions on the basis of past performance. Such as, on the basis of percentile rank of high school and SAT scores, colleges make decisions of first-year selection predicting the college grade point average of the first year. Here the independent variables are high-school rank and SAT score while college GPA is the dependent variable. About .5 is typical multiple correlation, with roughly 25% of first-year GPAs predictable. About 5% might be added by the SAT score to the prediction on the basis of high school rank ...