R-Squared Value
The R-squared value is a statistical measure that represents the proportion of variance in the dependent variable explained by the independent variables in a regression model. It provides insight into how well the model fits the observed data. The value of R-squared ranges from 0 to 1, where 0 indicates that the model explains none of the variance, and 1 signifies that it explains all the variance. A higher R-squared value typically indicates a better fit for the model, though it is essential to consider the context and avoid overfitting.
https://en.wikipedia.org/wiki/Coefficient_of_determination
Mathematically, R-squared is calculated as the square of the correlation coefficient between observed and predicted values. This makes it a measure of the model’s explanatory power. However, a key limitation of R-squared is that it always increases with the addition of independent variables, even if those variables are irrelevant. To address this issue, adjusted R-squared is often used as it penalizes the addition of unnecessary predictors, providing a more realistic evaluation of the model’s performance.
https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/r-squared/
R-squared is widely used in fields such as economics, data science, and machine learning to assess the goodness of fit of linear regression models. For instance, in predictive analytics, a high R-squared value can indicate the reliability of a model in forecasting outcomes. Tools like scikit-learn, R programming language, and SAS include functions for calculating and interpreting R-squared, making it accessible for analysts and data scientists. Despite its utility, care must be taken to understand the data context and pair R-squared with other metrics for a comprehensive analysis.