What does the R-squared measure in regression models?

What does the R-squared measure in regression models?

• A. The slope of the regression line
• B. The goodness of fit of the model
• C. The fraction of variation explained by independent variables
• D. The correlation between dependent and independent variables

Answer: (C)

R-squared, also known as the coefficient of determination, measures the proportion of the variance for the dependent variable that is explained by the independent variables in a regression model. By calculating R-squared, you can assess how well the independent variables explain the variability of the dependent variable. A higher R-squared value indicates that a greater proportion of the variability is accounted for by the predictors in the model, which reflects a better fit. While R-squared does relate to goodness of fit, the correct answer specifically focuses on its role in quantifying the extent to which independent variables explain the variation in the dependent variable. The other options touch on aspects related to regression, but they do not encapsulate the primary function of R-squared as accurately. For instance, the slope indicates the relationship between the variables, correlation refers to how closely the variables move together, and while R-squared does provide information about goodness of fit, the more precise focus is on the fraction of variation explained.

R-squared, also known as the coefficient of determination, measures the proportion of the variance for the dependent variable that is explained by the independent variables in a regression model. By calculating R-squared, you can assess how well the independent variables explain the variability of the dependent variable. A higher R-squared value indicates that a greater proportion of the variability is accounted for by the predictors in the model, which reflects a better fit.

While R-squared does relate to goodness of fit, the correct answer specifically focuses on its role in quantifying the extent to which independent variables explain the variation in the dependent variable. The other options touch on aspects related to regression, but they do not encapsulate the primary function of R-squared as accurately. For instance, the slope indicates the relationship between the variables, correlation refers to how closely the variables move together, and while R-squared does provide information about goodness of fit, the more precise focus is on the fraction of variation explained.