What does R-squared measure in regression analysis?

R-squared, often denoted as R², is a statistical measure used in regression analysis to determine the proportion of variance in the dependent variable that can be explained by the independent variable(s). This means that R-squared quantifies how well the independent variables in a model account for the variability of the dependent variable.

A higher R-squared value indicates a greater proportion of variance explained, suggesting that the model is a good fit for the data. For example, an R-squared value of 0.80 implies that 80% of the variance in the dependent variable can be accounted for by the independent variables included in the model. This provides valuable insight into the effectiveness of the model in explaining the relationship between variables.

In contrast, the other choices don't accurately reflect what R-squared measures: While accuracy related to predictions and the number of observations are important concepts in regression, they are not what R-squared specifically captures. Similarly, the difference between independent and dependent variables does not relate to how well one explains the variability in the other, which is the core purpose of R-squared in regression analysis.