Calculating Multiple Regression

Multiple Linear Regression

2+ independent variables predicting 1 dependent variable

In MLR, when all predictors are tested simultaneously each β has been

Adjusted for every other predictor in the regression (the β values are tested for significance)

In MLR, what does the β represent?

Independent relationship between that predictor and y (even after controlling/accounting for the presence of every other predictor in the model)

In MLR relationships between multiple predictors and y are treated simultaneously with

A series of matrix algebra calculation s(therefo

Research Design for MLR

Associational Design

For MLR, what is the typical variable?

Attributional (characteristics of the participants), the dependent variable must be measured as continuous or interval/ratio level, and the predictor variable is nominal

Assumptions of Multiple Linear Regression

Normal Distribution (dependent variable), linear relationship, independent observations, homoscedasticity, interval/ratio level 

Y in Y = BX + A

Dependent Variable

X in Y = BX + A

Indepdent Variable

B in in Y = BX + A

Slope

A in in Y = BX + A

Y-Intercept 

Homoscedasticity

Data that are evenly dispersed both above and below regression line (reflects equal variances of both variables)

Multicollinearity

When the independent variables in a multiple regression equation are strongly correlated (minimized by carefully selecting the predictors), doesn’t affect predictive power

What does Multicollinearity NOT affect?

Doesn’t affect predictive power (rather causes problems related to generalizability) 

What happens if multicollinearity is present?

Equation will NOT have predictive validity, amount of variance by each variable will be inflated, β values will not remain consistent across samples when cross-validation is performed

What do you perform before conducting the regression analysis?

Multiple Correlation Analysis

Variance Inflation Factor

Tolerance and VIF (ONLY USED IN SPSS)

To use categorical predictors in regression analysis, what is developed to represent group membership?

Coding System / Dummy Coding (examples of categorical variables: gender, income, ethnicity)