Regresión lineal múltiple en SPSS

Introduction to Multiple Linear Regression

Overview of Multiple Linear Regression

• Elías Alvarado introduces the concept of multiple linear regression, a statistical technique used to model the relationship between one dependent variable and two or more independent variables.

• The classical equation for multiple linear regression is presented, where 'y' represents the dependent variable and 'x1', 'x2', ..., 'xN' are the independent variables. The coefficients (Beta 1 to Beta N) indicate the relationship strength between these variables.

Objective of Multiple Linear Regression

• The main goal is to find optimal coefficient values that minimize the sum of squared residuals, which are differences between predicted and actual values.

• A dataset with 15 employees is introduced, focusing on estimating stress levels based on age, tenure, company size, and income.

Analyzing Regression Output

Model Summary Insights

• Upon running a regression analysis, key output tables appear. The correlation coefficient (R = 0.918) indicates a strong positive correlation among involved variables.

• An R-squared value of 0.842 suggests that approximately 84.2% of variability in stress levels can be explained by the independent variables.

Significance Testing

• In ANOVA results, rejection of the null hypothesis indicates at least one independent variable significantly affects the dependent variable.

• Significant variables identified include age, company size, and income based on t-values greater than or equal to 1.96 and significance levels below 0.05.

Coefficient Analysis

Understanding Coefficients

• For instance, an income coefficient of 0.002 implies that for each unit increase in income (in dollars or pesos), stress increases by 0.002 units.

• This positive coefficient indicates a direct relationship between income and stress levels among employees.

Model Optimization Techniques

Variable Selection Methods

• Discussion shifts to selecting significant variables from the outset using stepwise selection methods that add or remove independent variables based on their p-values.

Stepwise Selection Process

• To implement this method in regression analysis software: select "stepwise" under method options when analyzing linear regressions.

Final Model Recommendations