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Multivariate analysis is a branch of statistical data analysis concerned with the simultaneous study of several variables. In contrast to univariate analysis, which examines one variable at a time, and bivariate analysis, which examines the relationship between two variables, multivariate analysis considers multiple variables together. It is particularly useful when a phenomenon is influenced by several factors at the same time. In data analysis, multivariate techniques help researchers understand complex relationships, identify important factors, predict outcomes, classify observations, and make informed decisions. The basic purpose of multivariate analysis is to study how several dependent and independent variables interact with one another. For example, a researcher studying student academic performance may consider marks as the dependent variable and attendance, study hours, socioeconomic background, learning resources, and previous academic achievement as explanatory variables. Studying these variables jointly provides a more realistic understanding of academic performance than examining each factor separately. Multivariate analysis is based on the idea that real-world phenomena are rarely determined by a single variable. Economic growth, consumer behaviour, health outcomes, educational achievement, employee performance, and market demand are all influenced by multiple factors. Therefore, analysing variables simultaneously can reveal relationships that may remain hidden in separate analyses. It also allows researchers to control the influence of other variables while examining a particular relationship. One important technique is multiple regression analysis. Multiple regression is used when one dependent variable is influenced by two or more independent variables. The general form of the multiple regression equation can be expressed as: Y = a + b₁X₁ + b₂X₂ + b₃X₃ + … + bₖXₖ + e Here, Y represents the dependent ___ ________ ______ _____ _______.
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