Multiple Regression Using SPSS Statistics
A comprehensive guide to performing and interpreting multiple regression analysis with SPSS Statistics, including APA reporting.
Introduction to Multiple Regression
Multiple regression is a statistical technique used to predict the value of a dependent variable based on the values of two or more independent variables. It extends simple linear regression by enabling the analysis of more complex datasets with multiple predictors.
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Assumptions of Multiple Regression
Before conducting a multiple regression analysis, certain assumptions must be met:
- Linearity: The relationship between the dependent and independent variables should be linear.
- Independence: The observations should be independent of each other.
- Homoscedasticity: The variance of error terms should be constant across all levels of the independent variables.
- Normality: The residuals (errors) should be approximately normally distributed.
- No Multicollinearity: Independent variables should not be too highly correlated with each other.
Performing Multiple Regression in SPSS
- Data Entry: Enter your data into SPSS, ensuring each variable is appropriately labeled and formatted.
- Open the Regression Dialog Box: Go to Analyze > Regression > Linear… to open the Linear Regression dialog box.
- Select Variables: Move the dependent variable to the Dependent box and the independent variables to the Independent(s) box.
- Configure Options: Click on Statistics… to select additional statistics to display (e.g., R squared, ANOVA table) and Continue.
- Run the Analysis: Click OK to run the regression analysis.
Interpreting SPSS Output
The SPSS output for multiple regression includes several important tables:
- Model Summary: Provides R, R squared, adjusted R squared, and standard error of the estimate, indicating the model’s fit.
- ANOVA Table: Tests the overall significance of the model. A significant F-test indicates that the model explains a significant amount of the variance in the dependent variable.
- Coefficients Table: Displays the unstandardized coefficients (B), standardized coefficients (Beta), t-values, and significance levels (p-values) for each predictor.
Example Output Interpretation:
Model Summary: R = .872, R² = .761, Adjusted R² = .755
ANOVA: F(3, 96) = 102.9, p < .001
Coefficients:
- Constant: B = 1.23, t(96) = 2.34, p = .021
- Predictor 1: B = 0.45, β = .65, t(96) = 5.67, p < .001
- Predictor 2: B = 0.30, β = .40, t(96) = 3.78, p < .001
- Predictor 3: B = 0.20, β = .20, t(96) = 2.50, p = .014
To interpret the results:
- Examine the R squared value to understand the proportion of variance in the dependent variable explained by the independent variables.
- Look at the p-values in the coefficients table to determine the significance of each predictor. A p-value less than 0.05 typically indicates a significant predictor.
- Consider the standardized coefficients (Beta) to compare the relative importance of each predictor variable.
APA Reporting Example: The multiple regression model significantly predicted the outcome variable, F(3, 96) = 102.9, p < .001, R² = .761. Predictor 1 (β = .65, p < .001), Predictor 2 (β = .40, p < .001), and Predictor 3 (β = .20, p = .014) were significant predictors of the outcome variable.
Conclusion
Multiple regression analysis using SPSS Statistics is a powerful tool for examining the relationships between a dependent variable and multiple independent variables. By following the steps outlined in this guide, you can conduct and interpret multiple regression analysis effectively, gaining valuable insights from your data.