In a multivariate regression model, what does a coefficient of determination (r2) of 0.23 indicate about the predictors?

A coefficient of determination, denoted as r², quantifies how much of the variation in the dependent variable can be explained by the independent variables in the regression model. When r² is equal to 0.23, it means that 23% of the variance in intraocular eye pressure is accounted for by the predictors included in the model. This percentage provides insight into the explanatory power of the model concerning the dependent variable.

In practical terms, an r² value of 0.23 suggests that while the predictors have some level of influence on intraocular pressure, a significant majority (77%) of the variance remains unexplained, indicating that other factors or variables not included in the model may also play a role.

This understanding is pivotal when interpreting the effectiveness of the model; it helps in determining how well the chosen predictors can account for the variability in outcomes, which is crucial in fields like healthcare when making decisions based on statistical analysis.