November 20, 2017

Multiple Regression- Understanding the Relationship between Variables

The general purpose of multiple regression, as you may know, is to have a better understanding of the relationship between several independent (predictor) variables and a dependent (criterion) variable. In the field of social and natural sciences (mostly for the research purpose), the procedures of multiple regression have been used quite widely. In fact, a number of professional use these procedures to determine equitable compensation for various positions in the company.

These procedures allow you to determine several factors (or dimensions), like “amount of responsibility” (denoted as Resp) or “number of people to supervise” (denoted by No_Super) which you think can make a contribution to the value of a job. Once such information is gathered, you can conduct a salary survey among the similar companies in the market, and compare the salaries and respective elements (values of factors) for various positions. The gathered information can be later used in a multiple regression analysis to create a regression equation of the form.

Variables and Multiple Regression

As we all know, multiple regression is the statistical method to predict or determine the value of a dependent variable with the use of known values of the independent variables. This particular method is used when a person is interested in determining (or predicting) a continuous dependent variable from a number of independent variables. Logistic regression (another method to analyse a dataset where one or more independent variables predict the outcome) is used when the dependent variable is dividing into two. The objective of multiple regression is to determine which predictor is the strongest.

Think about the real estate business. A real estate agent usually keeps the record (for each listing) of the size of the apartment/house, the number of bedrooms, the per capita income in the respective neighborhood, and a subjective rating of the house depending on its appeal. When such information is gathered and compiled for various accommodations, it is quite fascinating to see how these variables or predictors determine the selling price of these accommodations. Often the number of bedrooms is a better predictor than the other elements; while sometimes, the subjective rating of the house makes a difference.

If there’s more than one predictor, it may help you answer a few interesting question. Such as:

  1. What amount of total difference in the criterion is described by the predictors?
  2. Which variables are specific predictors of the criterion?
  • Which variable is the strongest predictor of the criterion?

What can we achieve from multiple regression analysis?

Usually, a multiple regression analysis provides four major pieces of information: the R-Value, the R Squared Value, Unstandardized Regression Weight (B value or slope), and Standardized Regression Weight (beta weight).

  • R-Value: It shows the strength of the relationship between each and every predictors and the criterion.
  • R Squared: It shows the amount of variance in the criterion described by the predictors.
  • Unstandardised Regression Weight: For each predictor, the URW shows the relationship between that particular predictor and the criterion. The value (or number) is in the units of the predictor, which means you cannot use this to compare predictors.
  • Standardized Regression Weight: It shows which predictor is better and also determines whether a predictor has a unique relationship with the criterion. Since the value is standardised, it can compare the predictors pretty well. If the beta weight is noteworthy, it means the predictor shares a significant amount of unique variance with the criterion.
  • Multi-colinearity: This happens when the predictors are related to each other. The Beta weights describe the unique relationship between the criterion and the predictor. However, the unique amount of variance predicted by a single predictor can be small if the predictors are co-related.


The multiple regression procedures do not examine if the data are linear. Instead, it proceeds with the assumption that the relationship between the predictor and criterion is linear. Another significant assumption in the context of multiple regression is the non-existence of multi-collinearity, which basically says that the independent variables are not related among themselves. At the basic levels, this assumption can be tested by computing the correlation coefficient between every set of variables.

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