Linear Algebra and Differential Equations
The coefficient of determination, often denoted as $$R^2$$, is a statistical measure that explains the proportion of variance in a dependent variable that can be predicted from an independent variable in a regression model. It provides insight into how well the regression model fits the data, with values ranging from 0 to 1, where 0 indicates no explanatory power and 1 indicates perfect correlation between the variables. In the context of least squares approximations, it is a crucial metric for assessing the effectiveness of the model in minimizing the sum of squared errors.
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