A simple linear regression in SPSS prints four tables, and the same result shows up in three of them in different forms: as R², as an F test and as a t test on the slope. Knowing which number answers which question is the whole skill. This guide reads each table cell by cell with a worked example, sorts out the misreadings (R vs R Square, B vs Beta, the "ANOVA" that is not an ANOVA), and gives the APA 7 write-up. For the reporting format alone, see the linear regression APA guide; with several predictors, the multiple regression output guide.
What SPSS gives you
Analyze > Regression > Linear, with the outcome as Dependent and one predictor as Independent(s), and Confidence intervals ticked under Statistics, produces:
- Variables Entered/Removed: which predictor went in, and the method (Enter).
- Model Summary: how much variance the model explains.
- ANOVA: whether the model predicts better than nothing.
- Coefficients: the regression equation and the test of the slope.
Each table has footnotes naming the dependent variable ("a. Dependent Variable: Exam score") and the predictors ("b. Predictors: (Constant), Study hours"). The letters ᵃ and ᵇ in the tables point to them.
The worked example
Forty students recorded their weekly study hours before an exam (M = 9.01, SD = 3.32), and their exam scores (0 to 100) were recorded (M = 68.93, SD = 11.85). Does study time predict the score? All tables below come from one dataset.
Table 1: Model Summary
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |
|---|---|---|---|---|
| 1 | .570ᵃ | .325 | .307 | 9.869 |
- R = .570: the correlation between the observed scores and the scores the model predicts. With one predictor it equals the absolute value of Pearson's r between the two variables.
- R Square = .325: the proportion of variance in exam scores the model explains, 32.5%. This is the number you report as R².
- Adjusted R Square = .307: R² corrected for the number of predictors and the sample size, an estimate of how much the model would explain in the population. Report it too when your field expects it, and always with several predictors.
- Std. Error of the Estimate = 9.869: the typical distance between an observed score and the predicted one, in exam points (the residual SD).
Table 2: ANOVA
| Model | Sum of Squares | df | Mean Square | F | Sig. | |
|---|---|---|---|---|---|---|
| 1 | Regression | 1779.338 | 1 | 1779.338 | 18.267 | .000ᵇ |
| Residual | 3701.437 | 38 | 97.406 | |||
| Total | 5480.775 | 39 |
This is the overall test of the model, not an analysis of variance between groups.
- Regression row: the variation the model explains. Its df = number of predictors = 1.
- Residual row: the variation left over. Its df = N − predictors − 1 = 38.
- F = 18.267, Sig. = .000: the model predicts exam scores significantly better than the mean alone. Sig. = .000 means p < .001.
- R² can be recovered from this table: Regression SS / Total SS = 1779.338 / 5480.775 = .325.
Table 3: Coefficients
SPSS puts B and Std. Error under "Unstandardized Coefficients", Beta under "Standardized Coefficients", and the CI columns under "95.0% Confidence Interval for B".
| Model | B | Std. Error | Beta | t | Sig. | 95% CI for B Lower | 95% CI for B Upper | |
|---|---|---|---|---|---|---|---|---|
| 1 | (Constant) | 50.573 | 4.569 | 11.070 | .000 | 41.325 | 59.822 | |
| Study hours | 2.036 | .476 | .570 | 4.274 | .000 | 1.072 | 3.001 |
The (Constant) row is the intercept: the predicted exam score for a student who studied 0 hours, 50.57. Its t and Sig. test whether that prediction is zero, which is almost never an interesting question. You use B for the equation and usually ignore the rest of the row.
The Study hours row is the result:
- B = 2.036: each extra hour of study per week goes with an exam score about 2.04 points higher. This is the unstandardized coefficient, in the units of the variables.
- Std. Error = .476: the uncertainty of B. t = B / Std. Error = 2.036 / .476 = 4.27.
- Beta = .570: the standardized coefficient, the change in exam score, in SDs, for a one-SD change in study hours. With one predictor it equals r.
- t = 4.274 and Sig. = .000: the slope is significantly different from zero, p < .001. The df for this t is the Residual df, 38.
- 95% CI for B: 1.07 to 3.00 points per hour.
The regression equation: predicted exam score = 50.57 + 2.04 × study hours. A student who studies 10 hours a week is predicted to score 50.573 + 2.036 × 10 = 70.94.
Why three tests agree. With one predictor, the ANOVA's F is the slope's t squared (4.274² = 18.27), and their p values are identical. You report the F for the model and B with its CI for the slope; they are the same test seen twice.
Misreadings that cost marks
- Reporting R as the variance explained. R = .570 is a correlation. The variance explained is R Square, .325.
- Mixing up B and Beta. B is in the variables' units (points per hour) and goes in the equation. Beta is in SD units, for comparing predictors measured on different scales. Report B, with its CI, and add β if your field expects it.
- Interpreting the constant's Sig. It tests whether the predicted score at 0 hours is 0. That says nothing about whether study time matters.
- Thinking the ANOVA table compares groups. In regression it tests the whole model.
- Writing p = .000. Write p < .001.
- Reading prediction as causation. Study hours predict scores in these data; the regression does not show that studying more would raise anyone's score.
- Skipping the residual checks. A regression is only as good as its assumptions: a linear relationship, roughly normal residuals with constant spread, no extreme influential points. Ask SPSS for the residual plots under Plots (*ZRESID against *ZPRED, and a histogram).
The APA 7 format template
A simple linear regression showed that [predictor] significantly predicted [outcome], F(1, df) = X.XX, p = .XXX, R² = .XX. Each one-unit increase in [predictor] was associated with a X.XX-unit increase in [outcome], b = X.XX, 95% CI [X.XX, X.XX], t(df) = X.XX, p = .XXX.
The write-up for this example
A simple linear regression showed that weekly study hours significantly predicted exam score, F(1, 38) = 18.27, p < .001, R² = .32, adjusted R² = .31. Each additional hour of study per week was associated with an exam score 2.04 points higher, b = 2.04, 95% CI [1.07, 3.00], β = .57, t(38) = 4.27, p < .001.
Let KyroStat do the write-up for you
Already have the output? Paste the Model Summary and ANOVA tables from the SPSS Viewer into the box on the linear regression reporting guide to get the APA sentence for the model. Or upload the spreadsheet to KyroStat, which runs the regression, checks the residuals, and writes the APA 7 sentences and coefficients table with the code behind every number.
Also useful for the write-up (affiliate links): Proofreading for your thesis or paper (20% off with code PAP20): Paperpal
Frequently asked questions
What is the difference between R and R Square in SPSS? R is the correlation between the observed and predicted values. R Square is the proportion of variance explained, and it is the one you report as R².
Should I report R Square or Adjusted R Square? R² for a simple regression, often with adjusted R² beside it. With several predictors, report adjusted R² as well, because R² rises with every predictor added.
Do I report B or Beta? B, with its 95% CI, because it is in meaningful units. Add Beta (β) when readers need to compare the strength of predictors on different scales.
Why is the ANOVA p the same as the Coefficients p? With one predictor, the model test and the slope test are the same test: F = t². With several predictors they differ.
What does Sig. = .000 mean in the Coefficients table? The p value is below .0005. Report p < .001.
Which related guides might I need? Often these: Pearson correlation output, multiple regression output and assumption checks.