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Coefficient of determination

wikipedia.org
R² does not indicate whether: the independent variables are a cause of the changes in the dependent variable; omitted-variable bias exists; the correct regression was used; the most appropriate set of independent variables has been chosen; there is collinearity present in the data on the explanatory variables; the model might be improved by using transformed versions of the existing set of independent variables.
Coefficient of determination - wikipedia.org - Your Highlight Location 136-141 | Added on Sunday, 23 June 13 02:41:54
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because the R2 will never decrease as variables are added and will probably experience an increase due to chance alone. This leads to the alternative approach of looking at the . The explanation of this statistic is almost the same as R2 but it penalizes the statistic as extra variables are included in the model.
Coefficient of determination - wikipedia.org - Your Highlight Location 89-92 | Added on Saturday, 22 June 13 14:33:11
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In many (but not all) instances where R2 is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing SSerr. In this case R2 increases as we increase the number of variables in the model (R2 is monotone increasing with the number of variables included, i.e. it will never decrease). This illustrates a drawback to one possible use of R2, where one might keep adding variables (Kitchen sink regression) to increase the R2 value.
Coefficient of determination - wikipedia.org - Your Highlight Location 83-88 | Added on Saturday, 22 June 13 14:32:55
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Values of R2 outside the range 0 to 1 can occur where it is used to measure the agreement between observed and modeled values and where the "modeled" values are not obtained by linear regression and depending on which formulation of R2 is used. If the first formula above is used, values can never be greater than one. If the second expression is used, there are no constraints on the values obtainable.
Coefficient of determination - wikipedia.org - Your Highlight Location 79-82 | Added on Saturday, 22 June 13 14:31:23
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R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data.
Coefficient of determination - wikipedia.org - Your Highlight Location 76-79 | Added on Saturday, 22 June 13 14:31:00
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an R2 value can be calculated as the square of the correlation coefficient between the original and modeled data values. In this case, the value is not directly a measure of how good the modeled values are, but rather a measure of how good a predictor might be constructed from the modeled values (by creating a revised predictor of the form ? + ??i). According to Everitt (2002, p. 78), this usage is specifically the definition of the term "coefficient of determination": the square of the correlation between two (general) variables.
Coefficient of determination - wikipedia.org - Your Highlight Location 70-75 | Added on Saturday, 22 June 13 14:30:08
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In some cases the total sum of squares equals the sum of the two other sums of squares defined above,
Coefficient of determination - wikipedia.org - Your Highlight Location 53-54 | Added on Saturday, 22 June 13 14:28:09
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The "variability" of the data set is measured through different sums of squares: the total sum of squares (proportional to the sample variance); the regression sum of squares, also called the explained sum of squares. , the sum of squares of residuals, also called the residual sum of squares.
Coefficient of determination - wikipedia.org - Your Highlight Location 41-46 | Added on Saturday, 22 June 13 14:25:48
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