MVDA -multiple regression analysis

Multivariate Data Analysis


Week 1: Multiple Regression 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?

What are the linearity, homoscedasticity and normality of residuals?

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.

What does multicollinearity mean?

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.

Are there outliers, influential points, or outliers on the predictors?

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

What are the null and the alternative hypothesis to test the regression model?

Ho: b*1 =b2 =···=bk =0 (No relation between Y and X1, X2)

Ha: :at least one bj =/= 0

When can the null hypothesis be rejected?

When the hypothesis of no relation between variables can be rejected (no relation would mean all variables equal 0)

What are the null and the alternative hypothesis to test the individual coefficients?

H0: b1=0 and Ha = b1=/=0

H0: b2=0 and Ha = b2=/=0

What are the unstandardized and standardized regression equations?

Unstandardized (MRA): b0+b1X1+b2X2  

Standardized (MRAst): β1X1st+ β2X2st

How 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 variance of Y is uniquely explained by X2? What is the best predictor?

We look at part coefficient. r2x(1.2) and r2y(2.1) gives the answer. Whichever the highest value is, that’s the best predictor.

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