How to Report Linear Regression Results in APA Format

Master the standard two-line format for reporting simple regression: the model-fit statement followed by the coefficient line, plus the regression equation. Includes worked examples you can verify.

Quick start

Simple linear regression in APA format follows this pattern:

Model fit: F(1, 28) = 45.32, p = .001, R² = .618

Coefficient: b = 0.75, SE = 0.11, t(28) = 6.73, p = .001

Equation: ŷ = 12.50 + 0.75x

§1The APA regression report format

When you run a linear regression, APA style requires you to report two key pieces: how well the model fits the data overall (the F statistic and R²), and the strength and significance of the relationship between your predictor and outcome (the regression coefficient with its standard error and t statistic).

Key point

Simple linear regression means one predictor and one outcome. If you have multiple predictors, use multiple regression notation (β instead of b) and report multiple coefficient rows. This guide covers simple regression only.

The model-fit line

Start by reporting the overall fit of your regression model. This answers: "Does this predictor explain a significant proportion of the outcome's variance?" Report it like this:

F(df_regression, df_residual) = F-value, p = p-value, R² = R-squared

Example: F(1, 28) = 45.32, p < .001, R² = .618

What each part means:

  • F(1, 28) — the F statistic with 1 numerator degree of freedom (always 1 for simple regression) and 28 denominator degrees of freedom (n − 2)
  • 45.32 — the F statistic value. Larger values indicate a better-fitting model.
  • p = .001 — the p-value. Report as p < .001 if it's smaller. This is the probability of seeing an F this large if there were no relationship (if the true regression coefficient were zero).
  • R² = .618 — the coefficient of determination. This is the proportion of variance in the outcome explained by the predictor. Here, 61.8% of variance is explained.

The coefficient line

Next, report the regression coefficient itself—the slope of the line. This answers: "How much does the outcome change for each one-unit increase in the predictor?" Report it like this:

b = slope, SE = standard-error, t(df) = t-value, p = p-value

Example: b = 0.75, SE = 0.11, t(28) = 6.73, p < .001

What each part means:

  • b = 0.75 — the unstandardized regression coefficient. For simple regression, always use b (not β, which is for standardized coefficients). Each one-unit increase in the predictor is associated with a 0.75-unit increase in the outcome.
  • SE = 0.11 — the standard error of the coefficient. Smaller SE means more precision; larger SE means the estimate is less stable.
  • t(28) = 6.73 — the t statistic for testing whether the coefficient is significantly different from zero. The df (28) equals n − 2.
  • p < .001 — the two-tailed p-value. The probability of observing a coefficient this large (in absolute value) if the true coefficient were zero.

The regression equation

Always include the fitted regression equation in your paper. This is the practical takeaway—the line students use to make predictions:

ŷ = a + bx

where a is the intercept, b is the slope, and x is the predictor.

Example: ŷ = 12.50 + 0.75x

This means: "the predicted outcome is 12.50 plus 0.75 times the predictor." For a predictor value of 10, the predicted outcome is 12.50 + (0.75 × 10) = 19.0.

§2Worked example: study time and exam score

Here is a complete, hand-verifiable example. Five students recorded their study hours and their exam scores. We fit a regression to predict exam score from study hours.

The data

Study hours (x) Exam score (y)
255
460
675
885
1090

Calculation steps

  1. Compute means: x̄ = 6, ȳ = 73
  2. Sum of squared deviations for x: Σ(x − x̄)² = 40
  3. Sum of products of deviations: Σ(x − x̄)(y − ȳ) = 190
  4. Compute slope: b = 190 ÷ 40 = 4.75
  5. Compute intercept: a = 73 − (4.75 × 6) = 44.50
  6. Compute predicted values and residuals; then SSE = 27.5, SST = 930
  7. Compute R²: R² = (930 − 27.5) ÷ 930 = 0.9704
  8. Compute MSE: MSE = 27.5 ÷ 3 = 9.167 (df = n − 2 = 3)
  9. Compute SEb: SE = √(9.167 ÷ 40) = 0.4787
  10. Compute t: t = 4.75 ÷ 0.4787 = 9.92
  11. Look up p-value for t(3) = 9.92: p < .001
  12. Compute F: F = (902.5 ÷ 1) ÷ (27.5 ÷ 3) = 98.44

APA write-up

In-text format:

"A simple linear regression was conducted to predict exam score from study hours. Study hours significantly predicted exam scores, F(1, 3) = 98.44, p < .001, R² = .97. For each additional study hour, exam score increased by 4.75 points (b = 4.75, SE = 0.48, t(3) = 9.92, p < .001). The fitted equation was ŷ = 44.50 + 4.75x."

APA regression table

Predictor b SE t p
(Intercept) 44.50 3.10 14.35 < .001
Study hours 4.75 0.48 9.92 < .001

Note. This table shows the unstandardized regression coefficients (b) and standard errors for simple linear regression predicting exam score from study hours. R² = .97 for the model.

§3Formulas

Regression coefficients

b = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)²
b
Unstandardized regression coefficient (slope)
x̄, ȳ
Means of predictor and outcome
a = ȳ − bx̄
a
Intercept (predicted outcome when x = 0)

Residual standard error and t statistic

SE_b = √[ MSE / Σ(x − x̄)² ]
SE_b
Standard error of the regression coefficient
MSE
Mean squared error = SSE / (n − 2)
SSE
Sum of squared residuals
t = b / SE_b
t
t statistic for testing H₀: b = 0

Model fit

R² = SSR / SST = 1 − (SSE / SST)
R²
Coefficient of determination (proportion of variance explained)
SST
Total sum of squares = Σ(y − ȳ)²
SSR
Regression sum of squares = Σ(ŷ − ȳ)²
SSE
Error sum of squares = Σ(y − ŷ)²
F = MSR / MSE = (SSR / 1) / (SSE / (n − 2))
F
F statistic for testing model fit
MSR
Mean squared regression
df₁ = 1, df₂ = n − 2
Degrees of freedom for numerator and denominator

§4Common mistakes

Not reporting R² with F

Wrong: "The regression was significant, F(1, 28) = 45.32, p = .001."

Right: "The regression was significant, F(1, 28) = 45.32, p = .001, R² = .618."

The F statistic tells you whether the model explains variance; R² tells you how much variance.

Reporting b without SE

Wrong: "b = 0.75, t(28) = 6.73, p < .001."

Right: "b = 0.75, SE = 0.11, t(28) = 6.73, p < .001."

The standard error is essential—it shows how much uncertainty surrounds your estimate. Without it, readers cannot judge precision.

Omitting the regression equation

Wrong: Report only the coefficient values; assume readers reconstruct the equation themselves.

Right: Explicitly state the equation: "ŷ = 12.50 + 0.75x."

The equation is how applied readers use your results. Include it every time.

Forgetting to report the intercept

Include the intercept in the regression equation and (usually) in the table, even if it is not significant. The intercept is part of the model specification.

Confusing simple with multiple regression notation

Wrong (for simple regression): Use β for the coefficient; report multiple predictors simultaneously.

Right (for simple regression): Use b (unstandardized) or β (standardized) clearly labelled. Report one predictor per row.

This calculator covers simple regression only. Multiple regression uses β and reports multiple rows.

Reporting non-significant results without detail

Weak: "The regression was not significant."

Better: "Study hours did not significantly predict exam scores, F(1, 28) = 1.50, p = .232, R² = .05."

Report the full model fit and coefficient information even for non-significant results. Readers need to see what you tested.

§5FAQ

Do I report the standardized or unstandardized coefficient for simple regression?

For simple linear regression, APA style prefers unstandardized coefficients (b). Use standardized coefficients (β) only if your predictors were standardized before fitting, and always make that clear. Unstandardized coefficients are more interpretable: "for each one-unit increase in x, y increases by b units."

What goes in an APA regression table?

A minimal APA regression table has five columns: Predictor name | b | SE | t | p. Include one row for the intercept and one row for each predictor. Below the table, add a note that specifies what was predicted (the outcome) and the overall model R² and F statistic. Do not include degrees of freedom in the table; put them in the text instead.

How do I write the regression equation in a paper?

Write it as an inline equation, not a display block. For example: "The fitted regression equation was ŷ = 12.50 + 4.75x, where x is study hours and ŷ is predicted exam score." Always define what x and y represent in your context. Include the equation in the text, and if you include a regression table, also repeat it in the table note.

Do I need to report the intercept?

Yes. Include the intercept in your regression table and in the equation. It is part of the model specification. However, in the main text, you may emphasize the slope (the relationship of interest) more than the intercept, especially if the intercept is not statistically significant or is not meaningful in context (e.g., a predicted score when study hours = 0).

How do I report a non-significant regression result?

Report the full model fit and coefficient information: F, p, R², b, SE, t, and p for the coefficient. For example: "Study hours did not significantly predict exam scores, F(1, 28) = 1.50, p = .232, R² = .05. The regression coefficient was not significant, b = 0.10, SE = 0.08, t(28) = 1.22, p = .232." Readers need to see what you tested, even if the result was null.

What if my p-value is very small (less than 0.0001)?

APA style allows you to report p < .001 or p < .0001 (or even more precision if your software provides it), but do not report p = .000. The exact threshold depends on your field and journal guidelines; .001 is most common. Avoid simply saying p < .001 for very different p-values (.0001 vs. .01); if precision matters, report more decimal places or a range.

§6Related tools

Deepen your regression skills with these connected resources:

Sources