What does R-squared (r2) measure in statistics?

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R-squared, or the coefficient of determination, is a statistical measure that indicates the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model. Specifically, it quantifies how well the regression line approximates the real data points. An R-squared value of 0 means that the independent variable does not explain any of the variability of the dependent variable, while a value of 1 indicates that it explains all the variability. Thus, when assessing the performance of a regression model, a higher R-squared value typically implies a better fit with the data.

In the context of the other options, the first option references the concept of a regression line with a focus on costs, which does not pertain directly to what R-squared measures. The second option mentions regression coefficients and mean, which are separate statistical concepts that describe specific aspects of the regression but do not capture the essence of R-squared. The fourth option discusses dispersion and variance, which relate to the distribution of data rather than the relationship captured through R-squared. These details highlight why the choice that describes R-squared as related to the regression line and its fitting to data is the most accurate representation of its purpose in statistics.