Interpreting Regression Output

Running a regression model in SPSS is only the first step. The real value comes from correctly interpreting the output.

Many mistakes happen not during analysis, but during interpretation. This lesson focuses on understanding what SPSS regression tables actually mean.

Main Components of Regression Output

SPSS regression output typically includes:

• Model Summary table
• ANOVA table
• Coefficients table

Each table answers a different question about the model.

Model Summary Table

The Model Summary table provides overall information about model performance.

Key values include:

• R – correlation between observed and predicted values
• R Square (R²) – proportion of variance explained
• Adjusted R² – adjusted for number of predictors

Example interpretation:

• R² = 0.72 → 72% of variation in the outcome is explained
• Adjusted R² is preferred when comparing models

ANOVA Table in Regression

The ANOVA table tests whether the regression model is statistically significant overall.

It compares:

• Variation explained by the model
• Variation unexplained (error)

The key value is the Sig. (p-value).

Interpretation:

• p < 0.05 → the model explains a significant amount of variance
• p ≥ 0.05 → the model is not useful

Coefficients Table

The Coefficients table is the most important part. It shows how each predictor affects the outcome.

Key columns include:

• B – unstandardized coefficient
• Std. Error – uncertainty of estimate
• Beta – standardized coefficient
• Sig. – significance of predictor

Example interpretation:

• B = 3.5 → each unit increase in X increases Y by 3.5 units
• p < 0.05 → predictor is statistically significant

Confidence Intervals

SPSS also provides confidence intervals for regression coefficients.

A confidence interval that does not include zero indicates a significant predictor.

Confidence intervals give more information than p-values alone.

Example Interpretation

Assume the following results:

• R² = 0.80
• ANOVA p-value = 0.001
• Study_Hours coefficient B = 4.1 (p < 0.01)

Interpretation:

80% of the variation in exam scores is explained by study hours. The overall model is statistically significant, and each additional study hour increases the score by about 4.1 points.

Common Interpretation Mistakes

Beginners often make these errors:

• Interpreting R² as accuracy
• Ignoring insignificant predictors
• Overemphasizing p-values without context

Interpretation must always be logical, not mechanical.

Running Regression Again (Menu Reminder)

Regression is run using:

• Analyze → Regression → Linear

Focus on interpretation, not just execution.

Using SPSS Syntax

REGRESSION
  /DEPENDENT Score
  /METHOD=ENTER Study_Hours.

Quiz 1

What does R² represent?

Quiz 2

Which table tests overall model significance?

Quiz 3

What does coefficient B represent?

Quiz 4

Why is Adjusted R² important?

Quiz 5

What does a confidence interval excluding zero mean?

Mini Practice

Run a regression model with one predictor.

Write a short interpretation covering:

• R² value
• Overall model significance
• Meaning of the regression coefficient

What’s Next

In the next lesson, you will learn about Logistic Regression, used when the outcome variable is categorical.