Multiple Linear Regression-Introduction

Multiple Linear Regression

Introduction

This procedure performs linear regression on the selected dataset. This fits a linear model of the form

Y= b₀ + b₁X₁ + b₂X₂+ .... + b_kX_k+ e

where Y is the dependent variable (response) and X₁, X₂,.. .,X_k are the independent variables (predictors) and e is random error. b₀ , b₁, b₂, .... b_k are known as the regression coefficients, which have to be estimated from the data. The multiple linear regression algorithm in XLMiner™ chooses regression coefficients so as to minimize the difference between predicted values and actual values.

Linear regression is performed either to predict the response variable based on the predictor variables, or to study the relationship between the response variable and predictor variables. For example, using linear regression, the crime rate of a state can be explained as a function of other demographic factors like population, education, male to female ratio etc.