What is the equation that relates the expected value of the dependent variable to independent variables in a multiple regression analysis?

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The equation that relates the expected value of the dependent variable to independent variables in a multiple regression analysis is indeed a multiple regression equation. This equation is specifically designed to predict the dependent variable based on several independent variables.

In multiple regression, the expected value of the dependent variable is calculated as a linear combination of the independent variables, each multiplied by its corresponding coefficient. The multiple regression equation typically takes the form:

( E(Y) = \beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_nX_n )

where:

( E(Y) ) is the expected value of the dependent variable Y,
( \beta_0 ) is the y-intercept,
( \beta_1, \beta_2, \ldots, \beta_n ) are the coefficients for the respective independent variables ( X_1, X_2, \ldots, X_n ).

This formulation allows researchers to assess the impact of multiple independent variables on the dependent variable, leading to insights that can guide decision-making and strategy.

In contrast, while a linear regression equation can sometimes refer to a simple regression, it does not encapsulate the complexity of multiple independent variables