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Multivariate Data Analysis Multivariate means exploring the dynamics between 3 or more variables.Multiple regression analysis (MRA) can be done when all variables are interval level (e.g. weight, height, IQ score).The research question for MRA is: can Y be predicted from X1 and/or X2? Linearity: the relationship between the independent and dependent is linear. Can be tested with scatterplots.Homoscedasticity: variance of residuals is constant across values predictors. Can be seen on the scatterplot.Normality: approximate straight line on P-P plot. That there is a high intercorrelation between predictors. There is multicollinearity when the tolerance is higher than 0.10 and the VIF is lower than 10. Outliers: on dependent variable Y: Residuals, between −3 and 3. Influential points: Cook’s distance smaller than 1.Outliers on the predictors: on independent variable(s) X: Leverage, smaller than 3(k+1)/n Ho: b*1 =b∗2 =···=b∗k =0 (No relation between Y and X1, X2) Ha: :at least one b∗j =/= 0 When the hypothesis of no relation between variables can be rejected (no relation would mean all variables equal 0) H0: b1=0 and Ha = b1=/=0H0: b2=0 and Ha = b2=/=0What are the unstandardized and standardized regression equations?Unstandardized (MRA): b0+b1X1+b2X2 Standardized (MRAst): β1X1st+ β2X2stHow much variance of Y is explained in total by X1 and X2?The R2 gives the value for the explained data (X1 and X2).How much variance of Y is uniquely explained by X1? How much...
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