Overview
This lecture covers the basic concepts and practical steps of conducting multiple linear regression analysis using SPSS, including interpretation of key output tables and hypothesis testing.
Multiple Linear Regression Basics
- Multiple regression analysis determines the influence of two or more independent variables on one dependent variable.
- Used when there are at least two independent variables.
- Dependent variable must be measured on an interval or ratio scale.
Prerequisite Tests
- Normality test checks if data distribution is normal.
- Heteroscedasticity test checks if variance of errors is constant.
- Multicollinearity test checks if independent variables are highly correlated.
- Autocorrelation test applies to time series data to check correlation between residuals.
Performing Multiple Regression in SPSS
- Open SPSS and select "Analyze" > "Regression" > "Linear".
- Enter the dependent variable (Y) and independent variables (X1–X5) in appropriate columns.
- Click OK to generate output tables.
Interpretation of SPSS Output Tables
- Model Summary Table provides the adjusted R-square value; here, adjusted R-square = 0.360, meaning independent variables explain 36% of variation in Y.
- ANOVA Table (F test) checks model fit; significance value < 0.05 means model is a good fit (here, significance = 0.000).
- Coefficients Table is used for t test to assess each independent variable's effect on Y.
Hypothesis Testing (t Test)
- Significance value < 0.05 means the independent variable has a significant effect on the dependent variable.
- X1 (sig = 0.003), X2 (sig = 0.023), X4 (sig = 0.025) significantly affect Y.
- X3 (sig = 0.238) and X5 (sig = 0.273) do not significantly affect Y.
Regression Equation and Interpretation
- Regression equation: Y = 4.737 + 0.080X1 – 0.201X2 – 0.002X3 + 0.298X4 + 0.260X5.
- Positive coefficients mean as the independent variable increases, Y increases; negative means Y decreases.
Key Terms & Definitions
- Multiple Linear Regression — Statistical method to analyze the relationship between one dependent and multiple independent variables.
- Adjusted R-square — Percentage of variation in the dependent variable explained by the model, adjusted for number of predictors.
- ANOVA Table — Table assessing overall fit of the regression model using the F test.
- t Test — Statistical test to determine the significance of individual regression coefficients.
- Significance Value (p-value) — Probability the result is due to chance; <0.05 typically considered statistically significant.
Action Items / Next Steps
- Review the PDF file for detailed SPSS output interpretation.
- Practice running multiple regression analysis in SPSS using sample data.