What is Multiple Linear Regression ?
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Multiple linear regression (MLR), also known simply as multiple regression, is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. The goal of multiple linear regression is to model the linear relationship between the explanatory (independent) variables and response (dependent) variables. In essence, multiple regression is the extension of ordinary least-squares (OLS) regression because it involves more than one explanatory variable.
Definition
Multiple Linear Regression (MLR), also known as multiple regression, is a statistical technique that uses multiple explanatory variables to predict the outcome of a response variable. The goal of multiple linear regression is to establish a linear relationship model between explanatory variables and the response variable. Essentially, multiple regression is an extension of ordinary least squares (OLS) regression as it involves multiple explanatory variables.
Origin
The concept of multiple linear regression originated in the late 19th century and matured with the development of statistics. The method of least squares was introduced by Carl Friedrich Gauss in the early 1800s, and multiple regression was developed as an extension to address more complex data analysis needs.
Categories and Features
Multiple linear regression can be classified based on the number and type of explanatory variables. Common types include simple multiple regression (all explanatory variables are continuous) and categorical multiple regression (includes categorical variables). Its features include: 1. Linear relationship assumption: Assumes a linear relationship between the response variable and explanatory variables. 2. Multicollinearity: High correlation among explanatory variables can affect model stability. 3. Normality of residuals: Assumes residuals follow a normal distribution.
Case Studies
Case 1: In the real estate market, researchers use multiple linear regression to predict house prices, with explanatory variables including house size, number of bedrooms, and location. This method allows researchers to estimate house prices more accurately, providing references for buyers and sellers. Case 2: In the financial market, analysts use multiple linear regression to predict stock prices, with explanatory variables possibly including company financial metrics, market trends, and economic indicators. This analysis helps investors better understand the factors influencing stock prices.
Common Issues
Investors may encounter issues when applying multiple linear regression, such as: 1. Multicollinearity: High correlation among explanatory variables can lead to model instability. Solutions include removing highly correlated variables or using regularization techniques. 2. Model overfitting: When a model is too complex, it may fit the training data too well but perform poorly on new data. This can be addressed through cross-validation and model simplification.
