![]() For more information on this technique, see Regression Methods. To find the coefficients of these equations, Predictor uses singular value decomposition. When the regression equation has more than two independent variables, it defines a hyperplane. It further specifies that each predictor is related. When the regression equation has only two independent variables, it defines a plane. The multiple regression equation (Equation 4) estimates the additive effects of X1 and X2 on the response. Where b 0 is where the regression line crosses the graph's y axis, x is the independent variable, and e is the error. This uses a special case of multiple linear regression called simple linear regression, with the equation: Where b 1, b 2, and b 3, are the coefficients of the independent variables, b 0 is the y-intercept constant, and e is the error.Įquations with only one independent variable define a straight line. Multiple linear regression finds the coefficients for the equation: ![]() The linear equation describes how the independent variables ( x 1, x 2, x 3.) combine to define the single dependent variable ( y). ![]() “Linear” indicates that the regression equation is a linear equation. “Multiple” indicates that you can use more than one independent variable to define the dependent variable in the regression equation. The goal of multiple linear regression is to find an equation that most closely matches the historical data. The multiple linear regression equation is as follows:, where is the predicted or expected value of the dependent variable, X 1 through X p are p distinct independent or predictor variables, b 0 is the value of Y when all of the independent variables (X 1 through X p) are equal to zero, and b 1 through. For example, the yield of a lettuce crop depends on the amount of water provided, the hours of sunlight each day, and the amount of fertilizer used. Multiple linear regression is used for data where one data series (the dependent variable) is a function of, or depends on, other data series (the independent variables).
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