What is Adjusted R-Squared?

What is Adjusted R-Squared?

The adjusted R² modifies the standard R² to account for the degrees of freedom used when estimating model parameters. Adjusted R-Squared can be determined using the sum of squares formula. The degree of freedom is the only difference between R-square and Adjusted R-square equations. An adjusted R-squared value can be derived based on the r-squared value, the number of independent variables (predictors), and the total sample size.

R² is not comparable across models with different dependent (Y) variables.

Example of Adjusted R-Squared:

The adjusted R² value is expressed as:

$ R^{2}\, =\, 1\, -\, [(\frac{n-1}{n-k-1})\, \times (1\, -\, R^{2})] $

where:
n = number of observations
k = number of independent variables

Why is calculating Adjusted R-Squared important?

Adjusted R square adds further value to our analysis and assists analysts in analysing whether the newly added factor is bringing more value or not. Hence, it assists analysts in making better-informed risk decisions.

In addition to helping analysts make better-informed risk decisions, calculating adjusted R-squared is also important because it helps to avoid overfitting in regression models. Overfitting occurs when a model is too complex and captures noise in the data, rather than the underlying relationship between the variables. perfe R-squared penalizes models with a large number of variables, and thus encourages parsimony and simplicity in models. This, in turn, helps to improve the model’s ability to generalize to new data and make more accurate predictions. Therefore, adjusted R-squared is a valuable tool for model selection and evaluation in risk management and other fields.

Furthermore, ad R-squared can also help to prevent overfitting, which is a common problem in data analysis. Overfitting occurs when a model is too complex and captures noise or random variations in the data rather than the underlying relationships between variables. A high R-squared value in an overfit model can be misleading because the model is not generalizable to new data.

By penalizing the number of variables in a model, ad R-squared provides a more accurate estimate of the true explanatory power of the model. It allows us to compare the performance of models with different numbers of predictors and choose the best model that strikes a balance between goodness-of-fit and complexity. Overall, the use of ad R-squared is crucial for risk professionals to make informed decisions about the predictive power of their models. It helps to avoid misleading results and ensure that models are accurate and reliable for risk management purposes.