Go to Analyze > Regression > Binary Logistic, put your two-category outcome in the Dependent box and your predictors in Covariates, define any categorical predictors with the Categorical button, then run. This page shows the exact menu path, which output tables decide the result, and how to read Exp(B) as an odds ratio. When the model will not converge or the deadline is tight, a statistician can run and interpret it on your own file.
Binary logistic regression predicts a two-category outcome, such as pass or fail, from one or more predictors. Instead of a mean it models the odds of the outcome, so the key result is an odds ratio rather than a slope. This guide is part of our statistics homework help and our SPSS help hub. It gives the exact menu path, the assumption checks, and the one value in each output table that decides the result, then shows how to report it. The single idea to hold onto is that Exp(B) is an odds ratio, not a probability.
When you use it. Use binary logistic regression when the dependent variable has exactly two outcomes coded zero and one, and you have continuous or categorical predictors, or a mix of both. For an ordered outcome with three or more categories you need ordinal regression, and for three or more unordered outcomes you need multinomial regression.
Menu path, the setup that trips people up, then the five output tables to read in order. Example values follow a teaching dataset that predicts whether a student passes an exam.
The result depends on coding the outcome correctly and telling SPSS which predictors are categorical.
Code the outcome as zero and one. SPSS models the probability of the category coded one, so decide which outcome is the event of interest. If pass is the event, code pass as one and fail as zero, or the odds ratios describe the wrong direction. Laerd and Kent State both stress that a binary outcome and independent observations are requirements, not options.
Define categorical predictors, and pick the reference. A categorical predictor such as attended revision (yes or no) must go through the Categorical button so SPSS creates the indicator coding. The Exp(B) for that predictor is then the odds relative to the reference category you chose, which is why a stated reference group is part of any correct interpretation.
Assumptions to check. A binary outcome, independent observations, little multicollinearity among predictors, a linear relationship between each continuous predictor and the log odds of the outcome (the Box-Tidwell approach), and a large enough sample, with a common guide of at least 10 cases of the rarer outcome per predictor. There is no normality or equal-variance assumption, because the outcome is not continuous.
Tells you whether the predictors as a set improve on a model with no predictors.
What to read. The Omnibus Tests of Model Coefficients table, the Model row. It gives a chi-square, its degrees of freedom (which equals the number of predictors) and a Sig. value. You want this Sig. below .05, which means the model with your predictors fits significantly better than the intercept-only model. This is the logistic equivalent of the overall F test.
| Chi-square | df | Sig. | |
|---|---|---|---|
| Step | 27.402 | 2 | .000 |
| Block | 27.402 | 2 | .000 |
| Model | 27.402 | 2 | .000 |
Reports overall fit through the log likelihood and two pseudo R square measures.
What to read. The Model Summary table gives the -2 Log likelihood, where a smaller value means a better fit, and two pseudo R square values. Cox & Snell R Square cannot reach one, so Nagelkerke R Square rescales it to a zero-to-one range and is the one usually reported. Read these as approximate, not as the R square from linear regression.
| Step | -2 Log likelihood | Cox & Snell R Square | Nagelkerke R Square |
|---|---|---|---|
| 1 | 41.335 | .436 | .582 |
A goodness-of-fit test that compares predicted probabilities with observed outcomes.
The rule that reverses. Here you want a Sig. above .05. A non-significant result means the predicted and observed values are close, which is good fit. A Sig. of .05 or below flags poor fit. This is the opposite of the Omnibus test, where you want significance, so read the two tables with their different goals in mind.
| Step | Chi-square | df | Sig. |
|---|---|---|---|
| 1 | 4.219 | 8 | .837 |
Shows how many cases the model classifies correctly using a 0.5 cut value.
What to read. The Classification Table (the one for Block 1, not Block 0) gives the Overall Percentage correct in the bottom right. Compare it against the Block 0 baseline, which classifies everyone into the larger group, to see how much the predictors add. Also glance at the two group percentages to check the model is not accurate for one outcome only.
| Observed | Predicted: Pass | Percentage Correct | |
|---|---|---|---|
| Fail (0) | Pass (1) | ||
| Fail (0) | 17 | 3 | 85.0 |
| Pass (1) | 3 | 17 | 85.0 |
| Overall Percentage | 85.0 | ||
Holds the coefficients, the significance of each predictor, and the odds ratios.
What to read. The Variables in the Equation table is where the interpretation lives. For each predictor, B is the log-odds coefficient, S.E. its standard error, Wald the test statistic, df its degrees of freedom, and Sig. tells you whether that single predictor is significant at .05. The column that matters most is Exp(B), the odds ratio, with its 95% CI for EXP(B). An odds ratio above one means each one-unit rise in the predictor multiplies the odds of the outcome upward, below one means the odds fall, and near one means little effect. If the 95% confidence interval crosses one, the effect is not reliable.
| B | S.E. | Wald | df | Sig. | Exp(B) | 95% CI Lower | 95% CI Upper | |
|---|---|---|---|---|---|---|---|---|
| Hours studied | 1.152 | .429 | 7.210 | 1 | .007 | 3.164 | 1.365 | 7.334 |
| Revision(1) | 1.560 | .782 | 3.980 | 1 | .046 | 4.759 | 1.028 | 22.030 |
| Constant | -5.120 | 1.610 | 10.114 | 1 | .001 | .006 |
Reading Exp(B) as an odds ratio. For hours studied, Exp(B) = 3.164 means each extra hour of study multiplies the odds of passing by about 3.2, holding revision constant. For revision attendance, Exp(B) = 4.759 means students who attended revision have almost five times the odds of passing compared with the reference group of non-attenders. Both intervals stay above one, so both effects are reliable.
Common mistakes
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Binary logistic regression produces a long output. These six tables, read in this order, carry the marks. Everything else supports them.
| Table | What it answers | The value to read |
|---|---|---|
| Omnibus Tests of Model Coefficients | Is the model significant overall? | Model row Sig., want below .05 |
| Model Summary | How much does it explain? | Nagelkerke R Square, and -2 Log likelihood |
| Hosmer and Lemeshow Test | Does the model fit? | Sig., want above .05 |
| Classification Table | How accurate is it? | Overall Percentage correct |
| Variables in the Equation | Which predictors matter, and by how much? | Sig. and Exp(B) with its 95% CI |
| Categorical Variables Codings | Which group is the reference? | The row coded 0 is the reference |
The procedure on this page was checked against the IBM SPSS Statistics documentation and the UCLA statistical computing SPSS guides, alongside the Laerd Statistics and Kent State University binary logistic regression tutorials.
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Exp(B) is the odds ratio for a predictor in the Variables in the Equation table. It is the exponentiated B coefficient and tells you how the odds of the outcome change for a one-unit increase in that predictor, holding the others constant. A value above one means the odds increase, a value below one means they decrease, and a value near one means little effect. It is an odds ratio, not a probability.
Read the Omnibus Tests of Model Coefficients table. The Model row gives a chi-square, its degrees of freedom and a Sig. value. If that Sig. is below .05 the model with your predictors is a significantly better fit than the intercept-only model, so the predictors as a set help explain the outcome.
Nagelkerke R Square is a pseudo R square in the Model Summary table. It rescales the Cox and Snell R Square so it can reach a maximum of one, and it gives an approximate sense of how much variation in the outcome the model accounts for. It is not the same as the R square from linear regression, so report it as a pseudo R square.
It checks how well the model fits. Here you want a Sig. above .05, because a non-significant result means the predicted probabilities are close to the observed outcomes, which is good fit. A Sig. of .05 or below suggests the model does not fit well.
The reference category is the group a categorical predictor is compared against. When you define a predictor as categorical in SPSS you choose First or Last as the reference. Every Exp(B) for that predictor is the odds relative to the reference group, so you cannot interpret the odds ratio without knowing which category it is measured against.
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