Master Regression Result Reporting

Clear regression reporting includes model fit (R²), coefficients (B, β), significance (p-values), and confidence intervals. Follow APA 7th edition guidelines for tables and narrative summaries.

Simple Linear Multiple Regression Hierarchical APA Format Coefficients
Model Fit Statistics
R² (R-squared)
.524
52.4% variance explained
Adjusted R²
.508
Corrected for predictors (k=3)
F-statistic
F(3, 96) = 34.27
p < .001

Check These Regression Assumptions

Verify these assumptions before interpreting or reporting regression results

01
Linearity

The relationship between each predictor and outcome should be linear. Non-linear relationships require transformation.

How to Check Scatter plot of residuals vs. fitted values; look for random scatter pattern.
02
Normality of Residuals

Errors should be approximately normally distributed around zero for valid inference, especially with small samples.

How to Check Q-Q plot or Shapiro-Wilk test on standardized residuals (p > .05 indicates normality).
03
Homoscedasticity

Constant variance of residuals across all levels of predicted values. Heteroscedasticity biases standard errors.

How to Check Breusch-Pagan test (p > .05). Residual vs. predicted plot should show consistent spread.
04
No Multicollinearity

Predictors should not be highly correlated with each other. Severe multicollinearity inflates standard errors.

How to Check VIF < 5 (conservative) or VIF < 10 (lenient). Tolerance > 0.2.
05
Independence of Errors

Residuals should not be correlated (no autocorrelation). Critical for time series or nested data.

How to Check Durbin-Watson statistic between 1.5 and 2.5 indicates independence.
06
No Influential Outliers

Extreme values should not disproportionately influence regression coefficients.

How to Check Cook's D < 1.0. Leverage values < (2k+2)/n. Studentized residuals within ±3.

How to Write Up Your Findings

Step-by-step guide with APA format examples

Introduce the Model

State the type of regression used, variables entered, and the theoretical rationale for including each predictor.

"A multiple linear regression was conducted to predict job satisfaction from salary, years of experience, and autonomy scores."
Report Model Fit

Report R², adjusted R², F-statistic with degrees of freedom and p-value. Interpret how much variance your model explains.

"The model was statistically significant, F(3, 96) = 34.27, p < .001, and explained 52.4% of the variance in job satisfaction (R² = .524, adjusted R² = .508)."
Report Individual Predictors

For each predictor: unstandardised coefficient (B), standard error, standardised coefficient (β), t-statistic, p-value, and 95% CI.

"Salary was a significant positive predictor (B = 0.42, SE = 0.11, β = .35, t(96) = 3.82, p < .001, 95% CI [0.20, 0.64])."
Regression Reporting Checklist
Type of regression (simple, multiple, hierarchical, logistic)
Assumption checks and outcomes reported
R² and adjusted R² with interpretation
F-statistic with degrees of freedom and p-value
Unstandardised coefficient (B) for each predictor
Standard error (SE) for each predictor
Standardised coefficient (β) for comparison
t-statistic and exact p-value for each predictor
95% confidence intervals for unstandardised coefficients
Regression table formatted per APA 7th edition