Linear Regression Assumptions
Master the foundation of reliable statistical analysis. Understand, check, and interpret the five key pillars of regression.
Learning Goals
Understand
Grasp the key assumptions underlying linear regression models.
Check (SPSS)
Execute checks using plots, residuals, VIF, and Durbin–Watson stats.
Interpret
Analyze violations and decide on appropriate responses.
Why assumptions matter
Linear regression isn't magic; it rests on specific mathematical foundations. If these are not met, results can be misleading.
- Coefficients may be biased
- Significance tests unreliable
- Predictions inaccurate
The 5 Key Assumptions
Hover over cards to see how to check them.
Linearity
The relationship between predictors and outcome must be linear.
Independence of errors
Residuals (errors) are independent of one another.
Normality of residuals
Residuals should follow a normal distribution.
Homoscedasticity
Variance of residuals is constant across levels of predicted values.
Multicollinearity
Predictors should not be too highly correlated with each other.
SPSS Walkthrough
- Durbin–Watson (under Residuals)
- Collinearity diagnostics (under Estimates)
Example Interpretation
In a training dataset, the Durbin–Watson was 1.95 (✔ independence). The P–P Plot showed residuals close to the diagonal (✔ normality). VIF values ranged 1.2–2.3 (✔ no multicollinearity). Scatterplot showed no funnel pattern (✔ homoscedasticity).
Quick Check-in
1. Which plot checks linearity and homoscedasticity?
2. What is an acceptable range for Durbin–Watson?
3. If a predictor has VIF = 12, what problem does this indicate?