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Research Methods I

What is multiple regression analysis?. Predict the dependent variable from more than one independent variables (two or more).Independent variables are not correlated to each other (they are orthogonal)Mostly found in experimental designsIndependent variables are correlated to each otherMostly f

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Research Methods I

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    1. Research Methods I Multiple Regression Analysis

    2. What is multiple regression analysis? Predict the dependent variable from more than one independent variables (two or more). Independent variables are not correlated to each other (they are orthogonal) Mostly found in experimental designs Independent variables are correlated to each other Mostly found in real-world analyses

    3. When use Multiple Regression? Investigate relationship between a DV and several IVs Investigate relationship between a DV and some IVs while eliminating the effect of another IV Can be used with continuous or dichotomous variables for IVs Can be applied when IVs are correlated or uncorrelated.

    4. Features of Multiple Regression Goal: Improve prediction by using several prediction variables. Answers: If regression equation provides better-than-chance prediction (R2) Which IVs are important in multiple prediction and which are not If prediction can be improved significantly by adding another variable

    5. Limitations of Multiple Regression No causality can be implied Inclusion of IVs should be guided by theory not just data snooping Sample size must be large enough N> 50 + 8(m) m=number of IVs Outliers must be considered Multicollinearity Normality, Linearity, Homoscedasticity of Residuals

    6. Orthogonal Multiple Regressions The formula for the regression plane is: Y = a + bX + cT Like in linear regression – least squares method finds the best-fit regression plane Quality of prediction of variable X (through correlation between Y and X) shows proportion of the prediction of dependent variable that can be accounted for by X Quality of prediction of variable T (through correlation between Y and T) shows proportion of the prediction of dependent variable that can be accounted for by T ry.x2 + rY.T2 = RY.XT2

    7. Orthogonal Multiple Regression and Residuals Like in linear regressions each Y score can be divided into: Deviation of predicted score from the mean of Y Deviation of the score from the regression line (residual) SStotal = SSregression + SSresidual S(Y – MY)2 = (Ý – MY)2 + (Y – Ý)2 Y = a + bX + cT = My + b(X – Mx) + c(T – MT) + (Y – Y)

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