Description: Multivariate regression is a statistical technique that models the relationship between multiple independent variables and a dependent variable. Through this methodology, the aim is to understand how variations in independent variables affect the dependent variable, thus providing a framework for making predictions and analyses. This technique is based on the extension of simple linear regression, where more than one predictor variable is considered. The main features of multivariate regression include the ability to handle interactions between variables, the identification of nonlinear relationships, and the evaluation of the relative importance of each variable in the model. Additionally, it allows for the analysis of collinearity, where the correlation between independent variables is examined. Multivariate regression is particularly relevant in the context of Big Data, where large volumes of data are handled, and complex analysis is required to extract meaningful information. Its application spans various disciplines, from economics and biology to marketing and engineering, making it a fundamental tool for data-driven decision-making.
History: Multivariate regression has its roots in the development of statistics in the 20th century, with significant contributions from statisticians like Francis Galton and Karl Pearson. However, it was in the 1960s that it was formalized as a widely used statistical technique, thanks to advances in computational power that allowed for the analysis of large datasets. Over the years, various variants and methods of multivariate regression have been developed, including logistic regression and partial least squares regression, adapting to different types of data and analytical needs.
Uses: Multivariate regression is used in various fields, including economics to model the impact of different factors on economic growth, in biology to study the relationship between multiple environmental variables and organism health, and in marketing to analyze how different product attributes affect consumer purchasing decisions. It is also applied in engineering to optimize processes and in medicine to identify risk factors in diseases.
Examples: A practical example of multivariate regression is the analysis of factors influencing housing prices, where variables such as house size, location, number of rooms, and property age are considered. Another case is the study of medication effectiveness, where variables such as dosage, patient age, and presence of other medical conditions are analyzed to predict treatment response.
