Regression Analysis Using SPSS

Regression analysis is a statistical method for estimating how one or more predictor variables are associated with—and can be used to explain changes in—a dependent (outcome) variable. In its simplest form, the relationship is written as y = a + bX, where y is the dependent variable, X is the independent variable, a is the y-intercept, and b is the slope. The slope matters because it quantifies the direction and size of the relationship: a positive slope means increases in the predictor correspond to increases in the outcome, while a negative slope means increases in the predictor correspond to decreases in the outcome.

A key distinction underpins how results should be interpreted: correlation measures the strength of association between two variables, while regression focuses on how one variable affects another. Correlation is symmetric—correlating X with Y gives the same result as correlating Y with X—whereas regression is directional. Running regression with X as the predictor and Y as the outcome can produce different results than swapping the roles, because regression models a specific dependent variable. Graphically, correlation is often represented as a single point (or a correlation coefficient), while linear regression is represented by a line.

Several statistics guide interpretation. The coefficient of determination, commonly called R² (r square), indicates how much variation in the dependent variable can be explained by the predictor(s). In plain terms, R² describes how much of the “difference” in the outcome is accounted for by the model’s predictors. Another central output is the regression coefficient (beta), which indicates how much the dependent variable changes for a one-unit change in the predictor, assuming other model conditions hold. Beta can be positive or negative, and statistical significance determines whether the observed relationship is likely to reflect a real effect rather than random variation. For example, a beta of 0.90 (and significant) implies that each one-unit increase in the predictor is associated with a 0.90-unit increase in the outcome; a beta of -0.90 (and significant) implies a 0.90-unit decrease.

The practical walkthrough shows how to run these analyses in SPSS. The workflow starts under Analyze, then Regression, then Linear. For simple (single-predictor) regression, the dependent variable is placed in the Dependent box and the predictor in the Independent(s) box. Model fit options such as R² change can be selected, but the default setup is often sufficient for hypothesis testing. The output reports R² and the beta coefficients, including standardized beta and significance. In the example, transfer of training is the dependent variable and training retention is the independent variable. The model fit shows an R² of 0.223, and the beta value is 0.504 with a standardized beta of 0.473, marked significant—interpreted as: for each one-unit increase in training retention, transfer of training increases by about 0.473 units (using the standardized coefficient).

For multiple regression, the same SPSS path is used, but all independent variables are entered together. The output then provides a single R² for the overall model and separate beta and significance values for each predictor. In the example with three independent variables, the overall R² is 0.298. Only training retention shows a significant relationship with transfer of training, while the other predictors have insignificant coefficients—meaning their effects are not supported by the data under the model’s assumptions.