How to Do Regression Analysis in Research: A Complete Guide (2026)
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Shruti Sharma
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Regression analysis is a statistical method that examines the relationship between a dependent variable (outcome) and one or more independent variables (predictors). It is one of the most powerful and commonly used statistical techniques in academic research — used to predict outcomes, test hypotheses, and identify which factors have the strongest influence on a variable of interest.
Types of Regression Analysis
Types of Regression Analysis
Does study time predict exam score?
Do stress, motivation, and study time together predict score?
Tests incremental contribution of each block
Predicts probability of an event occurring
Does the effect of X on Y depend on Z?
Does M mediate the X → Y relationship?
Assumptions of Linear Regression
| Assumption | How to Check | What to Do If Violated |
|---|---|---|
| Linearity | Scatterplot of Y vs X; residual vs fitted plot | Transform variables (log, square root) |
| Normality of residuals | Histogram of residuals; P-P plot; Shapiro-Wilk on residuals | Transform outcome variable; use robust regression |
| Homoscedasticity | Residuals vs fitted values plot (no cone pattern) | Use robust standard errors; transform variables |
| No multicollinearity | VIF values (should be <10; <5 preferred) | Remove highly correlated predictors; use PCA |
| Independence of observations | Research design (check for repeated measures or nested data) | Use mixed-effects or multilevel models |
| No significant outliers | Cook's distance (<1); leverage values; standardised residuals (<±3) | Investigate outliers; consider removal if justified |
How to Run Multiple Regression in SPSS
- Go to Analyze → Regression → Linear
- Move your outcome variable to the Dependent box
- Move your predictor variables to the Independent(s) box
- Select Statistics: tick Estimates, Confidence Intervals, Model Fit, R-squared Change, Descriptives, Part and Partial Correlations, Collinearity Diagnostics
- Select Plots: add *ZRESID (Y) vs *ZPRED (X); tick Normal probability plot
- Select Save: tick Standardised residuals and Cook's Distance
- Click OK
How to Interpret Regression Output
| Output Section | What to Report | Interpretation |
|---|---|---|
| Model Summary | R, R², Adjusted R², F-statistic, p-value | How well the model fits overall; % variance explained |
| ANOVA table | F(df1, df2) = XX.XX, p = .XXX | Whether the overall model is statistically significant |
| Coefficients table — B | Unstandardised beta, SE, t-value, p-value, 95% CI | Direction and magnitude of each predictor's effect |
| Coefficients table — β | Standardised beta (Beta) | Relative importance of each predictor |
| Collinearity Statistics | Tolerance and VIF for each predictor | VIF < 10 (preferably <5) = acceptable multicollinearity |
Reporting Regression in APA Format
Example: "A multiple regression analysis was conducted to examine whether job satisfaction, organisational commitment, and workload predicted employee intention to quit. The model was statistically significant, F(3, 196) = 18.45, p < .001, R² = .22, adjusted R² = .21, indicating that the predictors explained 22% of the variance in intention to quit. Organisational commitment was the strongest negative predictor (β = −.38, p < .001), followed by job satisfaction (β = −.24, p = .002). Workload was a significant positive predictor (β = .17, p = .024)."
Hierarchical Regression Tip
In hierarchical regression, you enter predictors in theoretically justified blocks. Enter control variables (demographics) in Block 1, main predictors in Block 2, and interaction terms in Block 3. Report the R² change (ΔR²) and F-change significance for each block — this shows the incremental explanatory power added by each set of predictors. This is essential for theory-testing dissertations in management and psychology.
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Frequently Asked Questions
Click a question to expand the answer.
Regression analysis is a statistical technique used to examine the relationship between a dependent variable (outcome) and one or more independent variables (predictors). Simple linear regression uses one predictor; multiple regression uses two or more. Regression tells you how much the outcome variable changes for each unit change in a predictor, while controlling for other variables. It is widely used in management, psychology, economics, healthcare, and education research.
The key assumptions of multiple regression are: (1) Linearity — linear relationship between predictors and outcome; (2) Independence — observations are independent; (3) Normality — residuals are normally distributed; (4) Homoscedasticity — equal variance of residuals across fitted values; (5) No multicollinearity — predictors are not highly correlated with each other (check VIF < 10); (6) No significant outliers or high-leverage points. Always check and report assumption testing in your methodology chapter.
R² (R-squared) is the coefficient of determination — it represents the proportion of variance in the dependent variable explained by the independent variables. R² = 0.25 means the predictors explain 25% of the variance in the outcome. Adjusted R² is preferred in multiple regression as it accounts for the number of predictors. Effect size benchmarks (Cohen, 1988): small = 0.02, medium = 0.13, large = 0.26.
There are two types: unstandardised beta (B) shows the change in the dependent variable for a one-unit change in the predictor in original measurement units. Standardised beta (β) shows the relative contribution of each predictor in standard deviation units — used to compare the relative importance of predictors. A positive beta indicates a positive relationship; negative beta indicates an inverse relationship. Always report both along with standard errors and p-values.
Use regression analysis when: (1) You want to predict an outcome variable from one or more predictors; (2) You want to test whether specific variables significantly predict an outcome after controlling for other variables; (3) Your research hypothesis states that X will predict or influence Y; (4) You want to determine which of several predictors is the strongest predictor of the outcome. Regression is common in management, psychology, healthcare, and education dissertations.