Regression is the workhorse of quantitative research. It answers questions about how one or more predictors relate to an outcome: how much exam scores change with study hours, whether workload predicts burnout after accounting for experience, or which factors raise the odds of a patient being readmitted.
It is also where many students go wrong, because the output is dense and the assumptions are easy to overlook.
This guide explains which regression to use, how to prepare variables, how to check assumptions, how to read and interpret the key output, and how to report results in APA style, with worked examples for linear and logistic models.
Linear or logistic
Use linear regression when the outcome is continuous and logistic regression when it is binary (yes/no). Check assumptions (linearity, independence, homoscedasticity, normality of residuals, no severe multicollinearity) before interpreting. Report the overall model fit (R² and F for linear; chi-square and pseudo R² for logistic) and each predictor's coefficient, with its confidence interval and p-value, interpreted in plain language.
Which Regression?
| Type | Outcome | Use when |
|---|---|---|
| Simple linear | Continuous | One predictor |
| Multiple linear | Continuous | Several predictors, examined together |
| Hierarchical (sequential) | Continuous | Testing whether predictors add explanation beyond controls |
| Binary logistic | Two categories | Predicting yes/no outcomes such as readmission or pass/fail |
| Multinomial logistic | Three or more unordered categories | Predicting a choice among options |
| Ordinal logistic | Ordered categories | Predicting ratings such as low, medium, high |
| Poisson or negative binomial | Counts | Predicting numbers of events, such as visits or incidents |
Preparing Variables
- Categorical predictors need dummy coding: a variable with k categories becomes k − 1 dummy variables, with one category as the reference.
- Scale scores should be computed and checked for reliability before modeling.
- Centering continuous predictors (subtracting the mean) helps interpret interactions and the intercept.
- Missing data should be examined and handled consistently; report how many cases were used.
- Sample size: a common guide is at least 10 to 15 cases per predictor for linear regression, and at least 10 events per predictor in the smaller outcome group for logistic regression; a power analysis is better.
Building a Model: An Example Workflow
- State the question: does workload predict burnout among nurses, controlling for experience and shift type?
- Prepare variables: compute burnout and workload scale scores; dummy code shift type (day as reference).
- Explore: descriptive statistics, correlations, and scatterplots of workload against burnout.
- Fit the model: hierarchical regression, with experience and shift type in block 1 and workload in block 2.
- Check assumptions: residual plots, VIFs, Cook's distance.
- Interpret: ΔR² for workload and its coefficient with a confidence interval.
- Report: APA table and a plain-language paragraph.
Checking Assumptions (Linear Regression)
| Assumption | How to check | If violated |
|---|---|---|
| Linearity | Scatterplots; residuals vs predicted plot | Transform variables or add polynomial terms |
| Independence of errors | Study design; Durbin-Watson for ordered data | Multilevel or time-series models |
| Homoscedasticity | Residuals vs predicted plot shows even spread | Robust standard errors or transformation |
| Normality of residuals | Histogram or P-P plot of residuals | Usually minor in large samples; consider transformation or bootstrapping |
| Multicollinearity | VIF (concern above about 5 to 10) and tolerance | Remove or combine highly correlated predictors |
| Influential cases | Cook's distance (above 1 is a concern), leverage | Check data; report sensitivity analysis |
When Assumptions Fail
Violated assumptions do not always mean the analysis is invalid, but they must be addressed:
- Heteroscedasticity: use robust (heteroscedasticity-consistent) standard errors.
- Skewed outcomes: consider a log transformation, which changes interpretation to percentage effects.
- Non-linear relationships: model them with polynomial terms.
- Influential cases: check for data errors, then rerun the model with and without them as a sensitivity analysis.
Report what you found and what you did, so readers can judge the robustness of your results.
Interpreting Linear Regression Output
| Output | Meaning |
|---|---|
| R² | Proportion of variance in the outcome explained by the model |
| Adjusted R² | R² adjusted for the number of predictors |
| F test | Whether the model explains significant variance overall |
| b (unstandardised coefficient) | Change in the outcome for a one-unit increase in the predictor, holding others constant |
| β (standardized coefficient) | Change in standard deviations; allows comparison across predictors |
| p and 95% CI for b | Whether the predictor is significant and the plausible range of its effect |
Example: A multiple regression predicting exam score from weekly study hours, sleep hours and paid work hours. R² = .38, F(3, 196) = 39.9, p < .001. Study hours: b = 1.8, 95% CI [1.2, 2.4], p < .001. Sleep hours: b = 2.1, 95% CI [0.9, 3.3], p = .001. Work hours: b = −0.4, 95% CI [−0.7, −0.1], p = .008.
Interpretation: Together the predictors explained 38% of the variance in exam scores. Each additional weekly study hour was associated with a 1.8-point higher score, and each additional nightly hour of sleep with a 2.1-point higher score, holding the other variables constant. Each additional hour of paid work was associated with a 0.4-point lower score.
Example APA Regression Table
| Predictor | b | SE | β | p |
|---|---|---|---|---|
| Step 1: Years of experience | −0.04 | 0.02 | −.12 | .052 |
| Step 1: Night shift (vs day) | 0.31 | 0.11 | .17 | .006 |
| Step 2: Workload | 0.48 | 0.08 | .35 | < .001 |
A full APA table would add R² for each step, ΔR², the F change and a note explaining abbreviations. Italicize statistical symbols and align decimals in your final document.
Hierarchical Regression
Hierarchical regression enters predictors in blocks to test whether a variable of interest adds explanatory power beyond controls. For example, block 1 might contain age and experience, and block 2 adds workload.
The key result is the change in R² (ΔR²) and its significance: "After controlling for age and experience, workload explained an additional 9% of the variance in burnout, ΔR² = .09, F change(1, 245) = 27.6, p < .001."
Logistic Regression
Logistic regression models the odds of a binary outcome. Coefficients are on the log-odds scale, so report and interpret odds ratios (Exp(B)): values above 1 mean higher odds, below 1 lower odds.
Example: Predicting 30-day readmission (yes/no). Model χ²(3) = 41.2, p < .001, Nagelkerke R² = .22. Age: OR = 1.03, 95% CI [1.01, 1.05]. Lives alone: OR = 2.10, 95% CI [1.35, 3.27]. Follow-up call received: OR = 0.48, 95% CI [0.30, 0.77].
Interpretation: Patients living alone had about twice the odds of readmission, while those who received a follow-up call had about half the odds, holding other variables constant. Each additional year of age increased the odds by about 3%.
Also report model fit (for example, the Hosmer-Lemeshow test) and classification accuracy if your course asks for it, but treat classification rates with caution, especially for rare outcomes.
Interactions and Moderation
An interaction tests whether the effect of one predictor depends on another, for example whether the effect of workload on burnout is weaker when support is high. Create the product of the two (centered) predictors and add it to the model; a significant interaction term indicates moderation.
Probe it with simple slopes at low and high values of the moderator and plot the result. Mediation, where a variable explains how a predictor affects an outcome, uses different methods, such as the PROCESS macro.
Reporting Regression in APA Style
- State the type of regression and the variables entered.
- Report assumption checks briefly.
- Give overall model statistics: R², F with degrees of freedom and p (linear), or χ², pseudo R² (logistic).
- Present coefficients in a table: b, SE, β (or OR with 95% CI for logistic), t or Wald, and p.
- Interpret the key coefficients in plain language, noting the "holding other variables constant" condition.
- Avoid causal language unless the design supports it.
Common Mistakes
- Using linear regression for a binary outcome.
- Entering categorical variables without dummy coding.
- Ignoring multicollinearity among predictors.
- Interpreting logistic coefficients as probabilities rather than log-odds or odds ratios.
- Too many predictors for the sample size.
- Claiming causation from observational data.
- Reporting R² alone without the coefficients that answer the research question.
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A statistician prepares the variables, checks assumptions, runs the appropriate model, and returns the output, syntax or code, APA tables and a plain-language write-up. Analysis always uses your real data. Revisions within the scope of your original request are free.
Choosing Predictors
Choose predictors from theory and previous research, not by trying every variable in the dataset. Automated stepwise selection is widely criticized because it capitalizes on chance, inflates R² and produces models that do not replicate; many journals and committees discourage it.
Instead, specify the model in advance, include control variables that the literature identifies as confounders, and keep the number of predictors proportionate to your sample. If you explore alternative models, report them transparently as exploratory analyses.
Also think about what each coefficient will mean to a reader. Predictors measured on intuitive scales, such as hours or years, produce coefficients that are easy to explain, while standardized coefficients help compare predictors measured in different units.
Running Regression in Common Software
| Software | Linear regression | Logistic regression |
|---|---|---|
| SPSS | Analyze > Regression > Linear | Analyze > Regression > Binary Logistic |
| R | lm(outcome ~ x1 + x2, data = df) | glm(outcome ~ x1 + x2, family = binomial, data = df) |
| Stata | regress outcome x1 x2 | logistic outcome x1 x2 |
| Excel | Data Analysis ToolPak > Regression | Not built in |
Whatever the software, save your syntax or script so the analysis can be reproduced and checked, and request diagnostics such as residual plots and VIFs explicitly, since they are not always produced by default.
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Frequently Asked Questions
Correlation measures the strength and direction of a relationship between two variables. Regression models how one or more predictors relate to an outcome and can estimate the size of each predictor's effect while controlling for others.
When your outcome has two categories, such as yes/no, pass/fail or readmitted/not readmitted. Use multinomial or ordinal logistic regression for more categories.
The proportion of variance in the outcome explained by the model. An R² of .30 means the predictors together explain 30% of the variation in the outcome.
An odds ratio above 1 means higher odds of the outcome for each unit increase in the predictor (or compared with the reference category); below 1 means lower odds.
High correlation among predictors, which makes coefficients unstable and hard to interpret. Check variance inflation factors and consider removing or combining correlated predictors.
A rule of thumb is 10 to 15 cases per predictor for linear regression; a power analysis based on the expected effect size is more precise.
Single Likert items are ordinal; composite scale scores are usually treated as continuous. Treat single items cautiously and follow your field's conventions.
Yes. Tell us your required software, and you will receive the code or syntax along with the output and interpretation.
b is the unstandardised coefficient, expressed in the original units of the variables. Beta is standardized, expressed in standard deviations, which lets you compare the relative strength of predictors measured on different scales.
Yes. Report all predictors in the model, significant or not, in the coefficients table. Non-significant results are part of the findings.