SPSS Regression Analysis: How to Interpret R², Adjusted R², F and p-Values

 

SPSS regression banner explaining why R² should not be reported alone

If you are using SPSS for regression analysis, there is one common mistake you should avoid: reporting the R² value alone and concluding that your regression model is statistically significant.

For example, you may obtain:

R² = .25

A researcher might write:

“The regression model was significant and explained 25% of the variance in the dependent variable.”

The first part of that statement cannot be concluded from R² alone.

An R² of .25 means that the predictors in the regression model explain 25% of the variance in the dependent variable. However, you need additional statistics from the SPSS output to determine whether the overall regression model is statistically significant.

This distinction is important if you want your research findings to be statistically accurate.

What Does R² Mean in SPSS?

R², or R-squared, is the coefficient of determination.

It tells you the proportion of variance in the dependent variable that is explained by the predictor or predictors included in your regression model.

For example:

R² = .25

means that the predictors collectively explain 25% of the variance in the dependent variable.

The remaining 75% represents variance that is not explained by the predictors in that particular model.

However, this does not automatically mean that the model is statistically significant.

That is where the ANOVA table becomes important.

R² Does Not Tell You Whether the Model Is Significant

This is one of the most important things to understand when interpreting regression output.

Consider a hypothetical SPSS result:

R² = .25

You know that the model explains 25% of the variance.

But you still need to examine the F-statistic and its significance value (Sig.) in the ANOVA table to determine whether the overall regression model is statistically significant.

For example:

Statistic	Value
R²	.25
F	15.42
Sig.	.001

Because the Sig. value is .001, which is below the conventional .05 significance level, the overall regression model is statistically significant.

A correct interpretation would therefore be:

The regression model was statistically significant, F(..., ...) = 15.42, p < .001, explaining 25% of the variance in the dependent variable (R² = .25).

Notice that we did not conclude that the model was significant simply because R² was .25.

The Key SPSS Statistics You Should Examine

When interpreting a regression analysis, don't focus on just one number. Different statistics answer different questions.

1. R² — How Much Is Explained?

R² tells you how much variance in the dependent variable is explained by the predictors.

For example:

R² = .40

means that the predictors explain 40% of the variance in the dependent variable.

The higher the R², the greater the proportion of variance explained by the model.

However, whether an R² value is considered large or small depends heavily on the research field, phenomenon being studied, measurement quality and study design.

So avoid saying that an R² is automatically “good” simply because it is high.

2. Adjusted R² — A More Conservative Estimate

SPSS also reports Adjusted R².

Adjusted R² takes into account the number of predictors in the model and the sample size.

This becomes particularly useful when your regression model contains several predictors.

For example, your SPSS output might show:

R² = .40

Adjusted R² = .37

You can report both, but when discussing the explanatory power of a multiple regression model, researchers often pay particular attention to the adjusted value because it penalizes the model for adding predictors that do not contribute sufficiently.

3. F-Statistic — Is the Overall Model Significant?

The F-statistic appears in the ANOVA table.

It tests the overall regression model.

In simple terms, it helps answer:

Does the regression model as a whole significantly predict the dependent variable?

You should therefore examine the F value together with its significance value.

For example:

F = 18.63, p < .001

indicates that the overall regression model is statistically significant.

4. Sig. Value — Is the Model Statistically Significant?

The Sig. column in the ANOVA table provides the p-value for the overall F-test.

A commonly used significance level is:

α = .05

Therefore:

• p < .05 → statistically significant
• p ≥ .05 → not statistically significant

But remember: statistical significance does not tell you how large or practically important the effect is.

A statistically significant model can explain a relatively small amount of variance.

5. Beta (β) — What Is the Direction of the Relationship?

The standardized Beta coefficient (β) helps you understand the direction and relative contribution of individual predictors.

For example:

β = .42

indicates a positive relationship between the predictor and the dependent variable, controlling for the other predictors in the model.

A negative coefficient, such as:

β = −.31

indicates a negative relationship.

In multiple regression, Beta coefficients can also help you compare the relative strength of predictors measured on different scales.

6. p-Value — Is an Individual Predictor Significant?

While the ANOVA table tells you whether the overall model is significant, the coefficients table helps you determine whether individual predictors make statistically significant contributions.

For example:

Predictor	β	p
Employee Motivation	.42	.001
Job Satisfaction	.28	.014
Work Experience	.06	.421

Here:

• Employee Motivation is statistically significant.
• Job Satisfaction is statistically significant.
• Work Experience is not statistically significant at the .05 level.

Therefore, you should not simply say:

“All predictors significantly predicted the dependent variable.”

The coefficients table must support that conclusion.

A Simple Way to Remember It

When interpreting regression output in SPSS, remember:

R² = HOW MUCH?

How much variance does the model explain?

F and p = DOES THE MODEL WORK STATISTICALLY?

Is the overall regression model statistically significant?

β = WHICH DIRECTION AND HOW STRONG?

What is the direction and relative contribution of each predictor?

Individual p-values = WHICH PREDICTORS MATTER STATISTICALLY?

Are the individual predictors statistically significant?

This simple framework can prevent many common reporting errors.

A Common Reporting Mistake

❌ Incorrect:

“The regression analysis showed that R² = .32, indicating that the model was statistically significant.”

Why is this problematic?

Because R² does not test statistical significance.

Better:

“The regression model explained 32% of the variance in the dependent variable (R² = .32). The overall model was statistically significant, F(..., ...) = XX.XX, p < .001.”

The exact F statistic, degrees of freedom and p-value should come from your actual SPSS output.

What Should You Report From SPSS?

For a standard multiple regression, your results section will usually need information from several parts of the SPSS output.

Model Summary

Look at:

• R
• R²
• Adjusted R²
• Standard Error of the Estimate

ANOVA Table

Look at:

• F-statistic
• Degrees of freedom
• Sig. value

Coefficients Table

Look at:

• B
• Standard Error
• Beta (β)
• t
• Sig. (p-value)

Don't simply copy every number from the SPSS output into your research report. Select the statistics that are relevant to your research questions and hypotheses.

Final SPSS Wednesday Tip 

Don't report R² alone.

R² tells you the proportion of variance explained, but it does not by itself establish statistical significance.

For a proper interpretation, examine the Model Summary, ANOVA and Coefficients tables together.

And remember:

Statistical significance and explanatory power are not the same thing.

A strong SPSS interpretation goes beyond copying numbers from the output. You need to understand what each statistic means and what conclusion it actually supports.

Want to Learn SPSS Without the Confusion?

If you are a student, researcher or academic struggling to understand what to click in SPSS, which output to use, and how to interpret the results correctly, my practical SPSS Research Guide was created to make the process easier.

The guide takes you through SPSS analysis in a practical, research-focused way so that you can move from data → analysis → output → interpretation with greater confidence.

👉 Get the SPSS Research Guide here: 

Don't just learn how to generate SPSS tables.

Learn how to understand and report them correctly.

Frequently Asked Questions

Is R² the same as statistical significance?

No. R² measures the proportion of variance explained by the regression model. Statistical significance of the overall model is assessed using the F-test and its p-value.

What R² value is considered good?

There is no universal cutoff for a “good” R². Its interpretation depends on the research field, study design, measurement quality and the phenomenon being investigated.

What is the difference between R² and Adjusted R²?

R² indicates the proportion of variance explained by the predictors. Adjusted R² adjusts the estimate based on the number of predictors and sample size and is particularly useful in multiple regression.

Which SPSS table shows whether my regression model is significant?

The ANOVA table provides the F-statistic and its associated significance value for testing the overall regression model.

Which SPSS table shows whether individual predictors are significant?

The Coefficients table provides the significance value for each predictor, along with B, standard error, Beta and t statistics.