How to interpret regression output in SPSS and report it in a thesis

What should you tick in SPSS before reading regression output?

In Analyze, Regression, Linear, open Statistics and tick Estimates, Confidence intervals, Model fit, Collinearity diagnostics and Durbin-Watson (and R squared change if you enter predictors in blocks). Under Plots, put ZRESID on Y and ZPRED on X and tick Histogram and Normal probability plot. IBM’s SPSS documentation for Linear Regression lists what each option adds; collinearity diagnostics, for instance, give VIF and tolerance for each variable.

The example: a commerce scholar surveys 220 employees of public and private sector banks. The outcome is job satisfaction (mean of 5-point items). Predictors are workload, supervisor support and pay satisfaction (all 1–5), years of service, and bank type coded 1 = public, 0 = private. Her hypotheses name all five, so she enters them together.

Every number below is invented for teaching, but the arithmetic is consistent.

How do you interpret R, R square and adjusted R square?

R (.642), the correlation between predicted and actual scores, is rarely reported alone. R Square (.412) is the one to read: the five predictors together account for about 41% of the variance in job satisfaction in this sample. The rest is everything left out of the model, such as the branch manager, who was not surveyed.

Adjusted R Square (.398) allows for the number of predictors. With 220 people and five predictors the two are close; if yours are far apart, you may have too many predictors for your sample (see our sample size guide).

Std. Error of the Estimate (.559) is the typical prediction error in the outcome’s own units. On a 1–5 scale, predictions are typically about half a point off.

Durbin-Watson (1.94) runs from 0 to 4, and values near 2 suggest neighbouring residuals are uncorrelated.

Is 41% good? There is no universal bar. Compare with published studies on the same outcome, not with a number someone quoted at your RAC meeting.

What does the ANOVA table in regression tell you?

In the example, the ANOVA table shows regression SS 46.77 on 5 df, residual SS 66.76 on 214 df, and F = 29.99. It tests one narrow thing: whether all five slopes are zero at once, that is, whether the predictors together explain any variance in the population.

Check the degrees of freedom first, because they catch data errors. Regression df is the number of predictors (5); residual df is n − k − 1 = 214; total is n − 1 = 219. If the residual df doesn’t match your sample, SPSS has dropped cases with missing values (it excludes cases listwise by default), and you must report the number analysed.

Report it as F(5, 214) = 29.99, p < .001. A significant F is a low bar; it doesn’t say any single predictor matters.

How do you interpret B, Beta, t and p in the coefficients table?

B is in real units. For supervisor support, B = 0.29: an employee one scale point higher on support is predicted to be 0.29 points higher on job satisfaction, with the other four predictors held constant. The constant (1.12), the prediction when every predictor is zero, is impossible on a 1–5 scale: report it, don’t interpret it. (Centring changes that; our mediation and moderation guide explains what centring does and doesn’t change.)

Beta is in standard deviations. A one SD rise in support goes with a 0.34 SD rise in satisfaction. It lets you compare predictors measured in different units: support (.342) is strongest, then pay (.263), then workload (−.200). Use Beta for comparison and B for meaning, and treat the ranking loosely when predictors correlate with each other.

A dummy-coded predictor

Public sector employees score 0.17 points higher on job satisfaction than private sector employees with the same workload, support, pay satisfaction and service. Private (coded 0) is the reference group. With three cadres you would create two dummies, each compared with the reference group. Ignore Beta for dummies.

t, p and the confidence interval

Each t is B divided by its standard error (0.29 / 0.05 = 5.80), tested on 214 df. The 95% CI is more informative than p: for support, 0.19 to 0.39, with zero outside it.

Significant does not mean important, large, proven or causal. And years of service (p = .232) is not shown to have no effect; its interval runs from slightly negative to 0.016 per year.

Tolerance and VIF

These show how much each predictor overlaps with the others (tolerance is 1 divided by VIF). All VIFs here are below 1.5. High VIFs inflate standard errors; if two scales overlap heavily, your factor analysis should already have warned you.

Which regression assumptions should you check and report?

A paragraph on what you checked and found is enough.

• Linearity and homoscedasticity. In the plot of standardised residuals (ZRESID) against standardised predicted values (ZPRED), a curve suggests non-linearity and a funnel suggests unequal error variance, which makes standard errors and p values less trustworthy.
• Independence of errors. This comes mostly from your design (one questionnaire per person, no hidden clustering). Durbin-Watson matters mainly for time-ordered data.
• Normality of residuals. Check the histogram and P-P plot of the residuals, not of each raw variable.
• Multicollinearity. Report the actual VIF or tolerance values. Cut-offs such as VIF above 10, or 5 for stricter reviewers, are rules of thumb, not tests.
• Influential cases. Save Cook’s distance and look at the largest values. Textbook cut-offs vary, so say which you used and whether results changed without those cases.

Robert O’Brien’s 2007 paper in Quality & Quantity is titled “A caution regarding rules of thumb for variance inflation factors”, which tells you how settled those cut-offs are. Write “all VIF values were below 1.5”, not “there was no multicollinearity as VIF < 10”. If you see a funnel, heteroscedasticity-consistent standard errors (HC3 is a common choice) are a reasonable fix; name the version and the software.

How do you report regression results in APA style in a thesis?

The APA’s numbers and statistics guide (2024) says: don’t repeat the same statistics in text and table; give exact p values to two or three decimals, or p < .001; drop the leading zero only for statistics that cannot exceed 1, such as R² and p; italicise statistical symbols but not Greek letters such as β.

A model write-up paragraph

A multiple linear regression examined whether workload, supervisor support, pay satisfaction, years of service and bank sector predicted job satisfaction among bank employees (N = 220). The model was significant, F(5, 214) = 29.99, p < .001, and explained 41% of the variance (R² = .41, adjusted R² = .40, f² = 0.70). Supervisor support was the strongest predictor, followed by pay satisfaction; workload was negatively associated with job satisfaction. Public sector employees reported slightly higher satisfaction, controlling for the other predictors. Years of service was not a significant predictor. Coefficients are in Table 4.x. Residual plots showed no marked departure from linearity or homoscedasticity, and all VIF values were below 1.5.

No “proved”, no “caused”. If your supervisor wants each hypothesis marked supported or not, add a sentence after each finding.

A thesis results table template

Rebuild the table rather than pasting raw SPSS output, and check your department’s sample thesis; many Indian universities follow APA only loosely.

Effect size: R² and f²

R² is already an effect size. Some examiners also ask for Cohen’s f² = R² / (1 − R²), here .412 / .588 = 0.70. The G*Power manual gives Cohen’s (1988) conventions: 0.02 small, 0.15 medium, 0.35 large. Treat them as rough guides. For one predictor’s own contribution, use the change in R² when it is added, divided by 1 − R² of the full model.

What mistakes do scholars make when interpreting regression?

On causal language: a survey collected once can show that support and satisfaction move together. It cannot show which causes which, or rule out a third variable behind both. If your research design is cross-sectional, your verbs should be too.

On stepwise regression, I’d avoid it in a thesis unless your field routinely uses it. Whittingham and colleagues (2006, Journal of Animal Ecology) list its drawbacks as biased estimates, inconsistency between selection algorithms, a hidden multiple-testing problem and over-reliance on a single “best” model, and note these are well established in the statistical literature. Entering the predictors your hypotheses name, at once or in planned blocks, is easier to defend at the viva.

Want your outputs checked before the pre-submission seminar? Our statistical analysis support goes through them with you; you stay the one who can explain every number.