What statistical method is used to determine whether a relationship exists between variables and to assess the strength of that relationship?

What statistical method is used to determine whether a relationship exists between variables and to assess the strength of that relationship?

• A. Regression analysis
• B. ANOVA
• C. Factor analysis
• D. Chi-square test

Answer: (A)

Regression analysis is used to determine whether a relationship exists between variables and to quantify its strength. It builds a model that shows how a dependent variable changes when one or more independent variables change. By estimating the regression coefficients, you test whether the relationship is real—if the slope is significantly different from zero, there is evidence of a relationship. The size of the slope tells you how much the dependent variable changes with a unit change in the predictor, and standardized coefficients (or beta weights) allow comparison across different predictors. The overall strength of the relationship is often summarized by R-squared, which indicates the proportion of the outcome’s variance that the model explains. Other methods have different purposes: ANOVA compares average outcomes across groups to see if there are differences, not the strength of a relationship between continuous variables; factor analysis searches for underlying latent factors that explain patterns of correlations among observed variables; chi-square tests assess whether two categorical variables are associated, but do not provide a direct measure of the strength of that relationship in the way regression does.

Regression analysis is used to determine whether a relationship exists between variables and to quantify its strength. It builds a model that shows how a dependent variable changes when one or more independent variables change. By estimating the regression coefficients, you test whether the relationship is real—if the slope is significantly different from zero, there is evidence of a relationship. The size of the slope tells you how much the dependent variable changes with a unit change in the predictor, and standardized coefficients (or beta weights) allow comparison across different predictors. The overall strength of the relationship is often summarized by R-squared, which indicates the proportion of the outcome’s variance that the model explains.

Other methods have different purposes: ANOVA compares average outcomes across groups to see if there are differences, not the strength of a relationship between continuous variables; factor analysis searches for underlying latent factors that explain patterns of correlations among observed variables; chi-square tests assess whether two categorical variables are associated, but do not provide a direct measure of the strength of that relationship in the way regression does.