Multiple regression Analysis 多重回归分析 Multiple regression analysis defined Multiple regression analysis enables the researcher to predict the level of magnitude of a dependent variable based on the levels of more than one independent variable
Multiple Regression Analysis 多重回归分析 • Multiple Regression Analysis Defined – Multiple regression analysis enables the researcher to predict the level of magnitude of a dependent variable based on the levels of more than one independent variable
Multiple regression Analysis Basic equation(方程) Y=a+b1XI+ b2X2 +b3X3+.+ BnXn where dependent or criterion variable X estimated constant b I-n= coefficients associated with the predictor variables so that a change of one unit in X will cause a change of bl units in Y: the values for the coefficients are estimated from the regression analysis X I-n= predictor (independent) variables that influence the dependent variable
Multiple Regression Analysis • Basic Equation（方程） Y = a + b1X1 + b2X2 + b3X3 + …+ BnXn where Y = dependent or criterion variable X = estimated constant b 1-n = coefficients associated with the predictor variables so that a change of one unit in X will cause a change of b1 units in Y; the values for the coefficients are estimated from the regression analysis X 1-n = predictor (independent) variables that influence the dependent variable
Multiple regression analysis Measures(多量) Coefficient of Determination R-square This statistic can assume values from o to 1 and provides a measure of the percentage of the variation in the dependent variable that is explained by variation in the independent variables The b values Or regression coefficients, indicate the effect of the individual independent variables on the dependent variable
Multiple Regression Analysis • Measures（多量） – Coefficient of Determination R-square • This statistic can assume values from 0 to 1 and provides a measure of the percentage of the variation in the dependent variable that is explained by variation in the independent variables. • The b Values • Or regression coefficients, indicate the effect of the individual independent variables on the dependent variable
Multiple regression Analysis Measures(continued) Dummy variables(哑变量) In some situations, the anal yst needs to include nominally scaled independent variables such as gender, marital status, occupation, or race in a multiple regression analysis. Dummy variables can be created for this purpose Dichotomous nominally scaled independent variables can be transformed into dummy variables by coding one value(e.g. female) as 0 and the other (e.g. male)as 1
Multiple Regression Analysis • Measures (continued) – Dummy Variables（哑变量） • In some situations, the analyst needs to include nominally scaled independent variables such as gender, marital status, occupation, or race in a multiple regression analysis. Dummy variables can be created for this purpose. • Dichotomous nominally scaled independent variables can be transformed into dummy variables by coding one value (e.g. female) as 0 and the other (e.g. male) as 1
Multiple regression Analysis Potential Problems in Using and Interpreting Multiple regression analysis C ollineari iy(共线性) Occurs when the independent variables are correlated Collinearity leads to unstable regression coefficients Scaling of Coefficients(系数尺度 The magnitude of the regression coefficients associated with the various independent variables can be compared directly only if they are scaled in the same units of if the data have been standardized
Multiple Regression Analysis • Potential Problems in Using and Interpreting Multiple Regression Analysis – Collinearity（共线性） • Occurs when the independent variables are correlated. Collinearity leads to unstable regression coefficients. – Scaling of Coefficients（系数尺度） • The magnitude of the regression coefficients associated with the various independent variables can be compared directly only if they are scaled in the same units of if the data have been standardized