A higher value of r^2 indicates a better fit of the regression model to the data, suggesting that the model explains a larger proportion of the variability in the dependent variable.

Match the statistical measure with its meaning:

Coefficient of determination r^2 = A measure of the proportion of the variance in the dependent variable that is predictable from the independent variable(s) Mean squared error (MSE) = A measure of the average of the squares of the errors or deviations Correlation coefficient = A measure of the strength and direction of the linear relationship between two variables Standard error of the regression = A measure of the accuracy of predictions made with a regression analysis

Match the following terms with their definitions:

Goodness of fit = How well the model fits the observed data Variance = A measure of the variability or dispersion of a set of data points Prediction error = The difference between the observed value and the predicted value by the model Regression analysis = A statistical technique for modeling the relationship between a dependent variable and one or more independent variables

Match the following concepts with their descriptions:

Overfitting = When a statistical model describes random error or noise instead of the underlying relationship Underfitting = When a statistical model cannot capture the underlying trend of the data Residuals = The differences between observed and predicted values in a regression analysis Multicollinearity = A phenomenon in which two or more independent variables in a multiple regression model are highly correlated

Test your knowledge of the coefficient of determination, r^2, with this quiz. Explore what r^2 measures, how it is calculated, and what a higher value of r^2 indicates about the goodness of fit in statistical analysis.