Linear Regression in SPSS

Overview

This lecture covers how to perform linear regression analysis in SPSS Statistics, including assumptions to check, the step-by-step procedure, and interpretation of results.

Introduction to Linear Regression

• Linear regression predicts the value of a dependent variable based on an independent variable.
• The dependent variable is what we want to predict; the independent variable is the predictor.
• For more than one independent variable, use multiple regression.

Assumptions of Linear Regression

• The dependent variable must be continuous (interval or ratio scale).
• The independent variable must be continuous (interval or ratio scale).
• There must be a linear relationship between the variables (check with a scatterplot).
• There should be no significant outliers (review using scatterplots and diagnostics).
• Observations must be independent (test with Durbin-Watson statistic).
• Data should show homoscedasticity (equal variances along the line of best fit).
• Regression residuals (errors) should be approximately normally distributed (check with histogram or Normal P-P Plot).
• Assumptions #3-#7 can be checked using SPSS tools during analysis.

Example Scenario

• Example: Predicting car price (dependent) based on individual income (independent).
• Salesperson uses this relationship to suggest cars in areas with known average incomes.

Data Setup in SPSS

• Create variables in SPSS: 'Income' (independent), 'Price' (dependent), and optionally, 'caseno' for tracking cases.
• 'Caseno' helps identify and remove outliers but is not part of the regression analysis.

Procedure for Linear Regression in SPSS

• Navigate to Analyze > Regression > Linear in SPSS.
• Move 'Income' to Independent(s) and 'Price' to Dependent in the dialogue box.
• Use Statistics and Plots options to check for outliers, independence, homoscedasticity, and normality of residuals.
• Click OK to run the analysis and generate output tables.

Interpreting SPSS Output

• The Model Summary table provides R (correlation) and R² (variance explained by the model).
• The ANOVA table tests if the regression model significantly predicts the dependent variable (look for Sig. < 0.05).
• The Coefficients table gives the regression equation and indicates if the predictor is statistically significant.
• Example regression equation: Price = 8287 + 0.564(Income).

Key Terms & Definitions

• Dependent variable — The outcome variable being predicted.
• Independent variable — The predictor variable used in regression.
• Continuous variable — A variable measured on an interval or ratio scale.
• Linearity — The assumption that the relationship between variables is straight-line.
• Outlier — A data point far from the predicted value.
• Independence of observations — Each data point is not influenced by others.
• Homoscedasticity — Equal variance of errors along the regression line.
• Residuals — The differences between observed and predicted values.
• R² (R squared) — Proportion of variance in the dependent variable explained by the independent variable.

Action Items / Next Steps

• Practice entering and analyzing sample data in SPSS using the steps provided.
• Review scatterplots, diagnostics, and residual plots to check assumptions before interpreting results.
• Write out and interpret your own regression equation based on SPSS output.