How to Interpret Regression Results
Reading a regression output comes down to five things: the model's R² (what percentage of variance in the outcome the predictors explain together), adjusted R² (the version penalized for the number of predictors), each predictor's standardized beta (its relative effect size), the p-value (whether that predictor's effect could plausibly be chance), and VIF (how much the predictors overlap with each other). Looking at only one number — usually "the p-value was significant" — is the most common way this output gets misread.
This guide walks through the table you get from SPSS, R or Python row by row. Send us your own output and we'll explain what each number means for your specific data, delivered with APA-formatted interpretation sentences ready to drop into your report.
Who is this guide for?
Graduate students asked to explain a regression table at their thesis defense
Researchers reporting regression findings in a journal article
Anyone staring at SPSS/R output wondering what the numbers actually mean
Authors told by a reviewer or advisor that multicollinearity is a concern
Five steps to reading the output
- 01
Check the model summary first
R² and adjusted R² show how much variance in the outcome the model explains overall. The model's F-test p-value tells you whether the model as a whole beats a no-predictor baseline — check this before looking at individual coefficients.
- 02
Read each coefficient's B and p-value
The unstandardized B shows how much the outcome changes per one-unit increase in that predictor, holding others constant (meaningful only together with its unit). p < .05 means that predictor's effect is distinguishable from chance.
- 03
Compare relative strength with standardized beta
If predictors are on different scales (age, income, a survey score), their B values aren't comparable. Which predictor matters more is answered only by the standardized beta (β).
- 04
Check the assumptions
VIF flags multicollinearity, Durbin-Watson checks independence of residuals, and residual plots check linearity and homoscedasticity. If an assumption is violated, the coefficient interpretations above become unreliable.
- 05
Translate the numbers into a sentence
A report isn't complete until the numeric output becomes a sentence a reader can follow: which predictor, in which direction, how large an effect, and with how much confidence.
What the model summary tells you
Before touching individual coefficients, look at the model as a whole:
| Statistic | What it means |
|---|---|
| R² | Percentage of variance the predictors explain together (0-1 scale, e.g. .35 = 35%) |
| Adjusted R² | Corrects R² for the artificial inflation caused by adding unnecessary predictors; the expected figure to report with more than one predictor |
| F-test (model p-value) | Is the model as a whole significantly better than a baseline with no predictors? p < .05 means yes |
| Standard error of the estimate | How far the model's predictions typically fall from actual values, in the outcome's own units |
Reading the coefficients table
The columns you get for each predictor's row:
| Column | Interpretation |
|---|---|
| B (unstandardized) | Expected change in the outcome per one-unit increase in this predictor, holding the others constant |
| Std. Error | How stable the B estimate is — smaller means a more precise estimate |
| β (standardized beta) | B converted to standard-deviation units; this is where you compare relative effect strength across predictors |
| t and p | Whether B is statistically distinguishable from zero (no effect); p < .05 is the common threshold |
| 95% confidence interval | The range the true B likely falls in; if it crosses zero, the effect isn't considered reliable |
Common interpretation mistakes
Assuming "higher R² = better model": in the social sciences, an R² of .20-.30 is meaningful in many contexts — the right threshold depends on the field, so calling it "low" on its own is misleading.
Confusing p < .05 with "a strong or important effect": the p-value tells you whether an effect exists, not how large it is — a tiny effect can be significant in a large enough sample.
Comparing predictors using unstandardized B: B values on different scales can't be compared directly — use β for that.
Skipping the VIF check: severe multicollinearity can even flip a coefficient's sign; this is the most commonly omitted check in student reports.
Confusing correlation with causation: regression on non-experimental data shows association, not causation — "X is associated with Y" is more defensible than "X affects Y."
An example interpretation sentence (APA style)
"The regression model explained a significant proportion of variance in job satisfaction, R² = .34, adjusted R² = .32, F(3, 116) = 19.84, p < .001. Managerial support (β = .41, p < .001) and workload (β = -.22, p = .012) were significant predictors, while tenure (β = .09, p = .241) did not contribute significantly."
That single paragraph covers the model summary, each predictor's direction and size, which one didn't reach significance, and why (the p-value) — exactly what a committee or reviewer is looking for.
Frequently asked questions
How high should R² be — is there a "good" value?
There's no universal threshold — it depends on the field. Natural-science models are often expected above .60, while social-science models predicting human behavior commonly report .20-.30 as acceptable. Comparing against similar published studies in your own field is a better reference than any single rule of thumb.
What's the difference between R² and adjusted R², and which should I report?
R² always increases as you add predictors, even useless ones. Adjusted R² corrects for that inflation based on the number of predictors. With more than one predictor, reporting both is standard practice; with a single predictor the difference is negligible.
Why is standardized beta used for comparison?
Unstandardized B depends on each predictor's own unit (age in years, income in thousands, a scale score, etc.), so comparing one predictor's B against another's is meaningless. β converts every variable to standard-deviation units, making relative effect size comparable across predictors.
What VIF value signals a multicollinearity problem?
The common threshold is VIF > 10; some social-science sources are more conservative and flag VIF > 5 as a warning. If there's a problem, options include dropping a redundant predictor, combining correlated scales, or alternative methods like ridge regression.
My p-value is significant but R² is low — what does that mean?
They answer different questions: the p-value asks "could this effect be chance?" while R² asks "how well does this model explain the outcome overall?" In large samples, even a small, practically limited effect can be significant (p < .05) — a low R² shows that effect alone isn't a sufficient explanation, and both figures should be reported together.
Can I send you my own regression output for interpretation?
Yes — send your SPSS/R/Python output (or your raw data) and we'll walk through the table variable by variable, tell you which interpretation is defensible, and deliver APA-formatted sentences you can drop straight into your report.
Let's interpret your regression output together
Send your table or raw data — we'll reply with a plain explanation of what each number means, written as report-ready interpretation text.
Last updated: July 10, 2026