When assessing the effectiveness of a forecasting model, which statistic indicates the proportion of variance explained by the model?

The coefficient of determination, often represented as R-squared, is a key statistic used to evaluate the effectiveness of a forecasting model. It quantifies how much of the variability in the dependent variable can be explained by the independent variable(s) in the model. A higher R-squared value indicates that a greater proportion of the variance is accounted for by the model, thereby suggesting that the model provides a better fit to the data.

This statistic is particularly useful because it allows researchers and analysts to understand the strength of the relationship between the data sets involved in the forecasting model. By focusing on how well the model explains the variability, it becomes easier to assess the predictive power of the model and make informed decisions based on its output.

In contrast, the mean absolute deviation and root mean square error are metrics that assess forecast accuracy in terms of error magnitude but do not provide insight into the proportion of variance explained. The standard deviation measures the dispersion of data points but does not relate specifically to a model's explanatory power.