Linear regression
Linear regression predicts a scale outcome from one or more predictors and tells you how much variance the model explains (R²) and how much each predictor contributes (B and standardised beta).
Menu: Analyze → Regression → Linear…
When should I use Linear regression?
- Predicting or explaining a scale outcome from several predictors.
What are the assumptions?
- Linearity, independent errors (Durbin-Watson near 2), constant error variance (residual vs predicted plot shows no funnel), roughly normal residuals (residual histogram).
- No strong multicollinearity: VIF below about 5 (StatLab warns).
- Categorical predictors with more than two categories need dummy variables (Transform → Recode).
How do I run it in StatLab?
- Choose the dependent variable and the predictors (method: Enter — all at once).
- Keep Residual plots ticked; optionally save predicted values and residuals as new variables.
How do I read the output?
| Output | Meaning |
|---|---|
| Model Summary | R, R², adjusted R² (penalised for the number of predictors), standard error of the estimate, Durbin-Watson. |
| ANOVA | Whether the model as a whole predicts better than the mean: F and Sig. |
| B (Unstandardized) | Change in the outcome for a one-unit change in the predictor, holding the others constant. |
| Beta (Standardized) | Same, in SD units — compare predictors on one scale. |
| t, Sig., 95% CI for B | Whether each predictor contributes significantly. |
| Tolerance / VIF | Collinearity diagnostics. |
Worked example
Predict score from age, pre and q1 in the bundled sample dataset (File → Sample dataset: 150 survey respondents with gender, programme group, age, pre/post test scores, five satisfaction items, income, smoking and education): R² = .312, F(3, 146) = 22.08, p < .001.
How would I report it in APA style?
A multiple regression with age, pre-test score and satisfaction item 1 explained 31.2% of the variance in wellbeing, R² = .31, adjusted R² = .30, F(3, 146) = 22.08, p < .001. Significant predictors were age (β = .35, p < .001), pre-test score (β = .32, p < .001), satisfaction item 1 (β = .25, p < .001).
Numbers above were computed by StatLab’s validated engine from the sample dataset when this page was built.
What are common mistakes?
- Comparing B values of predictors measured in different units — use beta.
- Adding many predictors to a small sample (rule of thumb: at least 10–20 cases per predictor).