A multivariate regression model found a coefficient of determination (r2) of 0.23. How would you interpret this statistic?

The coefficient of determination, commonly referred to as r², quantifies the proportion of variance in the dependent variable that can be explained by the independent variables in a regression model. In this case, an r² value of 0.23 indicates that 23% of the variation in intraocular eye pressure can be attributed to the combined effects of seasonal allergies, contact lens use, and eye drop use.

This interpretation highlights the ability of the model to account for a portion of the observed differences in eye pressure based on the specified predictors. It implies that while the specified factors explain some variability, there is still a significant portion (77%) of the variation that is not explained by these variables. This is critical for understanding the effectiveness of the model, as it suggests that other factors may also play a role in influencing intraocular pressure.

The other choices do not correctly reflect the meaning of the coefficient of determination. Some pertain to significance testing or specific measurements, which are not directly related to the r² statistic, which purely summarizes the model’s explanatory power regarding variance.