Correlation and regression, Basic Statistics

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The square of the sample correlation coefficient is typically denoted r2 and called the coefficient of determination. It estimates the fraction of the variance in Y that is explained by X in a simple linear regression. So if we have the observed dataset {y1,...yn} and the fitted dataset {f1,...fn}, and we denote the fitted dataset {f1,...fn} with {y1,...yn}, then as a starting point the total variation in the Yi around their average value can be decomposed as follows

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