Linear regression in SPSS: run and interpret it for your thesis

Linear regression is one of the most widely used analyses in questionnaire-based theses. It lets you test hypotheses such as "X has a positive effect on Y". Here is how to run it in SPSS, check its assumptions, interpret the three output tables and report everything in your thesis.

In short: in SPSS, regression is run through Analyze, Regression, Linear. Put the outcome variable in "Dependent" and the explanatory variables in "Independent(s)". Then read three tables: Model Summary (R²: share of variance explained), ANOVA (is the model significant?) and Coefficients (B, Beta and Sig. for each variable). A variable has a significant effect if Sig. is below 0.05.

When should you use linear regression?

Use it when you want to explain or predict a quantitative variable (or a score from a Likert scale) from one or more other variables. Example questions:

• Does job satisfaction influence the intention to stay in the company?

• Do the perceived credibility and attractiveness of Instagram ads explain purchase intention?

• Which factors explain nurses' knowledge scores?

It is called simple regression with one explanatory variable and multiple regression with several. If your dependent variable is binary (yes / no), you need logistic regression. To relate two categorical variables, use the chi-square test instead.

Before you start: prepare the variables

If your variables are measured by several items (Likert scale), first check the reliability of each scale with Cronbach's alpha, then create a mean score per variable: Transform, Compute Variable, then the MEAN function applied to the items. This score is what goes into the regression.

Assumptions to check

• Linearity: the relationship between each explanatory variable and the dependent variable is roughly linear (check with a scatterplot).

• Independence of errors: the Durbin-Watson statistic should be close to 2 (in practice between 1.5 and 2.5).

• Normality of residuals: check with the histogram and the P-P plot of the residuals.

• Homoscedasticity: the spread of residuals is regular (standardized residuals against predicted values, with no funnel shape).

• No multicollinearity: explanatory variables are not too strongly correlated with each other. The VIF should stay below 5 (more tolerant threshold: 10).

For the sample, a frequently cited rule recommends at least 50 + 8 × k observations, k being the number of explanatory variables. See also sample size for a thesis.

Running the regression in SPSS, step by step

1. Menu Analyze, Regression, Linear.

2. Put the outcome variable in Dependent.

3. Put the explanatory variable(s) in Independent(s). Keep the "Enter" method.

4. Statistics button: tick Estimates, Model fit, Collinearity diagnostics and Durbin-Watson.

5. Plots button: put ZRESID on Y and ZPRED on X, and tick Histogram and Normal probability plot.

6. Click OK.

Interpreting the results

The "Model Summary" table

R² shows the share of the variance of the dependent variable explained by the model. An R² of 0.42 means the explanatory variables explain 42% of the variation in the dependent variable. In multiple regression, also report the adjusted R². This table also gives the Durbin-Watson value.

The "ANOVA" table

It tests whether the model as a whole is significant. If the Sig. value associated with F is below 0.05, the model significantly explains the dependent variable.

The "Coefficients" table

For each explanatory variable:

• B (unstandardized coefficient): how much the dependent variable changes when the explanatory variable increases by one unit, all else being equal;

• Beta (standardized coefficient): lets you compare the relative importance of the variables;

• Sig.: if it is below 0.05, the effect is significant and the corresponding hypothesis is supported;

• VIF: multicollinearity diagnostic.

How to report it in your thesis

Example wording: "A multiple linear regression was conducted to explain purchase intention from the perceived credibility and attractiveness of the ads. The model is significant, F(2, 381) = 138.6, p < 0.001, and explains 42% of the variance in purchase intention (adjusted R² = 0.42). Perceived credibility (β = 0.41, p < 0.001) and attractiveness (β = 0.32, p < 0.001) have a positive and significant effect. Hypotheses H1 and H2 are therefore supported." The values in this example are illustrative.

Present a clean summary table (not the raw SPSS output) with B, standard error, Beta, t, Sig. and VIF, then interpret the results in the discussion.

Common mistakes

• Using linear regression with a categorical dependent variable.

• Forgetting to check multicollinearity.

• Confusing significance with effect size: an effect can be significant but small.

• Claiming causality in a cross-sectional study: talk about "effect" or "relationship" carefully.

• Pasting raw SPSS tables into the thesis.

What if my model is more complex?

If your model includes several latent variables, mediations or several dependent variables, structural equation modeling is more suitable: see SmartPLS and PLS-SEM for beginners.

Official software documentation: IBM SPSS Statistics.

To test several relationships between latent variables at once, move on to our SmartPLS (PLS-SEM) course.

Frequently asked questions

What R² is acceptable?

There is no universal threshold: in social sciences and management, R² values of 0.20 to 0.40 are common. What matters is interpreting it and comparing it with similar studies.

Can I run a regression with Likert scale data?

Yes, with the mean score of several items, as is standard practice in most theses. For a single item, be cautious.

What if an assumption is not met?

Depending on the case: transform a variable, remove a highly correlated variable, use robust standard errors or another method. Mention it in the limitations.

Regression or correlation?

Correlation measures the strength of the link between two variables. Regression goes further: it models the effect of one or more variables on another while controlling for the other variables.

Going further

To master regression and other tests (chi-square, t-test, ANOVA) with your own data, take our online SPSS course. If you prefer support with your data analysis, discover our thesis and dissertation support.