If you have just run a multiple regression analysis, the hardest part is often not the statistics. It is knowing what to write. Examiners, supervisors, and journal reviewers all expect regression results to be reported in a clear, standard way, and APA style gives you that standard. Done well, your results section tells a reader exactly what you predicted, how well the model worked, and which predictors mattered. Done badly, it becomes a wall of numbers that nobody can interpret.
This guide walks you through how to report multiple regression results in APA style, step by step, with a worked example you can adapt to your own thesis or paper.
What Multiple Regression Does, in Plain English
Multiple regression predicts one outcome variable from two or more predictor variables at the same time. For example, you might predict students’ exam scores from study hours, sleep quality, and previous grades. The key advantage over running separate correlations is that each predictor is assessed while holding the others constant. That is why the phrase “controlling for” appears so often in regression write-ups: it means the effect of one predictor is estimated after accounting for the others in the model.
Before you write anything, make sure you can answer three questions about your own analysis. What is your outcome variable? Which predictors did you include, and why? And did you check the basic assumptions, such as linearity, normality of residuals, and multicollinearity? You do not need a long assumptions section in most student papers, but you should be able to state briefly that assumptions were checked and met, or note any problem you found.
What to Report: The APA Checklist
A complete APA regression write-up normally includes the following pieces, in this order:
- A sentence stating the purpose of the analysis and the variables involved.
- The overall model test: the F statistic with its degrees of freedom, the p value, and R squared.
- The adjusted R squared, especially when you have several predictors or a modest sample size.
- A coefficients table showing each predictor’s unstandardized coefficient (B), its standard error (SE), its standardized coefficient (beta), its t value, its p value, and ideally its 95 percent confidence interval.
- A plain-English interpretation: which predictors were significant, in which direction, and what that means in practical terms.
- A brief note on assumptions, if your supervisor or journal expects one.
You do not need to report every number your software produces. Focus on the numbers a reader needs to judge the model and reproduce your interpretation. That is the spirit of APA style: completeness without clutter.
Step 1: Report the Overall Model
Start with a sentence that names the analysis and its result. In APA style, statistics are reported in a standard format: the test statistic, degrees of freedom in parentheses, and the p value. For regression, the overall test uses an F statistic with two degrees of freedom: the number of predictors, and the residual degrees of freedom.
Here is a template you can adapt:
“A multiple linear regression was conducted to predict [outcome] from [predictor 1], [predictor 2], and [predictor 3]. The overall model was statistically significant, F(3, 116) = 24.38, p < .001, R squared = .39.”
Notice what this sentence achieves. It tells the reader the method, the variables, and the headline result in a single breath. R squared of .39 means the model accounted for 39 percent of the variance in the outcome. If you also report adjusted R squared, add it in the same sentence or the next one: “The adjusted R squared was .37, indicating that the model explained about 37 percent of the variance after adjusting for the number of predictors.”
One common mistake is to report R squared without the F test, or the F test without R squared. Readers need both: the F test says whether the model beats chance, and R squared says how much it actually explains. A model can be statistically significant yet explain very little, and that distinction matters.
Step 2: Present the Coefficients Table
The coefficients table is the heart of your regression report. Each row is one predictor, plus a row for the constant (intercept). The columns a reader expects are B, SE, beta, t, and p. Adding a 95 percent confidence interval for B makes your table stronger, because it shows the precision of each estimate, not just whether it passed a significance threshold.
In APA style, table titles are italicized and placed above the table, table notes go below it, and numbers are usually given to two decimal places. Keep the table simple: no coloured shading, no extra decimal places, and no predictors that were not in the model.
When you describe the table in words, do not repeat every number. Highlight the significant predictors and the most important non-significant ones. For example: “Of the three predictors, study hours and previous grades significantly predicted exam scores, while sleep quality did not reach significance when the other predictors were held constant.”
Step 3: Interpret Each Predictor in Words
For each significant predictor, state the direction of the effect and its size in plain language. The unstandardized coefficient B tells you the expected change in the outcome for a one-unit increase in the predictor, holding the other predictors constant. The standardized coefficient beta lets you compare predictors measured on different scales: larger absolute beta values indicate stronger relative contributions within this model.
Be careful with causal language. Regression shows association, not causation, unless your design supports a causal claim. Write “higher study hours were associated with higher exam scores” rather than “study hours caused higher scores,” unless you ran an experiment. Examiners notice this distinction, and so do reviewers.
Also report non-significant results honestly. A predictor that did not reach significance is still a finding. It tells future researchers that, in your sample and with your other predictors in the model, that variable did not add unique predictive value. Hiding it, or quietly dropping it from the model without explanation, is poor practice.
A Worked Example You Can Adapt
Imagine a study predicting final exam scores (out of 100) from three predictors: weekly study hours, sleep quality rated from 1 to 10, and previous grade point average. This is an illustrative example, not real data, but the reporting format is exactly what APA style expects.
The overall model was significant: F(3, 116) = 24.38, p < .001, R squared = .39, adjusted R squared = .37. In other words, the three predictors together explained 39 percent of the variance in exam scores.
The coefficients table would look like this in words. The constant was 18.42. Study hours had B = 1.85, SE = 0.42, beta = .38, t = 4.40, p < .001. Previous grade point average had B = 8.20, SE = 1.95, beta = .36, t = 4.21, p < .001. Sleep quality had B = 0.64, SE = 0.58, beta = .09, t = 1.10, p = .273.
Written up in text, this becomes:
“A multiple linear regression was conducted to predict final exam scores from weekly study hours, sleep quality, and previous grade point average. The overall model was statistically significant, F(3, 116) = 24.38, p < .001, R squared = .39, adjusted R squared = .37. Study hours (beta = .38, p < .001) and previous grade point average (beta = .36, p < .001) significantly predicted exam scores, whereas sleep quality did not (beta = .09, p = .273).”
Notice how the text version picks out the standardized coefficients and p values, while the full details live in the table. That division of labour — table for detail, text for interpretation — is the hallmark of a clean APA results section.
Common Mistakes to Avoid
First, do not report only p values. A tiny p value does not mean a large effect. Always pair it with an effect size: R squared for the model and beta for individual predictors.
Second, do not confuse B and beta. B is in the original units of your variables and is useful for practical interpretation. Beta is standardized and is useful for comparing predictors. Reporting one when you mean the other will confuse your reader and may cost marks.
Third, watch your degrees of freedom. The first number in F(3, 116) is the number of predictors, and the second is the residual degrees of freedom (sample size minus number of predictors minus one). Getting these wrong is one of the fastest ways to lose credibility with a marker.
Fourth, do not cherry-pick predictors. Report every predictor you entered into the model, significant or not, unless you have a clear, stated reason for a stepwise or hierarchical approach. If you did run a hierarchical regression, report each step’s change in R squared and say what each block added.
Fifth, check multicollinearity before you interpret. If two predictors are highly correlated, their individual coefficients can become unstable and hard to interpret. A brief statement that variance inflation factors were within acceptable limits reassures the reader that your coefficients can be trusted.
Reporting Hierarchical Regression: A Brief Note
If you entered predictors in blocks — for example, demographics first, then study habits — report the change in R squared for each step, with its F-change test. A sentence like “Adding study habits in Step 2 significantly improved the model, change in R squared = .18, F-change(2, 114) = 16.42, p < .001” tells the reader exactly what the second block contributed beyond the first. This is more informative than reporting only the final model, because it shows the incremental value of each set of predictors.
Frequently Asked Questions
Should I report the constant (intercept)?
Yes, include it in the coefficients table. You do not usually need to discuss it in the text unless it has a meaningful interpretation in your study, but a complete table includes it.
Do I need to report confidence intervals?
APA style encourages them, and many supervisors now expect them. A 95 percent confidence interval for each B value shows the range of plausible values and is more informative than a p value alone. If your software gives you confidence intervals, include them.
What if my overall model is significant but no individual predictor is?
This can happen when predictors share overlapping variance. Report it honestly, explain the likely overlap, and consider whether multicollinearity or a small sample is part of the story. Do not force an interpretation that the numbers do not support.
How many decimal places should I use?
Two decimal places are standard for most statistics in APA style, with p values reported exactly (for example, p = .032) unless they are below .001, in which case write p < .001. Keep this consistent throughout your results section.
Should I include an assumptions check in my results?
A brief sentence is usually enough for student work: state that assumptions of linearity, normality of residuals, homoscedasticity, and multicollinearity were checked and no serious violations were found, or describe any issue and how you handled it. Journal articles may require more detail.
Final Checklist Before You Submit
Before you hand in your results section, run through this quick checklist. Have you named the outcome and all predictors? Have you reported the overall F test with degrees of freedom, p value, and R squared? Have you included adjusted R squared? Does your coefficients table show B, SE, beta, t, and p for every predictor? Have you interpreted the significant predictors in plain English and mentioned the non-significant ones? And have you avoided causal language your design cannot support?
If you can answer yes to each of these, your regression write-up will read as professional, transparent, and easy to follow — exactly what APA style is designed to achieve. The numbers are only half the job. The other half is helping your reader understand what they mean.