A hierarchical regression enters predictors in blocks, in an order you set in advance, to test whether a new set of variables explains the outcome beyond the ones already in the model. The typical design: control variables first (age, gender), predictors of interest second. The key result is the change in R² between steps, so the write-up reports each step and the change between them.
What you need before you write a single word
- The blocks and the order you entered them.
- For each step: R² and the model's F test.
- For each added block: ΔR² with its F change test (both df and p).
- The final model's coefficients: b, SE, β, t, p and 95% CI for each predictor.
The APA 7 format template
A hierarchical multiple regression was conducted to predict [outcome]. In Step 1, [control variables] explained [X]% of the variance, R² = .XX, F(df1, df2) = X.XX, p = .XXX. Adding [predictors] in Step 2 explained a further [X]% of the variance, ΔR² = .XX, ΔF(df1, df2) = X.XX, p = .XXX. In the final model, [predictor] was a significant [positive] predictor, β = .XX, p = .XXX.
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Formatting rules reviewers actually check:
- Report ΔR² and its own F test: that is the hypothesis test of the step.
- No leading zero on R², ΔR², β or p; keep it on b and the CI.
- Give the full coefficients in a table rather than in the text.
A worked example
For 150 adults, you predicted wellbeing from age and gender (Step 1), then social support and loneliness (Step 2).
- Step 1: R² = .01, F(2, 147) = 0.99, p = .373
- Step 2: R² = .40, adjusted R² = .38, F(4, 145) = 24.16, p < .001
- Change: ΔR² = .39, ΔF(2, 145) = 46.72, p < .001
Written up in APA 7:
A hierarchical multiple regression was conducted to predict wellbeing. In Step 1, age and gender did not explain a significant share of the variance, R² = .01, F(2, 147) = 0.99, p = .373. Adding social support and loneliness in Step 2 explained a further 39% of the variance, ΔR² = .39, ΔF(2, 145) = 46.72, p < .001; the final model explained 40% overall, F(4, 145) = 24.16, p < .001. Social support predicted higher wellbeing, β = .43, p < .001, and loneliness lower wellbeing, β = −.36, p < .001.
The APA 7 table
| Predictor | b | 95% CI | SE | β | t | p |
|---|---|---|---|---|---|---|
| Step 1 | ||||||
| Age | 0.07 | [−0.06, 0.19] | 0.06 | .09 | 1.04 | .299 |
| Gender (female) | −1.25 | [−3.99, 1.50] | 1.39 | −.07 | −0.90 | .372 |
| Step 2 | ||||||
| Age | 0.07 | [−0.03, 0.17] | 0.05 | .09 | 1.34 | .181 |
| Gender (female) | −0.23 | [−2.40, 1.94] | 1.10 | −.01 | −0.21 | .835 |
| Social support | 0.37 | [0.25, 0.49] | 0.06 | .43 | 6.34 | < .001 |
| Loneliness | −0.37 | [−0.50, −0.23] | 0.07 | −.36 | −5.33 | < .001 |
Note. N = 150. Step 1: R² = .01; Step 2: ΔR² = .39, p < .001.
Mistakes reviewers catch
- Only reporting the final model. The point of a hierarchical regression is the change; report ΔR² and its test.
- Choosing the block order after seeing the results. The order should come from theory, set before the analysis.
- Confusing it with stepwise regression. Stepwise lets the software choose the predictors; hierarchical regression follows your plan.
Let KyroStat do the write-up for you
KyroStat fits each step, tests the change in R², and writes the paragraph and the stepwise coefficient table from your data.
Frequently asked questions
What is the difference from a standard multiple regression? A multiple regression enters all predictors at once; a hierarchical one tests what each block adds.
What if the outcome is binary? Use a hierarchical logistic regression and report the change in the model χ² between steps.
How do I check the assumptions? See how to check statistical test assumptions: linearity, normal residuals, equal variance and no severe multicollinearity.