“What is the effect of transformational leadership on organizational commitment?” How do you get from that question to a table stating that leadership explains 34% of the variance in commitment? The answer is linear regression, the analysis that turns questions about effect and prediction into an equation and a proportion of explained variance.
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It is also the most assumption-laden test in a typical thesis, and most examiner objections concern assumptions that were never checked or tables that were read incorrectly. This guide to multiple regression in SPSS explains the difference between simple and multiple models, the eight assumptions and how to check each in SPSS, how to read the three output tables, how to interpret B, beta and R², how large the sample must be, and how to report the model in APA style.
What is linear regression? Linear regression estimates the relationship between a continuous dependent variable and one predictor (simple regression) or several predictors (multiple regression) through a straight-line equation of the form Y = a + b1X1 + b2X2 + … + e. It reports the proportion of variance in the dependent variable that the predictors explain together (R²) and the relative contribution of each predictor while the others are held constant (the standardized coefficient, beta).
When do you use regression rather than correlation?
Correlation answers “is there a relationship and how strong is it”. Regression answers “what is the effect of X on Y”, “how well do these variables predict Y” and “which predictor matters most when the others are controlled”. Use simple regression with one predictor and multiple regression with two or more. The dependent variable must be continuous: for a binary outcome (pass or fail) use logistic regression, and for an ordinal outcome use ordinal regression.
What are the eight assumptions of multiple regression in SPSS, and how do you check them?
| Assumption | How to check it | Common threshold | If it fails |
|---|---|---|---|
| Continuous dependent variable; predictors continuous or binary coded 0/1 | Nature of the variables | A nominal predictor with several categories must be converted to dummy variables | Dummy coding |
| Linearity | Partial regression plots (Plots, then Produce all partial plots) | A clear linear trend | Transform a predictor or use a non-linear model |
| Independence of errors | Durbin-Watson statistic (Statistics, then Durbin-Watson) | Close to 2; values below 1 or above 3 are a concern (Field, 2018) | Reconsider the design; critical for time-ordered data |
| Homoscedasticity | Plot of ZRESID against ZPRED (Plots) | A shapeless cloud, no funnel | Robust standard errors or a transformation |
| No multicollinearity | Statistics, then Collinearity diagnostics | VIF below 10 and tolerance above 0.1 (Field, 2018); Hair et al. (2019) treat VIF above 5 as a warning | Remove or combine overlapping predictors |
| Normally distributed residuals | Plots, then Normal probability plot; Explore on the saved ZRE_1 variable | P-P points close to the line | Robustness in large samples, or bootstrap |
| No influential cases | Save, then Cook’s distance and Standardized residuals; Statistics, then Casewise diagnostics | Cook’s distance below 1; standardized residuals within ±3 | Inspect the case; document the decision |
| Adequate sample size | Green’s (1991) rule: N ≥ 50 + 8k to test the overall model and N ≥ 104 + k to test individual predictors, where k is the number of predictors | For four predictors, 82 and 108 cases respectively | Enlarge the sample or reduce the predictors |
Whenever you run multiple regression in SPSS, check the assumptions and report them in a short paragraph before the regression table. That paragraph is often what separates a results chapter that is accepted from one that is returned.
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How do you run multiple regression in SPSS?
- Analyze, then Regression, then Linear.
- Move the dependent variable to Dependent and the predictors to Independent(s). Leave Method as Enter (simultaneous entry), which suits theoretically specified models; Stepwise is criticized in theses because it lets the data, not the theory, select the predictors.
- Statistics: tick Estimates, Confidence intervals, Model fit, R squared change, Descriptives, Part and partial correlations, Collinearity diagnostics, Durbin-Watson and Casewise diagnostics.
- Plots: put ZRESID on the Y axis and ZPRED on the X axis, and tick Histogram, Normal probability plot and Produce all partial plots.
- Save: tick Standardized residuals and Cook’s distance.
- Click OK to run multiple regression in SPSS. For hierarchical regression (demographic controls in a first block, the main predictors in a second), use the Next button to define the second block; SPSS reports the change in R² for each block.
How do you read the three tables of multiple regression in SPSS?
Model Summary. R is the multiple correlation; R² is the proportion of variance explained (.34 means 34%); Adjusted R² corrects for the number of predictors and the sample size and is the value to report for multiple models; the standard error of the estimate is the typical prediction error; Durbin-Watson appears at the end of the row.
ANOVA. Tests the model as a whole. F and its p value say whether the predictors together explain a significant proportion of variance. The degrees of freedom are (k, N − k − 1).
Coefficients. For each predictor:
- B (unstandardized). The change in Y for a one-unit change in X with the other predictors held constant; used to write the equation and interpreted in the units of the variables.
- Beta (standardized). The effect in standard deviation units; used to compare predictors with each other because it removes differences in measurement units.
- t and p. Whether the predictor’s contribution is significant given the other predictors in the model.
- 95% CI for B. An interval that includes zero indicates a non-significant effect.
- Tolerance and VIF. The multicollinearity check.
In the output of multiple regression in SPSS, the constant is the predicted Y when all predictors are zero. In most Likert-scale studies it has no substantive meaning and is reported without interpretation.
How do you write the result in APA style?
For the model: “A multiple regression showed that the four dimensions of transformational leadership together explained 34% of the variance in organizational commitment, R² = .34, adjusted R² = .33, F(4, 295) = 37.9, p < .001.” For the predictors: “Inspirational motivation was the strongest predictor (B = 0.41, SE = 0.07, β = .36, t = 5.86, p < .001), followed by individualized consideration (β = .22, p = .001), whereas idealized influence did not contribute significantly (β = .06, p = .310).”
If your faculty wants the equation: commitment = 1.12 + 0.41 (inspirational motivation) + 0.25 (individualized consideration) + 0.14 (intellectual stimulation) + 0.07 (idealized influence).
Effect size for the whole model is R² itself or Cohen’s f²; Cohen’s (1988) benchmarks of .02, .15 and .35 for f² correspond roughly to R² values of .02, .13 and .26. When you report multiple regression in SPSS, the thesis table has one row per predictor with B, SE, β, t, p and VIF, and a note giving R², adjusted R², F, p and Durbin-Watson.
Worked example: four dimensions predicting commitment
This worked example of multiple regression in SPSS uses a sample of 300 employees; the dependent variable is organizational commitment and the predictors are the four dimensions of transformational leadership. The sample comfortably exceeds Green’s minimum of 50 + 8 × 4 = 82 cases for the model and 104 + 4 = 108 for the individual predictors.
Assumption checks: VIF between 1.8 and 3.4 (no problematic multicollinearity); Durbin-Watson = 1.93; the ZRESID against ZPRED plot shows a shapeless cloud; the P-P plot of residuals lies close to the line; the largest Cook’s distance is 0.08.
Model Summary: R = .58, R² = .34, adjusted R² = .33, standard error of the estimate = 0.56. ANOVA: F(4, 295) = 37.9, p < .001. Coefficients: inspirational motivation B = 0.41 (SE = 0.07), β = .36, t = 5.86, p < .001; individualized consideration B = 0.25 (SE = 0.08), β = .22, t = 3.33, p = .001; intellectual stimulation B = 0.14 (SE = 0.07), β = .12, t = 1.99, p = .048; idealized influence B = 0.07 (SE = 0.07), β = .06, t = 1.02, p = .310.
Interpretation: each one-point increase in inspirational motivation is associated with a 0.41-point increase in commitment, holding the other dimensions constant, and its beta is the largest, so it is the strongest predictor. Idealized influence adds no significant explanation once the other dimensions are in the model; given its correlation of .71 with inspirational motivation, that reflects overlap between the predictors rather than the absence of a relationship with commitment.
Which mistakes in multiple regression in SPSS do examiners mark most often?
- Interpreting B as if it were beta when comparing predictors, or the reverse.
- Skipping the multicollinearity check although dimensions of one instrument often correlate above .80.
- Using Stepwise and then presenting the result as a theoretically derived model.
- Entering a nominal variable with four categories (faculty) directly as a number from 1 to 4 instead of dummy coding it.
- Running eight predictors on 60 cases.
- Reporting R² rather than adjusted R² in small-sample multiple models.
- Turning “predicts” and “explains” into “causes” in the discussion of a cross-sectional design.
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Frequently asked questions
How many predictors can I include?
A practical rule is at least 10 to 15 cases per predictor, or Green’s (1991) formula of 50 + 8*k* for the overall model. Five predictors therefore need at least 90 cases, and about 109 to test each predictor individually. Every predictor should also have a theoretical justification.
One dimension has a VIF of 6.8. Should I drop it?
It is below the liberal cut-off of 10 but above the conservative warning level of 5. Inspect its correlations with the other predictors; if one exceeds about .85, the two dimensions measure almost the same thing. Options are to combine them into a total score, or to report one model with the total score and another with the dimensions, explaining the overlap.
What is the difference between multiple, hierarchical and stepwise regression?
Multiple regression (Enter) adds all predictors at once. Hierarchical regression adds them in blocks ordered by theory and reports the change in *R*² for each block, which is the preferred way to control for demographics. Stepwise lets the software choose predictors statistically and is criticized in academic work because it capitalizes on chance features of the sample.
How do I enter a nominal variable such as faculty?
With dummy coding: a variable with four categories becomes three binary (0/1) variables, with one category left out as the reference. Before running multiple regression in SPSS, use Transform, then Recode into Different Variables for each, or Create Dummy Variables in recent versions. Each *B* is then the difference from the reference category.
Do the predictors need to be normally distributed?
No. The normality assumption concerns the residuals, not the variables. A predictor can be binary or skewed; what matters is the residual plot and the P-P plot after the model has been run.
Sources
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE.
- Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson.
- Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage.
- Green, S. B. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26(3), 499–510. https://doi.org/10.1207/s15327906mbr2603_7
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Laerd Statistics. Multiple Regression Analysis using SPSS Statistics. https://statistics.laerd.com/spss-tutorials/multiple-regression-using-spss-statistics.php
- IBM. IBM SPSS Statistics documentation: Linear Regression. https://www.ibm.com/docs/en/spss-statistics
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.