Regression Analysis
Predict an outcome from several observed variables — linear or logistic — with coefficients, R², VIF checks, and APA-ready results.
What it is
Regression analysis estimates how one or more predictor variables relate to a single outcome variable. Linear regression (OLS) is used when the outcome is continuous — for example, a rating scale or a score. It gives you unstandardized coefficients (B) and their standard errors (SE), standardized coefficients (β) for comparing predictors, t-values and p-values for significance tests, and R² (the proportion of variance explained). Hierarchical regression adds predictors in blocks and reports ΔR² and the F-change test for each block, so you can see how much variance each set of predictors adds. Logistic regression is used when the outcome is binary (yes/no). It reports odds ratios (OR), model fit via −2 log-likelihood (−2LL) and pseudo-R², and a classification table with AUC to assess predictive accuracy. Both types report variance inflation factors (VIF) and tolerance to flag multicollinearity.
When to use it
- You want to predict a continuous outcome from several observed (directly measured) predictors — use linear regression.
- You want to predict a binary outcome (two categories) — use logistic regression.
- You want to show how much variance each block of predictors adds — use hierarchical linear regression.
- You are testing a theoretical model with observed variables and one outcome.
When not to use it
- Your predictors or outcome are latent constructs (measured by multiple items). Use CFA and then CB-SEM or PLS-SEM, which account for measurement error.
- You want to test mediation through a third variable. Use a dedicated mediation analysis with bootstrapped confidence intervals.
- You have more than one outcome variable measured simultaneously — consider multivariate approaches.
Assumptions
- Linearity — the relationship between each predictor and the outcome is linear. Check with residual plots.
- Normal residuals — the model's errors are roughly normally distributed. Check with a Q-Q plot of residuals.
- Homoscedasticity — the variance of residuals is constant across fitted values. A fan-shaped residual plot signals a problem.
- No severe multicollinearity — predictors are not too strongly correlated with each other. Check VIF; values above 10 are problematic.
- Independent observations — each row in your data comes from a different, independent respondent.
Thresholds & cutoffs
| Criterion | Rule of thumb | Source |
|---|---|---|
| Significance (α) | p < .05 conventional | Standard NHST convention |
| R² | Varies by field; report adjusted R² for smaller samples to correct for chance inflation | APA recommendations |
| VIF | VIF > 10 flags severe multicollinearity; VIF > 5 is a conservative warning | Hair et al. (2019) |
| Tolerance | Tolerance < .10 corresponds to VIF > 10; same concern | Hair et al. (2019) |
| AUC (logistic) | .70–.79 acceptable, .80–.89 excellent, ≥ .90 outstanding discrimination | Hosmer & Lemeshow (2000) |
How to report it in APA
The regression model was statistically significant, F(3, 244) = 18.43, p < .001, R² = .18, adjusted R² = .17, indicating that the three predictors explained 18% of the variance in purchase intention. Price sensitivity was the strongest predictor (B = −0.42, SE = 0.09, β = −.31, p < .001). VIF values ranged from 1.12 to 1.87, indicating no multicollinearity concern.
How Explonia runs it
In Explonia, open your study, choose Regression under Analyses, and select your outcome variable. Add predictors to one block, or build multiple blocks for hierarchical regression. Explonia fits the model, reports the coefficient table (B, SE, β, t, p), model fit (R², adjusted R², F), and a VIF column for every predictor. For logistic regression, choose a binary outcome and Explonia switches the output to odds ratios, −2LL, pseudo-R², and AUC. The Article description box drafts an APA paragraph from your results. All analyses are available on every tier; the limit across tiers is the number of responses in your study.
Frequently asked questions
What is the difference between B and β in a regression table?
B (unstandardized coefficient) shows how much the outcome changes per one-unit change in a predictor, in the predictor's original units. β (standardized coefficient) converts all predictors to the same scale so you can compare their relative importance within the model.
When should I use logistic instead of linear regression?
Use logistic regression when the outcome is binary (yes/no, bought/did not buy). Linear regression assumes a continuous outcome; applying it to a binary outcome can produce predicted values outside the 0–1 range, which is not meaningful.
What VIF value flags a multicollinearity problem?
A VIF above 10 is a widely cited threshold for severe multicollinearity. Some researchers use 5 as a more conservative cutoff. High VIF inflates standard errors and makes coefficient estimates unstable. If VIF is high, consider removing or combining correlated predictors.
When should I use SEM instead of regression?
Use regression when all your predictors are measured directly (observed variables). Use SEM — specifically CFA-based CB-SEM or PLS-SEM — when predictors or outcomes are latent constructs measured by several items, because SEM accounts for measurement error that regression ignores.
Last updated: July 2026
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