When to Use Linear Regression in Your Thesis

May 2026·5 min read

When to use linear regression is a question about your research question, not just your data type. Regression goes one step beyond correlation: it lets you predict an outcome from one or more predictors and quantify how much variance each predictor explains. This guide explains when regression is the right choice, how to check the four key assumptions in SPSS, and how to report R², β, and p-values in APA format.

Correlation vs. Regression: What’s the Difference?

Correlation measures the strength of the relationship between two variables — it is symmetrical (the correlation between A and B equals the correlation between B and A).

Regression specifies a direction: one variable is the predictor (independent variable) and the other is the outcome (dependent variable). It produces an equation that allows you to predict the outcome value from the predictor values, and it tells you how much of the outcome’s variance the predictor(s) explain (R²).

Use correlation when you want to describe association. Use regression when you want to predict an outcome or test whether a predictor explains unique variance after controlling for other variables.

Simple vs. Multiple Regression: Which One for Your Study?

• Simple linear regression: one predictor (IV), one outcome (DV). Use when your hypothesis is: "Variable X predicts variable Y."
• Example: Does the number of study hours predict exam grade?
• Multiple linear regression: two or more predictors, one outcome. Use when your hypothesis involves multiple IVs or when you want to control for confounders.
• Example: Do study hours and stress level together predict exam grade? After controlling for stress, does study time still matter?

When to Use Regression (vs. Correlation or ANOVA)

Use linear regression when:

• Your research question is predictive: “To what extent does X predict Y?”
• You have multiple predictors and want to control for confounders.
• You want to quantify the unique contribution of each IV to explaining variance in the DV.
• Do NOT use regression when:
• Your DV is categorical (use logistic regression — a different technique).
• You only want to describe association without prediction (use correlation).
• You are comparing group means (use t-test or ANOVA).

The 4 Assumptions: What to Check Before Running Regression

1. Linearity: the relationship between each predictor and the outcome should be linear. Check with scatter plots of each IV against the DV before running the analysis.

2. Normality of residuals: the errors (residuals) should be approximately normally distributed. After running regression, check the histogram and P-P plot of standardised residuals in the output (SPSS generates these via Statistics → Plots → Normal probability plot).

3. Homoscedasticity: residuals should have constant variance across all predicted values. Check the scatter plot of standardised residuals vs. standardised predicted values — it should show a random cloud, not a funnel shape.

4. No multicollinearity (multiple regression only): predictors should not be too highly correlated with each other. Check VIF in the Coefficients table — VIF < 10 is acceptable; VIF > 10 indicates problematic multicollinearity.

[TIP] Request assumption check plots in SPSS via: Analyze → Regression → Linear → Plots → move *ZRESID to Y and *ZPRED to X → tick Normal probability plot → OK.

Running Linear Regression in SPSS and Reading the Output

SPSS path: Analyze → Regression → Linear → move your DV to Dependent, IV(s) to Independent(s) → Statistics → tick Estimates, Confidence intervals, R squared change, Collinearity diagnostics → OK.

Key output sections:

Model Summary: R² = total variance in DV explained by all IVs. Adjusted R² = corrected for number of predictors (report this for multiple regression).

ANOVA table: tests whether R² is significantly greater than zero (overall model significance).

Coefficients table: B (unstandardised) and β (standardised) coefficients, t-statistic, p-value per predictor, and VIF for multicollinearity check.

Thesis Example: Predicting Exam Grade from Study Hours and Stress

Research question: Do study hours per week and perceived stress score together predict exam grade (0–100)?

• SPSS output:
• R² = .34, F(2, 118) = 30.4, p < .001 → the model explains 34% of variance in exam grade.
• Study hours: β = .51, t = 6.84, p < .001 → significant positive predictor.
• Stress: β = −.24, t = −3.12, p = .002 → significant negative predictor.
• VIF = 1.08 for both → no multicollinearity.
• APA reporting:
• "Multiple linear regression revealed that study hours (β = .51, p < .001) and stress (β = −.24, p = .002) significantly predicted exam grade. The model explained 34% of the variance in exam grade, R² = .34, adjusted R² = .33, F(2, 118) = 30.4, p < .001."

[INFO] Report the standardised coefficient β (not B) for comparing the relative importance of predictors. β is on a standard scale regardless of the original units of measurement.