How to Interpret SPSS Regression Output

When to use linear regression

Use linear regression when you want to predict a numeric outcome (the dependent variable, DV) from one or more predictors (independent variables, IVs), or to test how strongly each predictor is related to the outcome once the others are held constant. A typical thesis question is: "Do service quality, price fairness and brand trust predict customer satisfaction?" The DV is satisfaction, usually a mean score from a Likert scale, and the three predictors are the IVs. If your DV has only two categories, you need logistic regression instead.

In SPSS the path is Analyze > Regression > Linear. Before you read any table, tick the options for collinearity diagnostics, the Durbin-Watson statistic, confidence intervals and residual plots, so the checks in the next section are available.

Check the assumptions first

A regression result is only trustworthy when the data roughly meet its assumptions. Check these before you report anything:

• Linearity. Each predictor should relate to the outcome in a roughly straight line. Scatterplots show this.
• Independent errors. The Durbin-Watson value in the Model Summary should be near 2. Many lecturers accept roughly 1.5 to 2.5 as a rule of thumb.
• Constant spread of residuals. In the plot of standardised residuals against standardised predicted values, the points should form a shapeless band, not a funnel.
• Normal residuals. The histogram or P-P plot of residuals should look roughly normal.
• No serious multicollinearity. In the Coefficients table, VIF values above 5 or 10, or tolerance below .20 or .10, depending on the rule your supervisor follows, suggest predictors overlap too much.
• No influential outliers. Look at standardised residuals beyond about 3 and Cook's distance values above 1.

Also check your sample size against the rule your faculty uses. Many students cite a minimum number of cases per predictor, but the exact figure varies by source, so cite the one your supervisor accepts.

Table 1: Model Summary

This table tells you how much of the outcome your predictors explain.

• R is the correlation between the observed and predicted values of the DV.
• R Square (R²) is the proportion of variance in the DV explained by the model. If R² is .45, the predictors together explain 45% of the variation in the outcome.
• Adjusted R Square corrects R² for the number of predictors and the sample size. With several predictors or a small sample, report this one as well.
• Std. Error of the Estimate is the typical size of the prediction error, in the units of the DV.

Whether an R² is "good" depends on your field. Social science studies often report modest values, so judge it against similar published studies rather than a fixed cut-off.

Table 2: ANOVA

The ANOVA table tests whether the model as a whole predicts the DV better than simply using its mean. Read three things: the F value, the two degrees of freedom (Regression and Residual) and the Sig. value. If Sig. is below .05, the model is statistically significant overall. If it is not, stop here: individual coefficients should not be interpreted as evidence of an effect. When SPSS shows .000, report p < .001, not p = .000.

Table 3: Coefficients

This is the table your hypotheses depend on. For each predictor, read:

• Unstandardized B. The expected change in the DV for a one-unit increase in that predictor, holding the others constant. A negative B means the DV falls as the predictor rises.
• Standardized Beta (β). The same effect expressed in standard deviations, which lets you compare the relative strength of predictors measured on different scales.
• t and Sig. The test of whether that predictor's coefficient differs from zero. Below .05 means the predictor is significant after controlling for the others.
• 95% confidence interval for B. A range of plausible values. If it includes zero, the predictor is not significant at the .05 level.
• Tolerance and VIF. The multicollinearity check from the previous section.

The Constant is the predicted DV when every predictor equals zero. It is rarely meaningful for Likert-scale predictors and is usually reported without comment.

How to report the results in APA style

Write the result in the order a reader needs it: the overall model first, then each predictor. Use this template and replace the brackets with your own values from the output:

A multiple linear regression was conducted to predict [DV] from [IV 1], [IV 2] and [IV 3]. The model was [significant / not significant], F([df regression], [df residual]) = [F], p [= or <] [p], R² = [R²], adjusted R² = [adjusted R²]. [IV 1] [did / did not] significantly predict [DV] (B = [B], β = [β], t = [t], p = [p]).

Repeat the last sentence for each predictor. Then link the result to your hypotheses in plain words: "H1 was supported" or "H2 was not supported". Add one APA table listing B, SE B, β, t and p for every predictor, with the model R² and F in the table note. Round to two or three decimals consistently and italicise the statistical symbols as APA specifies.

A worked structure for your Results section

1. Sample and data screening. How many cases, how missing data and outliers were handled.
2. Descriptive statistics. Mean and standard deviation for each variable.
3. Reliability. Cronbach's alpha for each scale, if you used questionnaires.
4. Correlation matrix. A first look at relationships and a check for very high correlations between predictors.
5. Assumption checks. One short paragraph, with the plots in an appendix.
6. Regression results. The reporting template above and the table.
7. Hypothesis summary. A table of each hypothesis and whether the data supported it.

Common mistakes to avoid

• Saying a predictor "causes" the outcome when the data are cross-sectional survey responses. Say it "predicts" or "is associated with".
• Reporting only p values and leaving out B, β and the confidence interval.
• Interpreting individual predictors after a non-significant ANOVA.
• Skipping the assumption checks, or running them but not mentioning them.
• Entering a nominal variable such as ethnicity or faculty as if it were a number, instead of creating dummy variables.
• Using stepwise selection without a reason that suits your research question.
• Confusing R (a correlation) with R² (variance explained).

Where to go next

If you are still deciding which test fits your data, read our SPSS guide for thesis and questionnaire design and sampling guide. For PLS-SEM models, see the SmartPLS guide. If you would like a coach to explain your own output tables and review how you have written up the results, see our data analysis help page. SPSS support starts from RM150. You run and report your own analysis, and you should follow your supervisor's guidance on which standards to use.