“coefficient of determination”的概念、定义、翻译、参考文献-科学参考

coefficient of determination

Mathematics

The proportion of the variance of the dependent variable which is explained by the model used to fit the data. For a set of data {x_i, y_i}, 1 ≤ i≤n, if ŷ_i is the value of y predicted by the model when x = x_i, then the unexplained variance after fitting the model is $\frac{{\sum (y_{i} - {\hat{y}}_{i})}^{2}}{n}$ and the total variance is $\frac{{\sum (y_{i} - \bar{y})}^{2}}{n}$ . The explained variance is total variance-unexplained variance. When a linear model is fitted (by the least squares line of regression), the coefficient of $determination= \frac{explained variance}{total variance}$ is the square of the correlation coefficient.

Statistics

See ANOVA.

Economics

In a linear regression model, this is the proportion of sample variation in the dependent variable explained by the regression. It is denoted by R² and is equal to the squared correlation coefficient between the observed values of the dependent variable and the values predicted by the estimated regression equation. The coefficient of determination is only meaningful if the regression contains an intercept term.

单词	coefficient of determination
释义	coefficient of determination Mathematics The proportion of the variance of the dependent variable which is explained by the model used to fit the data. For a set of data {x_i, y_i}, 1 ≤ i≤n, if ŷ_i is the value of y predicted by the model when x = x_i, then the unexplained variance after fitting the model is $\frac{{\sum (y_{i} - {\hat{y}}_{i})}^{2}}{n}$ and the total variance is $\frac{{\sum (y_{i} - \bar{y})}^{2}}{n}$ . The explained variance is total variance-unexplained variance. When a linear model is fitted (by the least squares line of regression), the coefficient of $determination= \frac{explained variance}{total variance}$ is the square of the correlation coefficient. Statistics See ANOVA. Economics In a linear regression model, this is the proportion of sample variation in the dependent variable explained by the regression. It is denoted by R² and is equal to the squared correlation coefficient between the observed values of the dependent variable and the values predicted by the estimated regression equation. The coefficient of determination is only meaningful if the regression contains an intercept term.
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