What does the r^2-value indicate in a dataset?

The r²-value, or coefficient of determination, provides crucial information about how well a statistical model, such as a regression line, fits the data. It quantifies the proportion of variance in the dependent variable that can be explained by the independent variable(s) in the model.

When the r²-value is close to 1, it indicates that a large proportion of the variability in the data can be accounted for by the model, signifying a strong relationship between the variables. Conversely, an r²-value near 0 suggests that the model does not explain much of the variability in the data, indicating a weak relationship.

This metric is valuable in determining the effectiveness of a model in making predictions based on the dataset. It essentially answers the question of how well the chosen function captures the underlying trend in the data points.