SPSS Regression Analysis
Regression analysis (linear regression analysis) studies the influence relationships between variables. While correlation analysis describes whether relationships exist between analysis items, regression analysis studies how X (independent variables, usually quantitative data) influences Y (dependent variable, quantitative data). Having a correlation relationship does not necessarily mean there will be a regression influence relationship.
What is Regression Analysis
Regression analysis is essentially the study of how X (independent variables, usually quantitative data) influences Y (dependent variable, quantitative data). The analysis process consists of four steps:
Step 1: Analyze the model situation
- Model fit: R² indicates how much of Y's variation can be explained by all X variables. For example, R² = 0.3 means all X variables can explain 30% of Y's variation.
- Multicollinearity: VIF value less than 5 indicates no multicollinearity problem.
- F-test: Used to determine if at least one X has an influence on Y. If significant (marked with asterisk), it indicates that at least one X has an influence relationship on Y.
Step 2: Analyze the significance of X
- If significant (judged by p-value), it indicates an influence relationship exists; otherwise, no influence relationship exists.
Step 3: Determine the direction of X's influence on Y
- Regression coefficient B value greater than 0 indicates a positive influence; otherwise, a negative influence.
Step 4: Other analyses
- Compare the magnitude of influence (compare regression coefficient B values to determine the relative influence of different X variables on Y).
Important Note: Generally, correlation analysis should be performed before regression analysis to first understand if relationships exist. Regression analysis studies whether influence relationships exist. Having a correlation relationship does not necessarily mean there will be a regression influence relationship.
Feature Access
1. Navigate to the "Analyze Results" section of your questionnaire in the SurveyMars system.
2. Click on the "SPSS Analysis" option to access the analysis features.
3. Click on the "Analysis now" button and select "Regression Analysis" from the available analysis methods.
Performing Regression Analysis
1. Select the dependent variable (Y) that you want to analyze.
2. Select the independent variable(s) (X) that you want to analyze for their influence on Y.
3. If you want to save residual items for model validation, you can check the corresponding checkbox.
4. Click the "Confirm" button to generate regression analysis results.
Interpreting Regression Results
Regression analysis results are interpreted in four steps:
Step 1: Analyze the model situation
- Model fit (R²): R² indicates how much of Y's variation can be explained by all X variables. For example, R² = 0.3 means all X variables can explain 30% of Y's variation.
- Multicollinearity (VIF): VIF value less than 5 (strictly less than 5) indicates no multicollinearity problem. If VIF is greater than 10, it indicates poor model construction.
- F-test: Used to determine if at least one X has an influence on Y. If the F-value is marked with an asterisk (*), it indicates significance (p < 0.05). If there is no asterisk, it indicates p > 0.05.
Step 2: Analyze the significance of X
- Check the p-value for each X variable
- If p < 0.05 (marked with *), it indicates a significant influence relationship exists
- If p < 0.01 (marked with **), it indicates a highly significant influence relationship exists
- If p > 0.05 (no asterisk), it indicates no significant influence relationship exists
Step 3: Determine the direction of X's influence on Y
- Regression coefficient B value greater than 0: Positive influence (as X increases, Y also increases)
- Regression coefficient B value less than 0: Negative influence (as X increases, Y decreases)
Step 4: Compare the magnitude of influence
- Compare standardized coefficients (Beta values) to determine the relative influence of different X variables on Y
- When Beta > 0, the larger the value, the greater the positive influence
- When Beta < 0, the smaller the value, the greater the negative influence
Model Validation
After regression analysis, you can validate the regression model. The validation includes the following four aspects:
1. Multicollinearity:
- Check VIF values. If all VIF values are less than 10 (strictly less than 5), it indicates no multicollinearity problem and the model is well-constructed
- If VIF is greater than 10, it indicates poor model construction
- If multicollinearity exists, you can use stepwise regression analysis, ridge regression analysis, or perform correlation analysis to manually remove highly correlated items
2. Autocorrelation:
- If D-W value is around 2 (between 1.7 and 2.3), it indicates no autocorrelation and the model is well-constructed
- If D-W value significantly deviates from 2, it indicates autocorrelation exists and the model is poorly constructed
- When autocorrelation problems occur, it is recommended to check the dependent variable Y data
3. Residual Normality:
- Save residual items during analysis, then use "Histogram" to visually inspect residual normality
- If residuals visually satisfy normality, it indicates the model is well-constructed
- If residual normality is very poor, it is recommended to rebuild the model, such as taking the logarithm of Y and rebuilding the model
4. Heteroscedasticity:
- Create scatter plots using saved residual items with independent variables X or dependent variable Y
- Check if scatter points show obvious patterns, such as residual items increasing or decreasing as X values increase
- If obvious patterns exist, it indicates heteroscedasticity and poor model construction
- If obvious heteroscedasticity exists, it is recommended to rebuild the model, such as taking the logarithm of Y and rebuilding the model
Important Notes
- Regression analysis studies how X (independent variables) influences Y (dependent variable), where X is usually quantitative data and Y is quantitative data
- Generally, correlation analysis should be performed before regression analysis to first understand if relationships exist
- Having a correlation relationship does not necessarily mean there will be a regression influence relationship
- Model validation includes checking multicollinearity (VIF), autocorrelation (D-W), residual normality, and heteroscedasticity
- VIF values less than 5 indicate no multicollinearity problem; D-W values around 2 (1.7-2.3) indicate no autocorrelation
- If regression analysis shows various abnormalities, check for outliers in the data using descriptive analysis, box plots, scatter plots, etc.
Frequently Asked Questions (FAQs)
Q1: Do I need to perform correlation analysis before regression analysis?
A: Generally, correlation analysis should be performed before regression analysis to first understand if relationships exist. Regression analysis studies whether influence relationships exist. Having a correlation relationship does not necessarily mean there will be a regression influence relationship. You can also use scatter plots to visually examine data relationships before regression analysis.
Q2: How do I compare the magnitude of influence between different independent variables?
A: If independent variables X have already shown significant influence on dependent variable Y (p < 0.05), and you want to compare the magnitude of influence, you can use standardized coefficients (Beta values). When Beta > 0, it indicates positive influence, and the larger the value, the greater the influence. When Beta < 0, it indicates negative influence, and the smaller the value, the greater the influence.
Q3: What if regression analysis is missing Y (dependent variable)?
A: Regression analysis studies the influence of X on Y. Sometimes due to questionnaire design issues, Y is missing (no corresponding questionnaire items designed). It is recommended to calculate the average of all X items to represent Y (using the "Generate Variable" average function).
Q4: Why does a single X show influence but multiple X together show no influence?
A: Sometimes when only one X is included, it shows significant influence on Y; but when multiple X variables are included together, they show no significant influence. This is very normal. When multiple X variables are included, there may be "competition" relationships, and multicollinearity problems may occur. Researchers should combine this with actual situations. Generally, including multiple X variables at once is more common, equivalent to a model including multiple X variables; while including one X at a time repeatedly is equivalent to multiple models.
Q5: What do the two values in parentheses after the F-value represent?
A: To calculate the p-value from the F-value, two degrees of freedom values (df1 and df2) are needed. Generally, df1 equals the number of independent variables; df2 equals sample size - (number of independent variables + 1). These two values are only intermediate process values needed for standard format, with no other practical significance.
Q6: What is the difference between simple regression and multiple regression?
A: When the number of X variables is 1, it is usually called simple regression or univariate regression. When the number of X variables exceeds 1, it is called multiple regression. This naming is consistent in both linear regression and logistic regression.
