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

What should you tick in SPSS before reading regression output?

Go to Analyze, Regression, Linear and open Statistics. There, tick Estimates, Confidence intervals, Model fit, Collinearity diagnostics and Durbin-Watson. If you are entering predictors in blocks, tick R squared change also. Under Plots put ZRESID on Y and ZPRED on X, and in that same box tick Histogram and Normal probability plot. IBM’s SPSS documentation for Linear Regression lists what each option adds, for example Collinearity diagnostics gives VIF and tolerance for each variable.

Now the example we will use. A commerce scholar is surveying 220 employees from public and private sector banks. Her outcome is job satisfaction, taken as the mean of 5-point items. The predictors are workload, supervisor support and pay satisfaction (all 1–5), years of service, and bank type coded 1 = public, 0 = private. All five are named in her hypotheses, so she enters them together.

Every number below is invented for teaching and we kept the arithmetic correct.

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

R (.642) is the correlation between the predicted scores and the actual scores. Mostly nobody reports it alone. R Square (.412) is the value you should 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, like the branch manager, who was never surveyed.

Adjusted R Square (.398) takes the number of predictors into account. With 220 people and only five predictors, both come out close. If the two are far apart in your output, maybe you have too many predictors for the sample. Our sample size guide covers that.

Std. Error of the Estimate (.559) is the typical error of one prediction, in the outcome’s own units. On our 1–5 scale a prediction is mostly off by half a point or so.

Durbin-Watson (1.94) can take values from 0 to 4. With our 1.94 we are close to 2, so neighbouring residuals are probably not correlated.

Many scholars are asking us whether 41% is good, and the answer changes from field to field. See what R² published studies on your own outcome got, and don’t go by a figure somebody quoted in your RAC meeting.

What does the ANOVA table in regression tell you?

For our example, the ANOVA table gives 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 the same time. It asks if the predictors together explain any variance in the population.

Look at the degrees of freedom first, because data errors show up there. Regression df equals the number of predictors (5). Residual df is n − k − 1 = 214, and the total is n − 1 = 219. Sometimes the residual df will not match your sample. That happens when SPSS has dropped cases with missing values, since by default it excludes cases listwise. Report the number it actually analysed.

Write it as F(5, 214) = 29.99, p < .001. A significant F is easy to get, and it says nothing about whether any one predictor matters.

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

B is in real units. Take supervisor support, where B = 0.29. Take two employees who are same on the other four predictors but one point apart on support. The model predicts 0.29 points more job satisfaction for the higher one. The constant (1.12) is the predicted value when every predictor is zero. On a 1–5 scale that can never happen, so you report the constant but don’t interpret it. (Centring changes this. Our mediation and moderation guide explains what it does and doesn’t change.)

Beta is in standard deviations. When support goes up by one SD, satisfaction goes up by 0.34 SD. So Beta is handy for comparing predictors measured in different units. Support (.342) comes out strongest, then pay (.263), then workload (−.200). Use Beta to compare and B to explain what a finding means. If the predictors are correlated, don’t take this ranking too seriously.

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 here. With three cadres you would make two dummies, and each one get compared with the reference group. For dummies, ignore Beta.

t, p and the confidence interval

Each t is just B divided by its standard error (0.29 / 0.05 = 5.80), and it is tested on 214 df. The 95% CI gives more informations than p. For support the interval runs from 0.19 to 0.39, and zero falls outside it.

A significant result is not automatically important, large, proven or causal. Years of service (p = .232) has not been shown to have no effect. Its interval goes from slightly negative up to 0.016 per year.

Tolerance and VIF

Tolerance and VIF show how much one predictor overlaps with the rest. Tolerance is just 1/VIF. In this output every VIF is below 1.5. High VIFs inflate the standard errors. If two of your scales overlap heavily, your factor analysis should already have warned you.

Which regression assumptions should you check and report?

One short paragraph on what you checked and what came out is enough.

• Linearity and homoscedasticity. Plot the standardised residuals (ZRESID) against the standardised predicted values (ZPRED). Dots bending in a curve mean the straight-line model may not suit your data. A funnel spread means the error variance is probably unequal, and then the standard errors and p values can’t be trusted so much.
• Independence of errors. Mostly this comes from your design itself, one questionnaire per person and no hidden clustering. Durbin-Watson matters mainly when the data is time-ordered.
• Normality of residuals. The histogram and P-P plot you check should be of the residuals. Each raw variable on its own is not what this assumption is about.
• Multicollinearity. Give the actual VIF or tolerance values in the thesis. Cut-offs like VIF above 10, or 5 for stricter reviewers, are only rules of thumb, and they are not tests.
• Influential cases. Save Cook’s distance and go through the largest values. Textbooks differ on the Cook’s cut-off, so write which one you followed. Also say whether the results changed when those cases were taken out.

In 2007 Robert O’Brien published a paper in Quality & Quantity with the title “A caution regarding rules of thumb for variance inflation factors”. From the title itself you can guess how settled those cut-offs are. So write “all VIF values were below 1.5”, and avoid lines like “there was no multicollinearity as VIF < 10”. If your plot does show a funnel, use heteroscedasticity-consistent standard errors (HC3 is common) and 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) gives four rules. Don’t give the same statistics in the text and again in the table. Exact p values go to two or three decimals, or you write p < .001. Only for statistics that can never cross 1, like R² and p, you drop the leading zero. Italics are for statistical symbols. β and other Greek letters you keep in normal type only.

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 overall model was significant, F(5, 214) = 29.99, p < .001, and it explained 41% of the variance (R² = .41, adjusted R² = .40, f² = 0.70). Supervisor support was the strongest predictor and pay satisfaction was second. Workload showed a negative association with job satisfaction. After controlling for the other predictors, public sector employees reported slightly higher satisfaction. Years of service was not a significant predictor. Table 4.x presents the coefficients. The residual plots gave no sign of marked departure from linearity or homoscedasticity. All VIF values were below 1.5.

There is no “proved” and no “caused” in it. Some guides are particular that each hypothesis gets marked as supported or not supported. Then add one line after each finding saying so.

A thesis results table template

Make the table yourself instead of pasting the raw SPSS output. Also check sample thesis from your department, because many Indian universities follow APA only loosely.

Effect size: R² and f²

R² is itself an effect size. Still, some examiners will ask for Cohen’s f² = R² / (1 − R²) also. In our example it comes to .412 / .588 = 0.70. The G*Power manual gives Cohen’s (1988) conventions of 0.02 small, 0.15 medium and 0.35 large. Take them as rough guides only. To get the share of one predictor alone, find the change in R² when that predictor is added, and divide it by 1 − R² of the full model.

What mistakes do scholars make when interpreting regression?

The first one is causal language. A survey done only once can show that support and satisfaction move together. Which one causes the other, it cannot show. Some third variable may be behind both, and the survey can’t rule that out also. When your research design is cross-sectional, keep your verbs cross-sectional too.

Next comes stepwise regression. In a thesis I would not use it, except if your field uses it as a normal thing. Whittingham and colleagues (2006, Journal of Animal Ecology) list out its drawbacks. Biased estimates and a hidden multiple-testing problem are two of them. Different selection algorithms can give different models, they say, and people lean too much on a single “best” model. They also note that these problems are well established in the statistical literature. At the viva it is much easier to defend the predictors your hypotheses name, entered at once or in planned blocks.

If you want your outputs checked before the pre-submission seminar, our statistical analysis support goes through them with you, though at the viva you have to explain every number yourself.