Multiple Regression Analysis: A Complete Guide for Dissertations

By Dr. Sarah L., DBA in Strategic Management. Reviewed by Dr. Michael T.. 2025-09-12.

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Key takeaways

• Use multiple regression to predict a continuous outcome from multiple predictors
• Check all assumptions before interpretation: linearity, normality, homoscedasticity, and multicollinearity
• Prefer theoretically driven variable entry over stepwise selection methods
• Report both unstandardized (B) and standardized (β) coefficients
• For hierarchical regression, show R² change at each step with F-test significance
• Interpret findings substantively, connect statistics to practical meaning

Worked Example: Predicting GPA

Imagine predicting first-year graduate GPA (N = 180) from study hours, prior GPA, and self-efficacy. Before interpreting results, check assumptions: linearity and homoscedasticity (residuals versus fitted plot), normality of residuals (Q-Q plot), independence (Durbin-Watson near 2), multicollinearity (VIF below 5 to 10), and influential cases (Cook's distance). Then enter predictors (simultaneously, or hierarchically if theory specifies blocks) and interpret R squared, the overall F test, and each predictor's unstandardized B, standardized beta, and p value.

How to Report Multiple Regression in APA 7

Example: A multiple linear regression was conducted to predict first-year GPA from study hours, prior GPA, and self-efficacy. The model was significant, F(3, 176) = 28.41, p < .001, R squared = .33, adjusted R squared = .31. Prior GPA (B = 0.41, SE = 0.07, beta = .38, p < .001) and self-efficacy (B = 0.12, SE = 0.04, beta = .21, p = .003) were significant predictors; study hours were not (B = 0.01, SE = 0.01, beta = .09, p = .18).

Also report a table with B, SE, beta, t, p, and 95% CIs for each predictor, state that assumptions were checked and how violations were handled, and for hierarchical models report the change in R squared and F change for each block. Values shown are illustrative.

When to Use Multiple Regression

Multiple regression is appropriate when you want to predict a continuous outcome variable from two or more predictor variables. It answers questions like: 'Which factors predict student achievement?' or 'How much do work-life balance, salary, and autonomy contribute to job satisfaction?'

Multiple regression has several strengths for dissertation research: it can examine the unique contribution of each predictor while controlling for others, it can identify which predictors are most important, and it provides an overall measure of how well your set of predictors explains the outcome.

Before choosing multiple regression, verify that your dependent variable is continuous (interval or ratio level), you have at least two predictor variables, and relationships are approximately linear. If your outcome is categorical, you need logistic regression instead. If you want to test complex causal models with latent variables, consider SEM.

Checking Assumptions

Multiple regression requires several assumptions, and violating them can produce misleading results. Check each one before interpreting your findings.

Linearity: The relationship between each predictor and the outcome should be approximately linear. Check with scatter plots of residuals against predicted values. Non-linear patterns suggest you need transformations or polynomial terms.

Normality of residuals: Residuals should be approximately normally distributed. Check with histograms and normal probability plots. With large samples (n > 30), minor departures from normality are tolerable due to the central limit theorem.

Homoscedasticity: The variance of residuals should be constant across all levels of predicted values. Fan-shaped patterns in residual plots indicate heteroscedasticity. Weighted least squares regression or robust standard errors can address this.

No multicollinearity: Predictors should not be too highly correlated with each other. Check variance inflation factors (VIF), values above 10 (some say 5) indicate problematic multicollinearity. Consider removing or combining redundant predictors.

Independence of observations: Each case should be independent. This is violated in clustered or longitudinal data, requiring multilevel modeling instead.

Variable Entry Methods and Interpretation

How you enter predictors into the model matters for interpretation. Standard (simultaneous) entry enters all predictors at once, use when you have no theoretical basis for ordering. Hierarchical entry enters predictors in theoretically meaningful blocks, use when you want to test whether a new set of predictors adds predictive power beyond established ones.

Stepwise methods (forward, backward, stepwise) let the computer select predictors based on statistical criteria. These are controversial because they capitalize on chance and produce models that may not replicate. Most dissertation committees prefer theoretically driven entry methods.

For interpretation, focus on: R² (total variance explained), the F-test (overall model significance), and individual predictor coefficients. Report unstandardized coefficients (B) with standard errors for each predictor, as well as standardized coefficients (β) for comparing relative importance.

Standardized beta coefficients tell you the relative importance of each predictor: a β of .45 means a one standard deviation increase in that predictor is associated with a .45 standard deviation increase in the outcome, controlling for other predictors. Be cautious interpreting individual predictors when multicollinearity exists, coefficients may be unstable.

Reporting Multiple Regression in APA Format

Report your regression results in a structured format. Begin by describing your assumption checks and any actions taken to address violations. Present descriptive statistics and correlations for all variables in a preliminary table.

Create a regression table with: variable names, unstandardized coefficients (B), standard errors (SE B), standardized coefficients (β), t-values, and p-values. For hierarchical regression, show these for each step, along with R², ΔR², ΔF, and significance of the change.

In your narrative, report the overall model first: 'The regression model was statistically significant, F(k, n-k-1) = value, p < .001, R² = .value, accounting for X% of the variance in [outcome].' Then describe significant individual predictors with their coefficients and practical significance.

Always interpret your findings substantively, not just statistically. What does it mean, practically, that work-life balance (β = .38) was the strongest predictor of job satisfaction? Connect your statistical findings to your research questions and the broader literature.