When r2 is equal to 1, 100% ot the variation in Y can be explained by variation of X 100% of Ihe variation in X can be explained by the variation of Y 1% of the variation in Y can be explained by variation of X 1% of the variation in Xcan be explained by the variation of Y

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06-12-2022
Mathematics

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When r2 is equal to 1, 100% ot the variation in Y can be explained by variation of X 100% of Ihe variation in X can be explained by the variation of Y 1% of the variation in Y can be explained by variation of X 1% of the variation in Xcan be explained by the variation of Y

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zaibfatimarizvi zaibfatimarizvi · Answer 1 · 2022-12-14T19:52:42-05:00

When the coefficient of determination (R^2) is equal to 1, 100% of the variation in Y can be explained by variation of X.

The coefficient of determination (R²) measure how well a statistical model predicts an outcome. The R-squared, known as R² refers to the proportion of variation in the dependent variable that is predicted by the statistical model. It typically has a value in the range of 0 through to 1. A value of 1 indicates that predictions are identical to the observed values. In other words, an R-squared of 100% means that all movements of a dependent variable are completely explained by movements in the independent variable(s). Hence, R^2 = 1 means that all of the data points fall perfectly on the regression line. The predictor x accounts for all of the variation in y.

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