Which term is often used to describe the fraction of variation in the dependent variable explained by the independent variables?

Which term is often used to describe the fraction of variation in the dependent variable explained by the independent variables?

• A. Standard deviation
• B. Correlation coefficient
• C. R-squared
• D. Linear regression

Answer: (C)

R-squared, also known as the coefficient of determination, is the term used to quantify the proportion of variability in the dependent variable that can be explained by the independent variables in a regression model. It ranges from 0 to 1, where a value of 0 indicates no explanatory power (none of the variance in the dependent variable is explained) and a value of 1 indicates perfect explanatory power (all variance in the dependent variable is explained by the model). In regression analysis, R-squared is particularly useful for assessing the goodness-of-fit of the model, helping researchers understand how well their chosen independent variables account for changes in the dependent variable. For example, if an R-squared value is 0.75, it indicates that 75% of the variation in the dependent variable can be attributed to the independent variables included in the model. This measure allows for the comparison of models, particularly when considering adding more variables to see if they improve the explanatory capacity. Other terms in the choices do not serve the same function as R-squared. Standard deviation measures the dispersion of a dataset, providing information on the spread of data points. The correlation coefficient quantifies the strength and direction of a linear relationship between two variables but does not directly relate to

R-squared, also known as the coefficient of determination, is the term used to quantify the proportion of variability in the dependent variable that can be explained by the independent variables in a regression model. It ranges from 0 to 1, where a value of 0 indicates no explanatory power (none of the variance in the dependent variable is explained) and a value of 1 indicates perfect explanatory power (all variance in the dependent variable is explained by the model).

In regression analysis, R-squared is particularly useful for assessing the goodness-of-fit of the model, helping researchers understand how well their chosen independent variables account for changes in the dependent variable. For example, if an R-squared value is 0.75, it indicates that 75% of the variation in the dependent variable can be attributed to the independent variables included in the model. This measure allows for the comparison of models, particularly when considering adding more variables to see if they improve the explanatory capacity.

Other terms in the choices do not serve the same function as R-squared. Standard deviation measures the dispersion of a dataset, providing information on the spread of data points. The correlation coefficient quantifies the strength and direction of a linear relationship between two variables but does not directly relate to