Multiple linear regression (blocks, stepwise, diagnostics)
Predicts a numeric outcome from several predictors. Supports hierarchical blocks with R-square change, stepwise / forward / backward selection, collinearity statistics and residual diagnostics.
Menu: Analyze → Regression → Linear…
When should I use it?
- How much extra variance does motivation explain after age and income (hierarchical regression)?
- Which of ten candidate predictors are needed (stepwise, as an exploratory step)?
What are the assumptions?
- Linear relationships and independent errors (Durbin-Watson near 2).
- Constant error variance (residual vs predicted plot shows an even band).
- Roughly normal residuals (histogram, P-P plot).
- No severe collinearity (tolerance > .1, VIF < 10); no single case dominating (Cook's distance > 1 is a warning).
How do I run it in StatLab?
- Move the outcome to Dependent and the first set of predictors to block 1.
- Add later blocks for hierarchical regression and keep R squared change.
- Choose a method per block (Enter for theory-driven models).
- Tick collinearity diagnostics, casewise diagnostics and residual plots; Save adds residuals and influence values as new variables.
How do I read the output?
| Output | Meaning |
|---|---|
| Model Summary | R², adjusted R², and the R² change with its F test for each step. |
| ANOVA | Whether each model predicts better than the mean. |
| Coefficients | B (unstandardized), Beta (standardized), t, Sig., confidence intervals, part/partial correlations, tolerance and VIF. |
| Excluded Variables | What each omitted predictor would add. |
| Collinearity Diagnostics | Condition indices above 30 with two or more high variance proportions signal collinearity. |
| Residuals Statistics | Range of standardized/studentized residuals, Cook's distance and leverage. |
Worked example
On the practice survey dataset (File → Sample dataset), this command — which the dialog's Paste button also produces — runs the procedure:
PROC glmLinReg /dep=score /block1=(age) /wls='' /method1=enter /block2=(pre q1) /method2=enter /block3=() /method3=enter /ci=YES /rChange=YES /desc=NO /partCorr=NO /coll=YES /dw=NO /casewise=NO /outliers=3 /pin=0.05 /pout=0.1 /plots=NO /save=NO.
Output tables: Variables Entered/Removed · Model Summary · ANOVA · Coefficients · Excluded Variables · Collinearity Diagnostics.
How would I report it in APA style?
A multiple regression with 2 steps predicted Wellbeing score (N = 150). The final model explained 31.2% of the variance, R² = .312, adjusted R² = .298, F(3, 146) = 22.08, p < .001; the last step changed R² by .173, F(2, 146) = 18.41, p < .001. Predictors: Age (years) (b = 0.18, β = .35, t(146) = 5.09, p < .001); Pre-test score (b = 0.25, β = .32, t(146) = 4.73, p < .001); Satisfaction item 1 (b = 1.76, β = .25, t(146) = 3.65, p < .001).
Computed by StatLab's validated procedure code when this page was built. The example only illustrates the steps; choose variables that fit your own research question.
What are common mistakes?
- Treating stepwise selection as confirmatory — it capitalises on chance.
- Comparing B values of predictors on different scales (use Beta).
- Ignoring a high VIF when interpreting individual coefficients.