How to read SPSS regression output: R², ANOVA, Beta coefficients, VIF and Durbin-Watson

Preparing the data before regression

Multiple linear regression is the last step of the scale-analysis chain, not the first. Each construct must pass reliability testing Cronbach's Alpha and factor analysis with KMO, Bartlett and EFA. Only the items kept after these two steps are used to create the construct's score.

Regression in SPSS runs on variables, not groups of questions. So create a mean score for each construct: go to Transform → Compute Variable, enter a name under Target Variable (e.g. X1) and enter MEAN(X1_1,X1_2,X1_3,X1_4) under Numeric Expression. The mean keeps the 1–5 scale, so it is easier to interpret than a sum. Hair et al. (2019) recommend summated scales because they reduce measurement error compared with using a single question. Two notes: reverse negative items before computing the mean; and if you only want to compute it when all items are answered, use MEAN.4(...) thay cho MEAN(...).

The sample must also be large enough. A common rule of thumb is N ≥ 50 + 8m, where m is the number of independent variables (Green, 1991; Tabachnick & Fidell, 2013); with 3 predictors, you need at least 74 observations. A power-based calculation is in the article how to calculate research sample size.

Steps to run multiple linear regression in SPSS

1. Go to Analyze → Regression → Linear. Put the dependent variable in the box Dependent, the independent variables in Independent(s), keep Method: Enter.
2. Tap Statistics: tick Estimates, Model fit, Collinearity diagnostics; under Residuals tick Durbin-Watson and Casewise diagnostics (keep Outliers outside: 3 standard deviations).
3. Tap Plots: put *ZRESID in the Y box, *ZPRED in the X box; tick Histogram and Normal probability plot.
4. Tap OK, or Paste to save the syntax and rerun when needed.

The equivalent syntax (the line /CRITERIA doesn't affect the Enter method):

REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS R ANOVA COLLIN TOL
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN
  /DEPENDENT Y
  /METHOD=ENTER X1 X2 X3
  /SCATTERPLOT=(*ZRESID ,*ZPRED)
  /RESIDUALS DURBIN HISTOGRAM(ZRESID) NORMPROB(ZRESID)
  /CASEWISE PLOT(ZRESID) OUTLIERS(3).

Reading the Model Summary and ANOVA tables

R² and adjusted R²

R² = 0,463 means the three predictors explain 46,3% of the variation in Y in the sample. This is goodness of fit, not evidence of causation. R² always rises when variables are added, even meaningless ones, so SPSS also reports the Adjusted R Square:

The two values being close (0,463 and 0,455) shows the model isn't "inflated" by the number of variables. Report both; use adjusted R² when comparing models with different numbers of predictors.

Effect size f²

Per Cohen (1988), f² = 0,02; 0,15; 0,35 are small, medium and large effects, so 0,86 is a large effect. To assess one variable's own contribution, use f² = (R²_enough − R²_{without the variable}) / (1 − R²_enough).

The ANOVA table

Sig. < 0,001 shows the model has at least one regression coefficient different from 0, i.e. it explains Y better than a constant-only model. SPSS shows .000; when reporting, write p < 0,001, not "p = 0,000".

Durbin-Watson

The Durbin-Watson statistic (Durbin & Watson, 1951) ranges 0–4; a value near 2 means no first-order autocorrelation between residuals. Field (2018) considers values below 1 or above 3 a concern; 1,94 is in the safe zone. It mainly matters for time-ordered data. In a cross-sectional survey the row order is arbitrary, so Durbin-Watson changes when you re-sort the data; report it if the committee asks, but don't over-interpret it.

Reading the Coefficients table: B, Beta, Sig. and VIF

B: unstandardised coefficients, used for prediction

The regression equation written with B: Ŷ = 0,412 + 0,318X1 + 0,241X2 + 0,087X3. Holding the other variables constant, a 1-point rise in X1 raises predicted Y by 0,318 points. Someone with X1 = X2 = X3 = 4 has predicted Y 0,412 + 1,272 + 0,964 + 0,348 ≈ 3,00.

Beta: standardised coefficients, used for comparison

Beta puts every variable on the same standard-deviation unit, so it ranks relative impact: X1 (0,356) > X2 (0,262) > X3 (0,089). Don't put Beta into the prediction equation on the original scale.

Sig.: deciding the hypotheses

X1 and X2 have Sig. < 0,05 and positive coefficients in the expected direction, so H1 and H2 are supported. X3 has Sig. = 0,155 > 0,05, so H3 is not supported. The constant's Sig. (0,076) is not used to decide any hypothesis: the constant is the predicted Y when every X equals 0, a point outside the 1–5. scale. A non-significant constant is no reason to remove it from the model either.

VIF: multicollinearity

VIF = 1 / Tolerance. Classic threshold: VIF > 10 (Tolerance < 0,10) is severe multicollinearity (Hair et al., 2019). Many authors use a stricter one: VIF > 5 is already a concern, and even 3–5 may be a problem (Hair, Risher et al., 2019). Both are conventions; the example has VIF 1,38–1,57, so it passes either way.

Checking assumptions with residual plots

• Linearity and homoscedasticity: look at the chart *ZRESID theo *ZPRED. It passes when points scatter randomly in a horizontal band around 0. A curve (U shape) suggests a non-linear relationship; a widening funnel suggests heteroscedasticity (Field, 2018; Tabachnick & Fidell, 2013).
• Normality of residuals: the histogram is bell-shaped with Mean ≈ 0 and Std. Dev. ≈ 1; on the Normal P-P Plot the points hug the diagonal. The assumption applies to the residuals, not each variable; with n = 200, slight deviations are usually acceptable.
• Independence: mainly ensured by design (each person answers once, no duplicate responses); Durbin-Watson is only a supplementary indicator.
• Outliers: the table Casewise Diagnostics lists observations with |standardised residual| > 3. Check for data-entry errors or careless responses; if you drop them, state why and compare results with and without them. Don't drop them just to raise R².
• Multicollinearity: read VIF as above.

Common mistakes when reading regression output

• Interpreting the constant's Sig. as a hypothesis, or removing the constant because it's "not significant".
• Writing "p = 0,000" instead of p < 0,001.
• Putting Beta into the prediction equation, or comparing B across variables on different scales.
• Writing "X1, X2, X3 determine 46,3% of Y" as if causation were proven.
• Dropping X3 and rerunning to make the model "look good": an unsupported hypothesis is also a result to report.
• Running the regression on individual questions instead of construct scores, or computing MEAN before reversing negative items.
• Concluding mediation from a few separate regressions; the right way is testing the indirect effect as in the article mediators and bootstrapping.

Reporting the results and checklist

A sample paragraph in APA style (illustrative figures):

Multiple linear regression (Enter method, n = 200) showed the model is statistically significant, F(3, 196) = 56,33, p < 0,001, explaining 46,3% of the variation in purchase intention (R² = 0,463; adjusted R² = 0,455; f² = 0,86). Product quality (β = 0,356; t = 6,12; p < 0,001) and perceived value (β = 0,262; t = 4,16; p < 0,001) have significant positive effects on purchase intention, while the effect of advertising is not significant (β = 0,089; t = 1,43; p = 0,155). VIF from 1,38 to 1,57 and Durbin-Watson = 1,94 show no sign of multicollinearity or notable first-order autocorrelation.

• Scales have passed Cronbach's Alpha and EFA; construct scores computed with MEAN after reversing negative items.
• Sample size sufficient for the number of predictors; Method: Enter, no Stepwise.
• R², adjusted R², f² and F(df1, df2) reported with p.
• Hypotheses decided by each predictor's Sig. and sign, ignoring the constant's Sig.
• B used for the prediction equation; Beta used to compare impact.
• VIF compared with the 10 threshold and the stricter 5, with sources cited.
• The ZRESID–ZPRED chart, histogram, P-P Plot and Casewise Diagnostics table checked.
• Ghi p < 0,001 instead of 0,000; decimal separator used consistently.