🧩 HOW TO INTERPRET REGRESSION ANALYSIS RESULTS IN RESEARCH

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1. Introduction

Regression analysis is a statistical method used to determine the relationship between one dependent variable (Y) and one or more independent variables (X₁, X₂, X₃ …).

It helps researchers answer questions like:

• Does motivation affect employee performance?

• To what extent do study habits predict academic achievement?

• How strongly does income influence savings behavior?

Regression also allows prediction — that is, estimating how much Y will change if X changes.

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2. Types of Regression

Type	When Used	Example
Simple Linear Regression	One independent variable	Effect of motivation on performance
Multiple Regression	Two or more independent variables	Effect of motivation, training, and pay on performance
Logistic Regression	When dependent variable is categorical (Yes/No)	Likelihood of adopting e-learning (1 = Yes, 0 = No)

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3. Key Components of Regression Output (SPSS Example)

When you run regression in SPSS (Analyze → Regression → Linear), you typically get three main tables:

1. Model Summary Table

2. ANOVA Table

3. Coefficients Table

Let’s explain each in detail.

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4. MODEL SUMMARY TABLE

Model	R	R Square	Adjusted R Square	Std. Error of Estimate
1	.782	.611	.605	4.228

Interpretation:

• R (Correlation Coefficient):
  Shows the strength and direction of the linear relationship between independent and dependent variables.

  • R ranges from -1 to +1.

  • Positive value = direct relationship.

  • Negative value = inverse relationship.
    👉 Example: R = .782 → strong positive relationship between motivation and performance.

• R² (Coefficient of Determination):
  Shows how much of the variation in the dependent variable is explained by the independent variable(s).
  👉 Example: R² = 0.611 → 61.1% of changes in performance are explained by motivation.

• Adjusted R²:
  Adjusts R² for the number of predictors in the model (used for multiple regression).
  👉 Example: Adjusted R² = 0.605 → After adjusting, 60.5% of performance variation is still explained by motivation.

• Std. Error of Estimate:
  Indicates the average distance between observed and predicted values.
  The smaller it is, the better the model fits.

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5. ANOVA TABLE (F-Test)

Model	Sum of Squares	df	Mean Square	F	Sig.
Regression	1560.45	1	1560.45	87.29	.000
Residual	990.12	48	20.63
Total	2550.57	49

Interpretation:

• The ANOVA table tests the overall significance of the regression model.

• It checks whether the independent variable(s) significantly predict the dependent variable.

• F-value: Indicates how well the regression model fits compared to a model with no predictors.

• Sig. (p-value):

  • If p < 0.05, the regression model is statistically significant.

  • This means the independent variable(s) collectively have a significant effect on the dependent variable.

👉 Example Interpretation:

“The regression model is statistically significant, F(1,48) = 87.29, p < 0.05. This implies that motivation significantly influences employee performance.”

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6. COEFFICIENTS TABLE

Model	Unstandardized Coefficients (B)	Std. Error	Standardized Coefficients (Beta)	t	Sig.
(Constant)	25.612	2.845		9.00	.000
Motivation	0.672	0.072	.782	9.34	.000

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Interpretation:

This table provides the regression equation and individual predictor significance.

A. Regression Equation:

Y = a + bX
Where:

• Y = dependent variable (Performance)

• a (Constant) = intercept (value of Y when X = 0)

• b (Slope) = how much Y changes for each unit increase in X

👉 Using the table:
Performance = 25.612 + 0.672(Motivation)

Interpretation:

For every 1-unit increase in motivation, performance increases by 0.672 units, holding other factors constant.

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B. Beta Coefficient (Standardized Coefficient):

• Shows the relative importance of each independent variable (especially in multiple regression).

• Larger Beta means stronger influence on the dependent variable.

👉 Example:

Beta = 0.782 → Motivation has a strong positive impact on performance.

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C. t-value and Significance (p-value):

• Used to test whether each independent variable significantly predicts the dependent variable.

• Decision rule:

  • If p < 0.05, the variable has a statistically significant effect.

  • If p > 0.05, the effect is not significant.

👉 Example:

For Motivation: t = 9.34, p = .000 (< 0.05) → Motivation significantly affects performance.

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7. MULTIPLE REGRESSION EXAMPLE

Model	Unstandardized B	Std. Error	Beta	t	Sig.
(Constant)	15.124	3.221		4.70	.000
Motivation	0.482	0.086	.623	5.61	.000
Training	0.320	0.091	.402	3.51	.001
Supervision	0.105	0.084	.156	1.25	.216

Interpretation:

• The overall regression model is significant (check ANOVA: p < 0.05).

• Motivation (p = .000) and Training (p = .001) have significant positive effects on performance.

• Supervision (p = .216 > 0.05) does not significantly affect performance.

Regression Equation:
Performance = 15.124 + 0.482(Motivation) + 0.320(Training) + 0.105(Supervision)

Interpretation Summary:

A unit increase in motivation leads to a 0.482 increase in performance, while a unit increase in training leads to a 0.320 increase. Supervision shows no significant contribution. Motivation is the strongest predictor of performance (β = .623).

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8. How to Write Regression Results in Your Project (Example Write-Up)

Example (Chapter Four – Data Analysis):

Table 4.10: Regression Analysis Showing the Effect of Motivation on Employee Performance
The result of the regression analysis (Table 4.10) shows that motivation significantly predicts employee performance (β = 0.782, t = 9.34, p < 0.05). The R² value of 0.611 indicates that 61.1% of the variation in employee performance is explained by motivation. The ANOVA result further reveals that the overall model is statistically significant (F(1,48) = 87.29, p < 0.05). Hence, the null hypothesis that motivation has no significant effect on employee performance is rejected.

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Example (Chapter Five – Discussion of Findings):

The result of the regression analysis reveals that motivation significantly influences employee performance. This aligns with the findings of Adeyemi and Ojo (2023), who reported that motivated employees tend to be more productive and committed. The high R² value (0.611) suggests that motivation explains a substantial proportion of the variance in performance. Therefore, the study confirms that employee motivation is a key driver of performance outcomes in organizations.

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9. Decision Rules for Hypothesis Testing Using Regression

Condition	Decision	Conclusion
p < 0.05	Reject H₀	Variable has significant effect
p > 0.05	Fail to reject H₀	Variable has no significant effect

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10. Common Mistakes to Avoid

❌ Confusing correlation with causation — regression shows prediction, not guaranteed cause.
❌ Ignoring Adjusted R² in multiple regression.
❌ Misinterpreting negative coefficients (they mean inverse relationships, not errors).
❌ Forgetting to check p-values before concluding significance.

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11. Summary Table of Key Regression Terms

Statistic	Meaning	Interpretation Tip
R	Correlation strength	Closer to 1 = strong relationship
R²	% of variance explained	Higher R² = better model fit
Adjusted R²	Corrected R² for sample size/predictors	Use in multiple regression
F (ANOVA)	Overall model significance	p < 0.05 → model is significant
β (Beta)	Influence of each predictor	Higher β = stronger effect
t	Individual predictor test	Higher t = stronger significance
Sig. (p-value)	Significance level	p < 0.05 = statistically significant

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12. Final Summary

To interpret regression results effectively:

1. Check the Model Summary (R²): How much variation is explained.

2. Check ANOVA (F and p-value): Whether the model is statistically significant.

3. Check Coefficients Table (β, t, p): Identify which variables are significant and their direction.

4. Write the Equation: Express relationship mathematically.

5. Discuss Implications: Link results to your research objectives and literature.