How to Read and Report Multiple Regression Output

You run a multiple regression in SPSS, and the output drops four or five tables into your viewer window. Model Summary. ANOVA. Coefficients. Collinearity Statistics. Most students grab the R² value from the first table, copy a few numbers from the third, and ignore the rest. That approach almost always leads to mistakes in the results section. Each table answers a specific question about your model, and skipping any of them leaves gaps that supervisors will catch. Here is how to read every table, what to pull from each, and how to write it all up in APA format.

Model Summary: How Much Variance Does Your Model Explain?

The Model Summary table is short. It contains four columns that matter: R, R², Adjusted R², and Std. Error of the Estimate. Start with R². This number tells you the proportion of variance in your dependent variable that is explained by all of your predictors together. If R² = .42, that means 42% of the variation in exam scores is accounted for by the combination of predictors you entered into the model. The remaining 58% is explained by factors you did not measure.

R itself is just the square root of R². It represents the correlation between the observed values and the values your model predicts. In most thesis write-ups, you will report R² rather than R, because proportion of variance explained is more interpretable than a multiple correlation coefficient.

Now look at Adjusted R². This value will always be slightly lower than R², and the gap grows as you add more predictors. The reason is mathematical: every predictor you add to a model will increase R², even if that predictor is random noise. Adjusted R² penalizes you for adding predictors that do not genuinely improve the model. In a study with n = 150 and three predictors, you might see R² = .42 and Adjusted R² = .41. That small gap (.01) tells you all three predictors are carrying their weight. If you had R² = .42 and Adjusted R² = .35, the gap (.07) would signal that some of your predictors are not helping much. Report Adjusted R² whenever you have more than one predictor. It is the more honest number.

The Std. Error of the Estimate tells you the average distance between the observed values and the regression line, measured in the same units as your dependent variable. If you are predicting exam scores out of 100 and the standard error is 8.41, your model's predictions are off by about 8.4 points on average. Smaller is better.

ANOVA Table: Is the Overall Model Significant?

The ANOVA table tests one question: does this set of predictors, taken together, explain a statistically significant amount of variance? The F-statistic and its p-value give you the answer. If F(3, 146) = 35.24, p < .001, your model as a whole is significant. This tells you that at least some of the variance explained by the model is real and not due to chance.

Here is the part many students miss: if the overall F-test is not significant, the individual predictor coefficients in the next table are meaningless. A non-significant model means the combination of predictors does not explain the outcome variable better than simply using the mean. You would not interpret the individual slopes of a model that fails to outperform a flat line. Check the ANOVA table before you touch the Coefficients table. Always.

Coefficients Table: Which Predictors Matter and By How Much?

This is the table students spend the most time on, and it has the most room for error. The key columns are B (unstandardized coefficient), Beta (β, standardized coefficient), t, Sig., and the 95% confidence interval for B.

The B coefficient tells you the raw change in the dependent variable for each one-unit increase in the predictor, holding all other predictors constant. In our worked example below, a B of 2.34 for study hours means that each additional hour of weekly study is associated with a 2.34-point increase in exam score, after controlling for attendance and prior GPA. The units of B depend on the units of the predictor. Study hours are measured in hours. Attendance might be measured as a percentage. Prior GPA is on a 4.0 scale. Because these predictors live on different scales, their B values are not directly comparable. A B of 2.34 for study hours and a B of 0.51 for attendance do not mean study hours matter more. The scales are different.

That is what Beta fixes. The standardized coefficient expresses each predictor's effect in standard deviation units, stripping away the original measurement scale. A Beta of .38 for study hours and a Beta of .29 for attendance tells you that study hours have a somewhat larger relative contribution to explaining exam scores. When your thesis committee asks "which predictor was strongest?" they want the Beta values, not the B values. For a deeper look at effect sizes and how to interpret them, see our separate guide.

The Sig. column gives you the p-value for each individual predictor. A predictor with p < .05 makes a statistically significant unique contribution to predicting the outcome, after accounting for all other predictors in the model. A predictor with p = .23 does not. Even if that variable had a significant bivariate correlation with the outcome, its unique contribution may vanish once you control for the other predictors.

The 95% confidence interval for B tells you the range within which the true population coefficient likely falls. If the CI for study hours runs from 1.48 to 3.20, you can say with 95% confidence that each additional study hour is associated with between a 1.48- and 3.20-point increase in exam score. When the confidence interval crosses zero, the predictor is not significant at the .05 level.

Collinearity Statistics: Are Your Predictors Too Similar?

SPSS can include Tolerance and VIF (Variance Inflation Factor) in the Coefficients table if you request them under Statistics > Collinearity diagnostics. These numbers tell you whether your predictors overlap so much that the regression coefficients become unstable.

Tolerance is the proportion of a predictor's variance that is not explained by the other predictors. It ranges from 0 to 1. A Tolerance below .10 means that over 90% of that predictor's variance is shared with other predictors in the model, which signals a serious multicollinearity problem. VIF is simply 1 / Tolerance, so a Tolerance of .10 equals a VIF of 10. The common rule: VIF above 10 (or Tolerance below .10) is problematic. Some fields use a stricter cutoff of VIF above 5.

When multicollinearity is present, the standard errors of the affected coefficients inflate. That makes t-values smaller and p-values larger, so predictors that genuinely matter may appear non-significant. In a study predicting exam scores, if you include both "total study hours" and "study hours on weekdays" as separate predictors, those two variables will correlate at r = .90 or higher. Their VIF values will spike above 10, and the individual coefficients will be unreliable. The fix is usually to drop one of the redundant predictors or combine them into a single measure.

Worked Example: Predicting Exam Scores

Suppose you collected data from 150 university students and ran a multiple regression predicting final exam score (0–100) from three variables: weekly study hours, class attendance (percentage of sessions attended), and prior GPA (on a 4.0 scale). Here is what realistic SPSS output might look like.

Table	Key Values
Model Summary	R = .65, R² = .42, Adjusted R² = .41, Std. Error = 8.41
ANOVA	F(3, 146) = 35.24, p < .001
Coefficients — Study Hours	B = 2.34, SE = 0.44, β = .38, t = 5.32, p < .001, 95% CI [1.48, 3.20]
Coefficients — Attendance (%)	B = 0.51, SE = 0.14, β = .29, t = 3.64, p < .001, 95% CI [0.24, 0.78]
Coefficients — Prior GPA	B = 3.87, SE = 2.61, β = .10, t = 1.48, p = .141, 95% CI [−1.29, 9.03]
Collinearity — Study Hours	Tolerance = .82, VIF = 1.22
Collinearity — Attendance	Tolerance = .79, VIF = 1.27
Collinearity — Prior GPA	Tolerance = .91, VIF = 1.10

Reading these tables in order: the model explains 41% of the variance in exam scores (Adjusted R² = .41). The overall model is significant (p < .001), so we proceed to individual predictors. Study hours and attendance are both significant predictors; prior GPA is not, after controlling for the other two. Study hours has the largest standardized coefficient (β = .38), making it the strongest predictor. All VIF values are well below 10, so multicollinearity is not a concern. If you want Academic Stats Agent to generate this table and the write-up automatically from your data, you can upload your file and get publication-ready output in minutes.

How to Report This in APA Format

Here is a complete APA-7 reporting paragraph based on the output above. You can adapt this template for your own results by swapping in your numbers.

A multiple linear regression was conducted to examine whether weekly study hours, class attendance, and prior GPA predicted final exam scores. The overall model was statistically significant, F(3, 146) = 35.24, p < .001, R² = .42, Adjusted R² = .41, indicating that the three predictors together explained 41% of the variance in exam scores. Study hours significantly predicted exam scores, B = 2.34, SE = 0.44, t(146) = 5.32, p < .001, β = .38, 95% CI [1.48, 3.20]. Class attendance was also a significant predictor, B = 0.51, SE = 0.14, t(146) = 3.64, p < .001, β = .29, 95% CI [0.24, 0.78]. Prior GPA did not significantly predict exam scores, B = 3.87, SE = 2.61, t(146) = 1.48, p = .141, β = .10, 95% CI [−1.29, 9.03]. Collinearity diagnostics indicated no multicollinearity concerns, with all VIF values below 1.30.

Notice the structure: overall model first (F-test, R², Adjusted R²), then each predictor with all six numbers (B, SE, t, p, Beta, CI). Report exact p-values where possible, and use p < .001 only when SPSS displays .000. For more guidance on writing statistical results in prose, see our article on structuring the results section of your thesis.

Common Mistakes to Avoid

The first and most frequent mistake is reporting R² without the F-test. Saying "the model explained 42% of the variance" sounds impressive until you realize the model might not be statistically significant. With a small sample and many predictors, you can get a high R² by chance alone. In a regression with 25 participants and 8 predictors, R² might reach .55 even with random data. The F-test is what separates a real finding from noise. Always report both numbers together.

The second mistake is comparing unstandardized B coefficients across predictors measured on different scales. A student might write "study hours had a larger effect (B = 2.34) than prior GPA (B = 3.87)." Wait. That comparison is backwards, and also meaningless. Study hours are measured in hours per week; prior GPA is on a 4.0 scale. One unit of study hours and one unit of GPA are completely different quantities. To compare relative contributions, use the standardized Beta coefficients. That is the entire reason they exist.

The third mistake is ignoring collinearity diagnostics entirely. We have reviewed projects where two predictors correlated at r = .85, VIF values exceeded 12, and the student never mentioned it. The result was that one predictor appeared non-significant when it almost certainly mattered. Collinearity does not invalidate your model's overall R², but it makes individual coefficients unreliable. If you find VIF values above 10, address the issue before interpreting the Coefficients table. Drop one of the correlated predictors, or combine them into a composite score.