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Multiple Linear Regression (MLR)

Multiple linear regression (MLR) is a widely used statistical technique that uses multiple independent variables (explanatory variables) to explain the behavior of a dependent variable (response variable). This type of regression is an extension of linear (OLS) regression, which uses just one explanatory variable. MLR is widely used in economics, finance and business analytics.

MLR is particularly valuable when predicting one variable from various other related variables. MLR is the ideal technique for examining the relation between two or more independent variables and one dependent variable. For example, in economic contexts it can be used to analyze the relationship between sales, expenses, wages, raw material costs and consumer price indices.

To make a prediction using MLR, data from the explanatory variables are fitted to a linear equation, usually expressed in the form Y = β0 + β1X1 + β2X2 + ... + βnXn, where Y is the dependent variable, and each of the β terms is a coefficient that measure the strength of the association between each of the independent variables and the dependent variable.

Once an equation is formulated, it can be tested to determine the accuracy of its predictions. This is done by computing a statistic, such as the R-squared value or the adjusted R-squared value, which measure how closely the data fits the equation and assesses the overall predictive accuracy of the MLR model.

Beyond predictions, MLR can also be used to conduct inference or draw conclusions and assess causality between the independent variables and the dependent variable. This is done by measuring the statistical significance of each of the explanatory variables, which can reveal if a particular variable is ‘driving’ the observed effect on the dependent variable.

Overall, multiple linear regression is a powerful tool for many commercial and organizational contexts, including economics, financial analysis, data mining, and business intelligence. With the right data, MLR can be used to build predictive models, or infer causal relationships between multiple variables to understand how changes in one variable can affect another.

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