Assumptions for MLR

Preliminary: DV must be interval/ ratio level

  1. Independent observations - score of 1 person does not provide info about score of another (e.g. cheating on an exam, married couple etc.)

  1. Normality - implied that error terms are normally distributed in population

    • assessed using Histogram of residuals + Q-Q plot

    • Formal test: Shapiro-Wilk test

    If violated:

  • transform the dependent variable → log-transformation/ square-root transformation

  1. Homoscedasticity - equal variance of all predicted scores → residuals should be evenly distributed along the line e = 0

    • use residuals plot - standardize & predicted. '“fitted“ values

    If violated:

  • transform DV

  1. Linearity - can data be described w straight line

    • use scatterplot - only SLR

    • use Residual plot (standardized vs predicted) - is band of residuals horizontal?

    • Formal test: Sequential regression to test quadratic model → Model 2: hat(y) = b0 +b1x - b2x2 → if Model 2 is an improvement = linearity violated

  1. Multicollinearity - high correlation bet. predictors

    • diagnosed by variance inflation factor (VIF) or Tolerance - tests in JASP

  

    If violated:

  • increase sample size

  • combine/ remove predictors

  1. Outliers

    a. in y-space - use Standardized residuals

b. in x-space -use Mahalanobis distance

large values in table indicates outlier

c. in xy-space - use Cook’s distance