4061:
2734:." In other words, while correlations may sometimes provide valuable clues in uncovering causal relationships among variables, a non-zero estimated correlation between two variables is not, on its own, evidence that changing the value of one variable would result in changes in the values of other variables. For example, the practice of carrying matches (or a lighter) is correlated with incidence of lung cancer, but carrying matches does not cause cancer (in the standard sense of "cause").
163:
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4076:. When we consider the performance of a model, a lower error represents a better performance. When the model becomes more complex, the variance will increase whereas the square of bias will decrease, and these two metrices add up to be the total error. Combining these two trends, the bias-variance tradeoff describes a relationship between the performance of the model and its complexity, which is shown as a u-shape curve on the right. For the adjusted
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are not zero vectors. Therefore, the equations are expected to yield different predictions (i.e., the blue vector is expected to be different from the red vector). The least squares regression criterion ensures that the residual is minimized. In the figure, the blue line representing the residual is
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may still be negative, for example when linear regression is conducted without including an intercept, or when a non-linear function is used to fit the data. In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according
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The coefficient of partial determination can be defined as the proportion of variation that cannot be explained in a reduced model, but can be explained by the predictors specified in a full(er) model. This coefficient is used to provide insight into whether or not one or more additional predictors
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indicates a lower bias error because the model can better explain the change of Y with predictors. For this reason, we make fewer (erroneous) assumptions, and this results in a lower bias error. Meanwhile, to accommodate fewer assumptions, the model tends to be more complex. Based on bias-variance
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On the other hand, the term/frac term is reversely affected by the model complexity. The term/frac will increase when adding regressors (i.e. increased model complexity) and lead to worse performance. Based on bias-variance tradeoff, a higher model complexity (beyond the optimal line) leads to
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The smaller model space is a subspace of the larger one, and thereby the residual of the smaller model is guaranteed to be larger. Comparing the red and blue lines in the figure, the blue line is orthogonal to the space, and any other line would be larger than the blue one. Considering the
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value. For example, if one is trying to predict the sales of a model of car from the car's gas mileage, price, and engine power, one can include probably irrelevant factors such as the first letter of the model's name or the height of the lead engineer designing the car because the
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predictor (equivalent to a horizontal hyperplane at a height equal to the mean of the observed data). This occurs when a wrong model was chosen, or nonsensical constraints were applied by mistake. If equation 1 of Kvålseth is used (this is the equation used most often),
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varies between 0 and 1, with larger numbers indicating better fits and 1 representing a perfect fit. The norm of residuals varies from 0 to infinity with smaller numbers indicating better fits and zero indicating a perfect fit. One advantage and disadvantage of
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are the sample variances of the estimated residuals and the dependent variable respectively, which can be seen as biased estimates of the population variances of the errors and of the dependent variable. These estimates are replaced by statistically
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1153:. This implies that 49% of the variability of the dependent variable in the data set has been accounted for, and the remaining 51% of the variability is still unaccounted for. For regression models, the regression sum of squares, also called the
4049:(due to the inclusion of a new explanatory variable) is more than one would expect to see by chance. If a set of explanatory variables with a predetermined hierarchy of importance are introduced into a regression one at a time, with the adjusted
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This equation corresponds to the ordinary least squares regression model with two regressors. The prediction is shown as the blue vector in the figure on the right. Geometrically, it is the projection of true value onto a larger model space in
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can yield negative values. This can arise when the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data. Even if a model-fitting procedure has been used,
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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
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91:, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Knowledge.
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sufficiently increases to determine if a new regressor should be added to the model. If a regressor is added to the model that is highly correlated with other regressors which have already been included, then the total
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automatically increasing when extra explanatory variables are added to the model. There are many different ways of adjusting. By far the most used one, to the point that it is typically just referred to as adjusted
2715: = 0.7 may be interpreted as follows: "Seventy percent of the variance in the response variable can be explained by the explanatory variables. The remaining thirty percent can be attributed to unknown,
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is to 1. The areas of the blue squares represent the squared residuals with respect to the linear regression. The areas of the red squares represent the squared residuals with respect to the average value.
240:, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.
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2068:{\displaystyle \rho _{{\widehat {\alpha }},{\widehat {\beta }}}={\operatorname {cov} \left({\widehat {\alpha }},{\widehat {\beta }}\right) \over \sigma _{\widehat {\alpha }}\sigma _{\widehat {\beta }}},}
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can be seen to be related to the fraction of variance unexplained (FVU), since the second term compares the unexplained variance (variance of the model's errors) with the total variance (of the data):
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2994:) are added, by the fact that less constrained minimization leads to an optimal cost which is weakly smaller than more constrained minimization does. Given the previous conclusion and noting that
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may be smaller than 0 and, in more exceptional cases, larger than 1. To deal with such uncertainties, several shrinkage estimators implicitly take a weighted average of the diagonal elements of
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2682: = 0 indicates no 'linear' relationship (for straight line regression, this means that the straight line model is a constant line (slope = 0, intercept =
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will hardly increase, even if the new regressor is of relevance. As a result, the above-mentioned heuristics will ignore relevant regressors when cross-correlations are high.
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concluded that in most situations either an approximate version of the Olkin–Pratt estimator or the exact Olkin–Pratt estimator should be preferred over (Ezekiel) adjusted
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2199:). According to Everitt, this usage is specifically the definition of the term "coefficient of determination": the square of the correlation between two (general) variables.
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is more appropriate when evaluating model fit (the variance in the dependent variable accounted for by the independent variables) and in comparing alternative models in the
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of the residuals, or standard deviation of the residuals. This would have a value of 0.135 for the above example given that the fit was linear with an unforced intercept.
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Ritter, A.; Muñoz-Carpena, R. (2013). "Performance evaluation of hydrological models: statistical significance for reducing subjectivity in goodness-of-fit assessments".
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model with one regressor. The prediction is shown as the red vector in the figure on the right. Geometrically, it is the projection of true value onto a model space in
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evaluation, as the former can be expressed as a percentage, whereas the latter measures have arbitrary ranges. It also proved more robust for poor fits compared to
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alone cannot be used as a meaningful comparison of models with very different numbers of independent variables. For a meaningful comparison between two models, an
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when they gradually shrink parameters from the unrestricted OLS solutions towards the hypothesized values. Let us first define the linear regression model as
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The values are between 0 and 1, with 0 denoting that model does not explain any variation and 1 denoting that it perfectly explains the observed variation;
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3079:. When the extra variable is included, the data always have the option of giving it an estimated coefficient of zero, leaving the predicted values and the
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is at least weakly increasing with an increase in number of regressors in the model. Because increases in the number of regressors increase the value of
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reaches a maximum, and decreases afterward, would be the regression with the ideal combination of having the best fit without excess/unnecessary terms.
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Under more general modeling conditions, where the predicted values might be generated from a model different from linear least squares regression, an
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Do not translate text that appears unreliable or low-quality. If possible, verify the text with references provided in the foreign-language article.
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Shieh, Gwowen (2008-04-01). "Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient".
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The better the linear regression (on the right) fits the data in comparison to the simple average (on the left graph), the closer the value of
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and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
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197:. Because of the many outliers, neither of the regression lines fits the data well, as measured by the fact that neither gives a very high
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Legates, D.R.; McCabe, G.J. (1999). "Evaluating the use of "goodness-of-fit" measures in hydrologic and hydroclimatic model validation".
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Colin
Cameron, A.; Windmeijer, Frank A.G. (1997). "An R-squared measure of goodness of fit for some common nonlinear regression models".
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but it penalizes the statistic as extra variables are included in the model. For cases other than fitting by ordinary least squares, the
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7703:"The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation"
6815:"The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation"
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coefficient of determination is a statistical measure of how well the regression predictions approximate the real data points. An
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will increase only when the bias eliminated by the added regressor is greater than the variance introduced simultaneously. Using
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6761:(1987). "The Coeffecient of Determination for Regression without a Constant Term". In Heijmans, Risto; Neudecker, Heinz (eds.).
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is the square of the correlation between the constructed predictor and the response variable. With more than one regressor, the
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The optimal value of the objective is weakly smaller as more explanatory variables are added and hence additional columns of
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for a derivation of this result for one case where the relation holds. When this relation does hold, the above definition of
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3824:{\displaystyle {\bar {R}}^{2}={1-{SS_{\text{res}}/{\text{df}}_{\text{res}} \over SS_{\text{tot}}/{\text{df}}_{\text{tot}}}}}
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This is an example of residuals of regression models in smaller and larger spaces based on ordinary least square regression.
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5385:{\displaystyle R^{\otimes }=(X'{\tilde {y}}_{0})(X'{\tilde {y}}_{0})'(X'X)^{-1}({\tilde {y}}_{0}'{\tilde {y}}_{0})^{-1},}
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4527:, which results by using the population variances of the errors and the dependent variable instead of estimating them.
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unchanged. The only way that the optimization problem will give a non-zero coefficient is if doing so improves the
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7080:"Methodology review: Estimation of population validity and cross-validity, and the use of equal weights in prediction"
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6176:{\displaystyle R^{2}=1-e^{{\frac {2}{n}}(\ln({\mathcal {L}}(0))-\ln({\mathcal {L}}({\widehat {\theta }}))}=1-e^{-D/n}}
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tradeoff, a higher complexity will lead to a decrease in bias and a better performance (below the optimal line). In
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Content in this edit is translated from the existing German
Knowledge article at ]; see its history for attribution.
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Despite using unbiased estimators for the population variances of the error and the dependent variable, adjusted
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with the number of variables included—it will never decrease). This illustrates a drawback to one possible use of
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This set of conditions is an important one and it has a number of implications for the properties of the fitted
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is often interpreted as the proportion of response variation "explained" by the regressors in the model. Thus,
1441:{\displaystyle R^{2}={\frac {SS_{\text{reg}}}{SS_{\text{tot}}}}={\frac {SS_{\text{reg}}/n}{SS_{\text{tot}}/n}}}
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5935:{\displaystyle R^{2}=1-\left({{\mathcal {L}}(0) \over {\mathcal {L}}({\widehat {\theta }})}\right)^{2/n}}
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of residuals is used for indicating goodness of fit. This term is calculated as the square-root of the
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is the likelihood of the estimated model (i.e., the model with a given set of parameter estimates) and
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the model might be improved by using transformed versions of the existing set of independent variables;
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will never decrease as variables are added and will likely experience an increase due to chance alone.
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4647:{\displaystyle {\frac {SS_{\text{ res, reduced}}-SS_{\text{ res, full}}}{SS_{\text{ res, reduced}}}},}
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values are all multiplied by a constant, the norm of residuals will also change by that constant but
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can be interpreted as the variance of the model, which is influenced by the model complexity. A high
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To demonstrate this property, first recall that the objective of least squares linear regression is
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is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing
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and the term / frac and thereby captures their attributes in the overall performance of the model.
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3094:. Next, an example based on ordinary least square from a geometric perspective is shown below.
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476:{\displaystyle R^{2}=1-{\frac {\color {blue}{SS_{\text{res}}}}{\color {red}{SS_{\text{tot}}}}}}
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will stay the same. As a basic example, for the linear least squares fit to the set of data:
4543:, which is known as Olkin–Pratt estimator. Comparisons of different approaches for adjusting
2928:{\displaystyle \min _{b}SS_{\text{res}}(b)\Rightarrow \min _{b}\sum _{i}(y_{i}-X_{i}b)^{2}\,}
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can be calculated for any type of predictive model, which need not have a statistical basis.
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to quantify the relevance of deviating from a hypothesis. As
Hoornweg (2018) shows, several
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It is consistent with the classical coefficient of determination when both can be computed;
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outside the range 0 to 1 occur when the model fits the data worse than the worst possible
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Principles and
Procedures of Statistics with Special Reference to the Biological Sciences
4143:. These two trends construct a reverse u-shape relationship between model complexity and
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is the total number of explanatory variables in the model (excluding the intercept), and
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is the degrees of freedom of the estimate of the population variance around the mean. df
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statistic can be calculated as above and may still be a useful measure. If fitting is by
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In the best case, the modeled values exactly match the observed values, which results in
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The creation of the coefficient of determination has been attributed to the geneticist
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3291:{\displaystyle Y=\beta _{0}+\beta _{1}\cdot X_{1}+\beta _{2}\cdot X_{2}+\varepsilon \,}
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4265:{\displaystyle R^{2}={1-{{\text{VAR}}_{\text{res}} \over {\text{VAR}}_{\text{tot}}}}}
4137:. Nevertheless, adding more parameters will increase the term/frac and thus decrease
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The intuitive reason that using an additional explanatory variable cannot lower the
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2437:{\displaystyle Y_{i}=\beta _{0}+\sum _{j=1}^{p}\beta _{j}X_{i,j}+\varepsilon _{i},}
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6971:(Second ed.). Pacific Grove, Calif.: Duxbury/Thomson Learning. p. 556.
5051:{\displaystyle R^{2}=1-{\frac {(y-Xb)'(y-Xb)}{(y-X\beta _{0})'(y-X\beta _{0})}}.}
275:) between the observed outcomes and the observed predictor values. If additional
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Shrinkage in
Multiple Regression: A Comparison of Different Analytical Methods"
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to quantify the relevance of deviating from a hypothesized value. Click on the
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of 75% means that the in-sample accuracy improves by 75% if the data-optimized
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can be calculated appropriate to those statistical frameworks, while the "raw"
831:{\displaystyle SS_{\text{res}}=\sum _{i}(y_{i}-f_{i})^{2}=\sum _{i}e_{i}^{2}\,}
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This partition of the sum of squares holds for instance when the model values
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The interpretation is the proportion of the variation explained by the model;
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is relatively straightforward after estimating two models and generating the
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that are only sometimes equivalent. One class of such cases includes that of
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can be negative, and its value will always be less than or equal to that of
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Raju, Nambury S.; Bilgic, Reyhan; Edwards, Jack E.; Fleer, Paul F. (1997).
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6431:{\displaystyle {\text{norm of residuals}}={\sqrt {SS_{\text{res}}}}=\|e\|.}
4723:{\displaystyle {\frac {SS_{\text{tot}}-SS_{\text{res}}}{SS_{\text{tot}}}}.}
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specifically, the model complexity (i.e. number of parameters) affects the
2711:) between the response variable and regressors). An interior value such as
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the squared
Pearson correlation coefficient between the dependent variable
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refer to the hypothesized regression parameters and let the column vector
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The coefficient of determination can be more intuitively informative than
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where the covariance between two coefficient estimates, as well as their
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measures based on Wald and likelihood ratio joint significance tests".
7421:"regression – R implementation of coefficient of partial determination"
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Its value is maximised by the maximum likelihood estimation of a model;
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are not the same as in the equation for smaller model space as long as
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of 1 indicates that the regression predictions perfectly fit the data.
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It should not be confused with the correlation coefficient between two
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to the source of your translation. A model attribution edit summary is
6347:: thus, Nagelkerke suggested the possibility to define a scaled
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that may be attributed to some linear combination of the regressors (
7380:"A Note on a General Definition of the Coefficient of Determination"
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originally proposed by Cox & Snell, and independently by Magee:
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As explained above, model selection heuristics such as the adjusted
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Schemetic of the bias and variance contribution into the total error
531:= ), each associated with a fitted (or modeled, or predicted) value
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Maximum
Likelihood Estimation of Functional Relationships, Pays-Bas
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of the estimate of the population variance around the model, and df
1575:{\displaystyle f_{i}={\widehat {\alpha }}+{\widehat {\beta }}q_{i}}
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The most general definition of the coefficient of determination is
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is a positively biased estimate of the population value. Adjusted
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the most appropriate set of independent variables has been chosen;
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relating the regressor and the response variable. More generally,
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is an element of and represents the proportion of variability in
324:
180:
3167:{\displaystyle Y=\beta _{0}+\beta _{1}\cdot X_{1}+\varepsilon \,}
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is a column vector of coefficients of the respective elements of
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may still be useful if it is more easily interpreted. Values for
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6737:(8th ed.). Boston, MA: Cengage Learning. pp. 508–510.
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can be interpreted as a less biased estimator of the population
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increases as the number of variables in the model is increased (
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and the modelled values. In particular, under these conditions:
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Chicco, Davide; Warrens, Matthijs J.; Jurman, Giuseppe (2021).
7593:(Fifth ed.). New York: McGraw-Hill/Irwin. pp. 73–78.
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Chicco, Davide; Warrens, Matthijs J.; Jurman, Giuseppe (2021).
4509:{\displaystyle {\text{VAR}}_{\text{tot}}=SS_{\text{tot}}/(n-1)}
4444:{\displaystyle {\text{VAR}}_{\text{res}}=SS_{\text{res}}/(n-p)}
4108:) will be lower with high complexity and resulting in a higher
1310:{\displaystyle SS_{\text{res}}+SS_{\text{reg}}=SS_{\text{tot}}}
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equals the sum of the two other sums of squares defined above:
1234:{\displaystyle SS_{\text{reg}}=\sum _{i}(f_{i}-{\bar {y}})^{2}}
922:{\displaystyle SS_{\text{tot}}=\sum _{i}(y_{i}-{\bar {y}})^{2}}
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which is analogous to the usual coefficient of determination:
4153:, which will always increase when model complexity increases,
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The above gives an analytical explanation of the inflation of
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then the variability of the data set can be measured with two
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Inserting the degrees of freedom and using the definition of
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1011:{\displaystyle R^{2}=1-{SS_{\rm {res}} \over SS_{\rm {tot}}}}
711:{\displaystyle {\bar {y}}={\frac {1}{n}}\sum _{i=1}^{n}y_{i}}
7560:
Wright, Sewall (January 1921). "Correlation and causation".
6305:
6232:
6115:
6084:
5988:
5954:
5888:
5870:
3536:
the independent variables are a cause of the changes in the
3203:(without intercept). The residual is shown as the red line.
2945:
is a row vector of values of explanatory variables for case
6735:
Probability and
Statistics for Engineering and the Sciences
4374:{\displaystyle {\text{VAR}}_{\text{tot}}=SS_{\text{tot}}/n}
4321:{\displaystyle {\text{VAR}}_{\text{res}}=SS_{\text{res}}/n}
4008:{\displaystyle {\bar {R}}^{2}=1-(1-R^{2}){n-1 \over n-p-1}}
2627:
is a measure of the global fit of the model. Specifically,
6445:
and the norm of residuals have their relative merits. For
4865:
is centered to have a mean of zero. Let the column vector
4773:
Alternatively, one can decompose a generalized version of
4566:
may be useful in a more fully specified regression model.
2295:. The explanation of this statistic is almost the same as
2238:
can be less than zero. If equation 2 of Kvålseth is used,
1841:(with fitted intercept and slope), this is also equal to
100:
to this template: there are already 1,886 articles in the
7261:"Unbiased estimation of certain correlation coefficients"
6557:= 0.998, and norm of residuals = 0.302. If all values of
6340:{\displaystyle R_{\max }^{2}=1-({\mathcal {L}}(0))^{2/n}}
4845:
is standardized with Z-scores and that the column vector
2288:
This leads to the alternative approach of looking at the
1616:
is just one special case), and the coefficient estimates
6992:
Kvalseth, Tarald O. (1985). "Cautionary Note about R2".
5978:
is the likelihood of the model with only the intercept,
3569:
there are enough data points to make a solid conclusion.
2737:
In case of a single regressor, fitted by least squares,
2619:
are unknown coefficients, whose values are estimated by
1839:
linear least squares regression with a single explanator
1674:
are obtained by minimizing the residual sum of squares.
1455:
is the number of observations (cases) on the variables.
370:
quantifies the degree of any linear correlation between
6015:{\displaystyle {{\mathcal {L}}({\widehat {\theta }})}}
27:
Indicator for how well data points fit a line or curve
7548:
http://www.originlab.com/doc/Origin-Help/LR-Algorithm
6682:
Primer of
Applied Regression and Analysis of Variance
6464:
6387:
6275:
6229:
6035:
5984:
5951:
5840:
5773:
5746:
5711:
5676:
5649:
5622:
5602:
5575:
5544:
5517:
5490:
5459:
5401:
5210:
5187:
5167:
5140:
5102:
5075:
4921:
4912:
denote the estimated parameters. We can then define
4898:
4871:
4851:
4806:
4666:
4590:
4457:
4392:
4334:
4281:
4212:
3922:
3722:
3696:) is an attempt to account for the phenomenon of the
3670:
3638:
3602:
3483:
3446:
3418:
3391:
3364:
3337:
3308:
3212:
3187:
3114:
3051:
3000:
2969:
2829:
2688:
2664:
2579:
2548:
2486:
2457:
2344:
2169:
2149:
2092:
1939:
1909:
1889:
1847:
1820:
1800:
1754:
1690:
1651:
1622:
1521:
1337:
1261:
1166:
1100:
1026:
938:
854:
736:
651:
622:
415:
6258:{\displaystyle {\mathcal {L}}({\widehat {\theta }})}
6210:
It is asymptotically independent of the sample size;
5134:
of deviating from a hypothesis can be computed with
2817:(the number of explanators including the constant).
1146:
implies a more successful regression model. Suppose
344:) values, it is not appropriate to base this on the
84:
8106:
8083:
8062:
8039:
8011:
7983:
7920:
7852:
7784:
1594:are arbitrary values that may or may not depend on
80:
a machine-translated version of the German article.
7637:
7438:
7436:
7434:
7373:
7371:
7369:
6480:
6430:
6339:
6257:
6175:
6014:
5970:
5934:
5786:
5759:
5732:
5697:
5662:
5635:
5608:
5588:
5557:
5530:
5503:
5472:
5445:
5384:
5193:
5173:
5153:
5115:
5088:
5050:
4904:
4884:
4857:
4830:
4722:
4646:
4508:
4443:
4373:
4320:
4264:
4007:
3823:
3688:
3656:
3624:
3505:
3461:
3431:
3404:
3377:
3350:
3323:
3290:
3195:
3166:
3067:
3022:
2975:
2927:
2703:
2670:
2611:
2561:
2530:
2472:
2436:
2175:
2155:
2124:
2067:
1915:
1895:
1875:
1826:
1806:
1782:
1724:
1666:
1637:
1574:
1440:
1309:
1233:
1127:
1048:
1010:
921:
830:
710:
637:
475:
330:When evaluating the goodness-of-fit of simulated (
7644:(Second ed.). New York: Macmillan. pp.
6572:Another single-parameter indicator of fit is the
4577:tables for them. The calculation for the partial
3563:present in the data on the explanatory variables;
726:The sum of squares of residuals, also called the
6281:
6223:However, in the case of a logistic model, where
5123:is a vector of zeros, we obtain the traditional
4199:statistic can be seen by rewriting the ordinary
4114:, consistently indicating a better performance.
4053:computed each time, the level at which adjusted
2866:
2831:
6569:remains the same, but norm of residuals = 302.
6026:is the sample size. It is easily rewritten to:
5069:solutions are used instead of the hypothesized
4523:is not an unbiased estimator of the population
3469:, giving the minimal distance from the space.
3331:(without intercept). Noticeably, the values of
1598:or on other free parameters (the common choice
1466:(variance of the model's predictions, which is
6623:Pearson product-moment correlation coefficient
5446:{\displaystyle {\tilde {y}}_{0}=y-X\beta _{0}}
2743:Pearson product-moment correlation coefficient
126:accompanying your translation by providing an
71:Click for important translation instructions.
58:expand this article with text translated from
7761:
7526:. Lecture Notes in Statistics. Vol. 69.
2139:value can be calculated as the square of the
8:
7259:Olkin, Ingram; Pratt, John W. (March 1958).
6422:
6416:
6200:noted that it had the following properties:
5705:might increase at the cost of a decrease in
4118:increasing errors and a worse performance.
3038:follows directly from the definition above.
2612:{\displaystyle \beta _{0},\dots ,\beta _{p}}
7028:"Linear Regression – MATLAB & Simulink"
6680:Glantz, Stanton A.; Slinker, B. K. (1990).
6613:Nash–Sutcliffe model efficiency coefficient
6561:are multiplied by 1000 (for example, in an
7768:
7754:
7746:
2726:, as to other statistical descriptions of
1063:. A baseline model, which always predicts
7728:
7718:
7327:
7317:
7276:
6840:
6830:
6472:
6463:
6405:
6396:
6388:
6386:
6327:
6323:
6304:
6303:
6285:
6280:
6274:
6241:
6240:
6231:
6230:
6228:
6163:
6156:
6124:
6123:
6114:
6113:
6083:
6082:
6060:
6059:
6040:
6034:
5997:
5996:
5987:
5986:
5985:
5983:
5953:
5952:
5950:
5922:
5918:
5897:
5896:
5887:
5886:
5869:
5868:
5865:
5845:
5839:
5778:
5772:
5751:
5745:
5724:
5716:
5710:
5689:
5681:
5675:
5654:
5648:
5627:
5621:
5601:
5580:
5574:
5549:
5543:
5522:
5516:
5495:
5489:
5464:
5458:
5437:
5415:
5404:
5403:
5400:
5370:
5360:
5349:
5348:
5338:
5327:
5326:
5313:
5281:
5270:
5269:
5248:
5237:
5236:
5215:
5209:
5186:
5166:
5145:
5139:
5107:
5101:
5080:
5074:
5033:
5003:
4941:
4926:
4920:
4897:
4876:
4870:
4850:
4805:
4708:
4693:
4677:
4667:
4665:
4632:
4617:
4601:
4591:
4589:
4486:
4480:
4464:
4459:
4456:
4421:
4415:
4399:
4394:
4391:
4363:
4357:
4341:
4336:
4333:
4310:
4304:
4288:
4283:
4280:
4253:
4248:
4241:
4236:
4233:
4226:
4217:
4211:
4072:can be interpreted as an instance of the
3973:
3964:
3936:
3925:
3924:
3921:
3811:
3806:
3800:
3794:
3779:
3774:
3768:
3762:
3752:
3745:
3736:
3725:
3724:
3721:
3680:
3675:
3669:
3648:
3643:
3637:
3632:, pronounced "R bar squared"; another is
3616:
3605:
3604:
3601:
3491:
3482:
3453:
3449:
3448:
3445:
3423:
3417:
3396:
3390:
3369:
3363:
3342:
3336:
3315:
3311:
3310:
3307:
3287:
3275:
3262:
3249:
3236:
3223:
3211:
3189:
3188:
3186:
3163:
3151:
3138:
3125:
3113:
3059:
3050:
3008:
2999:
2968:
2924:
2918:
2905:
2892:
2879:
2869:
2847:
2834:
2828:
2690:
2689:
2687:
2663:
2603:
2584:
2578:
2553:
2547:
2516:
2491:
2485:
2463:
2458:
2456:
2425:
2406:
2396:
2386:
2375:
2362:
2349:
2343:
2272:, where one might keep adding variables (
2168:
2148:
2113:
2100:
2091:
2047:
2046:
2030:
2029:
2007:
2006:
1992:
1991:
1977:
1961:
1960:
1946:
1945:
1944:
1938:
1908:
1888:
1852:
1846:
1819:
1799:
1759:
1753:
1721:
1707:
1706:
1692:
1691:
1689:
1653:
1652:
1650:
1624:
1623:
1621:
1566:
1551:
1550:
1536:
1535:
1526:
1520:
1512:reads as follows: The model has the form
1427:
1421:
1404:
1398:
1388:
1376:
1361:
1351:
1342:
1336:
1301:
1285:
1269:
1260:
1225:
1210:
1209:
1200:
1187:
1174:
1165:
1120:
1105:
1099:
1034:
1025:
992:
991:
969:
968:
958:
943:
937:
913:
898:
897:
888:
875:
862:
853:
827:
821:
816:
806:
793:
783:
770:
757:
744:
735:
702:
692:
681:
667:
653:
652:
650:
624:
623:
621:
463:
455:
446:
438:
435:
420:
414:
7363:, Volume 48, Issue 2, 1994, pp. 113–117.
6728:
6726:
6507:
5740:. As a result, the diagonal elements of
1725:{\displaystyle {\bar {f}}={\bar {y}}.\,}
405:
161:
7378:Nagelkerke, N. J. D. (September 1991).
7073:
7071:
6765:. Dordrecht: Kluwer. pp. 181–189.
6661:Steel, R. G. D.; Torrie, J. H. (1960).
6653:
4831:{\displaystyle y=X\beta +\varepsilon .}
2333:more than a single explanatory variable
1834:data values of the dependent variable.
7445:"Part II: On Keeping Parameters Fixed"
7155:Yin, Ping; Fan, Xitao (January 2001).
3105:A simple case to be considered first:
2531:{\displaystyle X_{i,1},\dots ,X_{i,p}}
105:
7611:Statistics: A Foundation for Analysis
7608:Hughes, Ann; Grawoig, Dennis (1971).
7265:The Annals of Mathematical Statistics
7211:
7209:
7207:
7205:
7168:The Journal of Experimental Education
5484:. If regressors are uncorrelated and
3856:is given in terms of the sample size
2755:coefficient of multiple determination
1322:Partitioning in the general OLS model
327:on the test datasets in the article.
236:of future outcomes or the testing of
177:of the regression is relatively high.
7:
7614:. Reading: Addison-Wesley. pp.
4793:– make use of this decomposition of
4555:Coefficient of partial determination
4169:could thereby prevent overfitting.
4127:, more parameters will increase the
4045:increases only when the increase in
2732:correlation does not imply causation
1638:{\displaystyle {\widehat {\alpha }}}
1128:{\displaystyle R^{2}=1-{\text{FVU}}}
4537:minimum-variance unbiased estimator
4172:Following the same logic, adjusted
3888:is given in the same way, but with
2983:(the explanatory data matrix whose
2623:. The coefficient of determination
1744:(with fitted intercept and slope),
1667:{\displaystyle {\widehat {\beta }}}
285:coefficient of multiple correlation
267:is simply the square of the sample
6944:Cambridge Dictionary of Statistics
4195:The principle behind the adjusted
3689:{\displaystyle R_{\text{adj}}^{2}}
1736:As squared correlation coefficient
999:
996:
993:
976:
973:
970:
645:is the mean of the observed data:
437:
138:{{Translated|de|Bestimmtheitsmaß}}
25:
7480:(2nd ed.). Chapman and Hall.
7302:"Improving on Adjusted R-Squared"
7084:Applied Psychological Measurement
6946:(2nd ed.). CUP. p. 78.
6705:Draper, N. R.; Smith, H. (1998).
6588:and was first published in 1921.
6366:Comparison with norm of residuals
5971:{\displaystyle {\mathcal {L}}(0)}
5733:{\displaystyle R_{jj}^{\otimes }}
5698:{\displaystyle R_{ii}^{\otimes }}
5096:values. In the special case that
3440:orthogonal to the model space in
3179:ordinary least squares regression
3034:, the non-decreasing property of
1462:is expressed as the ratio of the
1049:{\displaystyle SS_{\text{res}}=0}
454:
243:There are several definitions of
232:whose main purpose is either the
7666:; Skalaban, Andrew (1990). "The
7562:Journal of Agricultural Research
6603:Fraction of variance unexplained
4569:The calculation for the partial
3705:, is the correction proposed by
3657:{\displaystyle R_{\text{a}}^{2}}
3462:{\displaystyle \mathbb {R} ^{2}}
3324:{\displaystyle \mathbb {R} ^{2}}
2562:{\displaystyle \varepsilon _{i}}
2289:
1086:Fraction of variance unexplained
1080:Relation to unexplained variance
348:of the linear regression (i.e.,
193:(blue) for a set of points with
45:
8124:Pearson correlation coefficient
7670:-Squared: Some Straight Talk".
7522:Nagelkerke, Nico J. D. (1992).
7218:Organizational Research Methods
7130:Methods Of Correlation Analysis
6481:{\displaystyle SS_{\text{tot}}}
5817:, there are several choices of
5511:is a vector of zeros, then the
4121:Considering the calculation of
3892:being unity for the mean, i.e.
3513:will lead to a larger value of
3068:{\displaystyle SS_{\text{res}}}
2772:regression using typical data,
2214:of a model. In regression, the
1792:Pearson correlation coefficient
7509:10.1080/00031305.1990.10475731
7045:Faraway, Julian James (2005).
6628:Proportional reduction in loss
6320:
6316:
6310:
6300:
6252:
6237:
6138:
6135:
6120:
6110:
6098:
6095:
6089:
6079:
6070:
6008:
5993:
5965:
5959:
5908:
5893:
5881:
5875:
5409:
5367:
5354:
5332:
5322:
5310:
5295:
5288:
5275:
5257:
5254:
5242:
5224:
5039:
5017:
5010:
4987:
4982:
4967:
4960:
4944:
4841:It is assumed that the matrix
4503:
4491:
4438:
4426:
4180:, whereas the observed sample
3970:
3951:
3930:
3730:
3625:{\displaystyle {\bar {R}}^{2}}
3610:
2915:
2885:
2862:
2859:
2853:
2695:
2110:
2093:
2086:of the coefficient estimates,
1876:{\displaystyle \rho ^{2}(y,x)}
1870:
1858:
1783:{\displaystyle \rho ^{2}(y,f)}
1777:
1765:
1712:
1697:
1222:
1215:
1193:
910:
903:
881:
790:
763:
658:
629:
300:to this particular criterion.
136:You may also add the template
1:
8063:Deep Learning Related Metrics
7550:. Retrieved February 9, 2016.
6929:10.1016/j.jhydrol.2012.12.004
6800:10.1016/S0304-4076(96)01818-0
6190:is the test statistic of the
5531:{\displaystyle j^{\text{th}}}
4734:Generalizing and decomposing
2331:Consider a linear model with
2125:{\displaystyle (X^{T}X)^{-1}}
7350:Richard Anderson-Sprecher, "
7300:Karch, Julian (2020-09-29).
6763:The Practice of Econometrics
5787:{\displaystyle R^{\otimes }}
5760:{\displaystyle R^{\otimes }}
5558:{\displaystyle R^{\otimes }}
5473:{\displaystyle R^{\otimes }}
5154:{\displaystyle R^{\otimes }}
4765:Geometric representation of
3860:and the number of variables
3196:{\displaystyle \mathbb {R} }
3177:This equation describes the
3075:is equivalent to maximizing
2813:is the number of columns in
2792:, similar to the F-tests in
211:coefficient of determination
18:Squared multiple correlation
7907:Sensitivity and specificity
7478:The Analysis of Binary Data
6707:Applied Regression Analysis
6633:Regression model validation
6376:sum of squares of residuals
5453:. The diagonal elements of
4131:and lead to an increase in
3532:does not indicate whether:
108:will aid in categorization.
8184:
7054:. Chapman & Hall/CRC.
6638:Root mean square deviation
6265:cannot be greater than 1,
6219:It does not have any unit.
5565:simply corresponds to the
5504:{\displaystyle \beta _{0}}
5116:{\displaystyle \beta _{0}}
5089:{\displaystyle \beta _{0}}
4885:{\displaystyle \beta _{0}}
4783:Bayesian linear regression
4749:examine whether the total
4558:
3913:, it can be rewritten as:
3585:
3378:{\displaystyle \beta _{0}}
3351:{\displaystyle \beta _{0}}
2753:can be referred to as the
2722:A caution that applies to
2719:or inherent variability."
2704:{\displaystyle {\bar {y}}}
2480:is the response variable,
2327:In a multiple linear model
2311:, alternative versions of
1083:
638:{\displaystyle {\bar {y}}}
398:+ 0 (i.e., the 1:1 line).
83:Machine translation, like
36:Coefficient of correlation
29:
8132:
7497:The American Statistician
7449:Science: Under Submission
7443:Hoornweg, Victor (2018).
7360:The American Statistician
7180:10.1080/00220970109600656
7096:10.1177/01466216970214001
6994:The American Statistician
6967:Casella, Georges (2002).
6617:hydrological applications
5130:The individual effect on
4192:stage of model building.
2730:and association is that "
2309:generalized least squares
2242:can be greater than one.
1903:and explanatory variable
60:the corresponding article
7640:Elements of Econometrics
7230:10.1177/1094428106292901
3596:(one common notation is
3506:{\displaystyle SS_{tot}}
3023:{\displaystyle SS_{tot}}
2788:can be performed on the
2082:, are obtained from the
1814:and modeled (predicted)
1740:In linear least squares
1246:simple linear regression
1155:explained sum of squares
249:simple linear regression
191:simple linear regression
32:Coefficient of variation
30:Not to be confused with
7935:Calinski-Harabasz index
7399:10.1093/biomet/78.3.691
7278:10.1214/aoms/1177706717
6942:Everitt, B. S. (2002).
6788:Journal of Econometrics
6733:Devore, Jay L. (2011).
5827:One is the generalized
3592:The use of an adjusted
2790:residual sum of squares
2473:{\displaystyle {Y_{i}}}
2274:kitchen sink regression
2245:In all instances where
2141:correlation coefficient
728:residual sum of squares
516:(collectively known as
269:correlation coefficient
228:used in the context of
147:For more guidance, see
8158:Regression diagnostics
7707:PeerJ Computer Science
7664:Lewis-Beck, Michael S.
7352:Model Comparisons and
6819:PeerJ Computer Science
6709:. Wiley-Interscience.
6482:
6432:
6341:
6259:
6177:
6016:
5972:
5936:
5805:in logistic regression
5788:
5761:
5734:
5699:
5664:
5637:
5610:
5590:
5559:
5532:
5505:
5474:
5447:
5386:
5195:
5175:
5155:
5117:
5090:
5052:
4906:
4886:
4859:
4832:
4770:
4724:
4648:
4510:
4445:
4375:
4322:
4266:
4074:bias-variance tradeoff
4065:
4009:
3825:
3690:
3658:
3626:
3507:
3463:
3433:
3406:
3379:
3352:
3325:
3292:
3197:
3168:
3102:
3069:
3024:
2977:
2929:
2705:
2672:
2613:
2563:
2532:
2474:
2438:
2391:
2305:weighted least squares
2177:
2157:
2126:
2069:
1917:
1897:
1877:
1828:
1808:
1784:
1726:
1668:
1639:
1576:
1504:have been obtained by
1442:
1311:
1235:
1129:
1050:
1012:
923:
832:
712:
697:
639:
489:
477:
290:There are cases where
202:
178:
167:Ordinary least squares
8098:Intra-list Similarity
6969:Statistical inference
6483:
6433:
6342:
6260:
6192:likelihood ratio test
6178:
6017:
5973:
5937:
5789:
5762:
5735:
5700:
5665:
5663:{\displaystyle x_{j}}
5638:
5636:{\displaystyle x_{i}}
5611:
5591:
5589:{\displaystyle x_{j}}
5560:
5533:
5506:
5475:
5448:
5387:
5196:
5176:
5156:
5118:
5091:
5053:
4907:
4887:
4860:
4833:
4789:, and the (adaptive)
4764:
4725:
4649:
4511:
4446:
4376:
4323:
4267:
4063:
4010:
3826:
3691:
3659:
3627:
3544:omitted-variable bias
3508:
3477:, a smaller value of
3464:
3434:
3432:{\displaystyle X_{2}}
3407:
3405:{\displaystyle X_{1}}
3380:
3353:
3326:
3293:
3198:
3169:
3100:
3070:
3025:
2978:
2930:
2741:is the square of the
2706:
2673:
2642:explanatory variables
2614:
2573:term. The quantities
2564:
2533:
2475:
2439:
2371:
2178:
2158:
2143:between the original
2127:
2070:
1928:explanatory variables
1918:
1898:
1878:
1829:
1809:
1794:between the observed
1785:
1727:
1669:
1640:
1577:
1443:
1312:
1244:In some cases, as in
1236:
1138:As explained variance
1130:
1051:
1013:
924:
844:(proportional to the
833:
713:
677:
640:
478:
409:
283:is the square of the
184:
165:
149:Knowledge:Translation
120:copyright attribution
7720:10.7717/peerj-cs.623
7583:Gujarati, Damodar N.
7319:10.1525/collabra.343
7306:Collabra: Psychology
7048:Linear models with R
6909:Journal of Hydrology
6886:10.1029/1998WR900018
6832:10.7717/peerj-cs.623
6462:
6385:
6273:
6227:
6033:
5982:
5949:
5838:
5771:
5744:
5709:
5674:
5647:
5620:
5600:
5573:
5542:
5538:diagonal element of
5515:
5488:
5457:
5399:
5208:
5185:
5165:
5138:
5100:
5073:
4919:
4896:
4869:
4849:
4804:
4779:shrinkage estimators
4664:
4588:
4455:
4390:
4332:
4279:
4210:
4026:is the sample size.
3920:
3720:
3668:
3636:
3600:
3481:
3444:
3416:
3389:
3362:
3335:
3306:
3210:
3185:
3112:
3049:
3045:is this: Minimizing
2998:
2967:
2827:
2686:
2662:
2577:
2546:
2484:
2455:
2342:
2210:is a measure of the
2167:
2147:
2090:
1937:
1907:
1887:
1845:
1818:
1798:
1752:
1688:
1649:
1620:
1519:
1510:sufficient condition
1335:
1259:
1250:total sum of squares
1164:
1098:
1024:
936:
852:
842:total sum of squares
734:
649:
620:
413:
7686:10.1093/pan/2.1.153
7546:OriginLab webpage,
7491:Magee, L. (1990). "
6921:2013JHyd..480...33R
6878:1999WRR....35..233L
6643:Stepwise regression
6290:
5811:logistic regression
5729:
5694:
5346:
5201:matrix is given by
4561:Partial correlation
4539:for the population
3685:
3653:
2266:monotone increasing
2080:standard deviations
1742:multiple regression
1090:In a general form,
826:
321:regression analysis
255:is used instead of
187:Theil–Sen estimator
8163:Statistical ratios
8119:Euclidean distance
8085:Recommender system
7965:Similarity measure
7779:evaluation metrics
7673:Political Analysis
7591:Basic Econometrics
7451:. Hoornweg Press.
6598:Anscombe's quartet
6492:the value. If the
6478:
6428:
6370:Occasionally, the
6337:
6276:
6255:
6173:
6012:
5968:
5932:
5815:maximum likelihood
5784:
5757:
5730:
5712:
5695:
5677:
5660:
5633:
5616:. When regressors
5606:
5586:
5555:
5528:
5501:
5480:exactly add up to
5470:
5443:
5382:
5325:
5191:
5171:
5161:('R-outer'). This
5151:
5113:
5086:
5048:
4902:
4882:
4855:
4828:
4771:
4745:criterion and the
4720:
4644:
4634: res, reduced
4603: res, reduced
4506:
4441:
4371:
4318:
4262:
4066:
4005:
3842:degrees of freedom
3821:
3686:
3671:
3654:
3639:
3622:
3538:dependent variable
3503:
3459:
3429:
3402:
3375:
3348:
3321:
3288:
3193:
3164:
3103:
3065:
3020:
2973:
2925:
2884:
2874:
2839:
2701:
2668:
2609:
2559:
2528:
2470:
2434:
2276:) to increase the
2173:
2153:
2122:
2065:
1913:
1893:
1873:
1824:
1804:
1790:the square of the
1780:
1722:
1664:
1635:
1572:
1464:explained variance
1438:
1307:
1231:
1192:
1142:A larger value of
1125:
1046:
1008:
919:
880:
828:
812:
811:
762:
708:
635:
607:(forming a vector
490:
473:
470:
453:
263:is included, then
230:statistical models
203:
185:Comparison of the
179:
128:interlanguage link
8145:
8144:
8114:Cosine similarity
7950:Hopkins statistic
7655:978-0-02-365070-3
7600:978-0-07-337577-9
7533:978-0-387-97721-8
7458:978-90-829188-0-9
7032:www.mathworks.com
6953:978-0-521-81099-9
6866:Water Resour. Res
6744:978-0-538-73352-6
6716:978-0-471-17082-2
6691:978-0-07-023407-9
6550:
6549:
6475:
6411:
6408:
6391:
6390:norm of residuals
6269:is between 0 and
6249:
6132:
6068:
6005:
5912:
5905:
5813:, usually fit by
5609:{\displaystyle y}
5525:
5412:
5357:
5335:
5278:
5245:
5194:{\displaystyle p}
5174:{\displaystyle p}
5043:
4905:{\displaystyle b}
4858:{\displaystyle y}
4715:
4711:
4696:
4680:
4639:
4635:
4620:
4604:
4483:
4467:
4462:
4418:
4402:
4397:
4360:
4344:
4339:
4307:
4291:
4286:
4259:
4256:
4251:
4244:
4239:
4190:feature selection
4003:
3933:
3818:
3814:
3809:
3797:
3782:
3777:
3765:
3733:
3678:
3646:
3613:
3588:Omega-squared (ω)
3062:
2976:{\displaystyle X}
2875:
2865:
2850:
2830:
2794:Granger causality
2717:lurking variables
2698:
2671:{\displaystyle y}
2176:{\displaystyle f}
2156:{\displaystyle y}
2084:covariance matrix
2060:
2055:
2038:
2015:
2000:
1969:
1954:
1916:{\displaystyle x}
1896:{\displaystyle y}
1827:{\displaystyle f}
1807:{\displaystyle y}
1715:
1700:
1661:
1632:
1559:
1544:
1506:linear regression
1436:
1424:
1401:
1383:
1379:
1364:
1328:is equivalent to
1304:
1288:
1272:
1218:
1183:
1177:
1123:
1037:
1006:
906:
871:
865:
802:
753:
747:
675:
661:
632:
471:
466:
449:
160:
159:
72:
68:
16:(Redirected from
8175:
8137:Confusion matrix
7912:Logarithmic Loss
7777:Machine learning
7770:
7763:
7756:
7747:
7742:
7732:
7722:
7697:
7659:
7643:
7629:
7604:
7570:
7569:
7557:
7551:
7544:
7538:
7537:
7519:
7513:
7512:
7488:
7482:
7481:
7469:
7463:
7462:
7440:
7429:
7428:
7417:
7411:
7410:
7384:
7375:
7364:
7348:
7342:
7341:
7331:
7321:
7297:
7291:
7290:
7280:
7256:
7250:
7249:
7213:
7200:
7199:
7165:
7152:
7146:
7144:
7126:Mordecai Ezekiel
7122:
7116:
7115:
7075:
7066:
7065:
7053:
7042:
7036:
7035:
7024:
7018:
7017:
6989:
6983:
6982:
6964:
6958:
6957:
6939:
6933:
6932:
6904:
6898:
6897:
6861:
6855:
6854:
6844:
6834:
6810:
6804:
6803:
6783:
6777:
6776:
6759:Barten, Anton P.
6755:
6749:
6748:
6730:
6721:
6720:
6702:
6696:
6695:
6677:
6671:
6670:
6658:
6508:
6487:
6485:
6484:
6479:
6477:
6476:
6473:
6437:
6435:
6434:
6429:
6412:
6410:
6409:
6406:
6397:
6392:
6389:
6346:
6344:
6343:
6338:
6336:
6335:
6331:
6309:
6308:
6289:
6284:
6264:
6262:
6261:
6256:
6251:
6250:
6242:
6236:
6235:
6182:
6180:
6179:
6174:
6172:
6171:
6167:
6142:
6141:
6134:
6133:
6125:
6119:
6118:
6088:
6087:
6069:
6061:
6045:
6044:
6021:
6019:
6018:
6013:
6011:
6007:
6006:
5998:
5992:
5991:
5977:
5975:
5974:
5969:
5958:
5957:
5941:
5939:
5938:
5933:
5931:
5930:
5926:
5917:
5913:
5911:
5907:
5906:
5898:
5892:
5891:
5884:
5874:
5873:
5866:
5850:
5849:
5798:for an example.
5793:
5791:
5790:
5785:
5783:
5782:
5766:
5764:
5763:
5758:
5756:
5755:
5739:
5737:
5736:
5731:
5728:
5723:
5704:
5702:
5701:
5696:
5693:
5688:
5670:are correlated,
5669:
5667:
5666:
5661:
5659:
5658:
5642:
5640:
5639:
5634:
5632:
5631:
5615:
5613:
5612:
5607:
5595:
5593:
5592:
5587:
5585:
5584:
5564:
5562:
5561:
5556:
5554:
5553:
5537:
5535:
5534:
5529:
5527:
5526:
5523:
5510:
5508:
5507:
5502:
5500:
5499:
5479:
5477:
5476:
5471:
5469:
5468:
5452:
5450:
5449:
5444:
5442:
5441:
5420:
5419:
5414:
5413:
5405:
5391:
5389:
5388:
5383:
5378:
5377:
5365:
5364:
5359:
5358:
5350:
5342:
5337:
5336:
5328:
5321:
5320:
5305:
5294:
5286:
5285:
5280:
5279:
5271:
5267:
5253:
5252:
5247:
5246:
5238:
5234:
5220:
5219:
5200:
5198:
5197:
5192:
5180:
5178:
5177:
5172:
5160:
5158:
5157:
5152:
5150:
5149:
5122:
5120:
5119:
5114:
5112:
5111:
5095:
5093:
5092:
5087:
5085:
5084:
5057:
5055:
5054:
5049:
5044:
5042:
5038:
5037:
5016:
5008:
5007:
4985:
4966:
4942:
4931:
4930:
4911:
4909:
4908:
4903:
4891:
4889:
4888:
4883:
4881:
4880:
4864:
4862:
4861:
4856:
4837:
4835:
4834:
4829:
4787:ridge regression
4729:
4727:
4726:
4721:
4716:
4714:
4713:
4712:
4709:
4699:
4698:
4697:
4694:
4682:
4681:
4678:
4668:
4653:
4651:
4650:
4645:
4640:
4638:
4637:
4636:
4633:
4623:
4622:
4621:
4618:
4606:
4605:
4602:
4592:
4515:
4513:
4512:
4507:
4490:
4485:
4484:
4481:
4469:
4468:
4465:
4463:
4460:
4450:
4448:
4447:
4442:
4425:
4420:
4419:
4416:
4404:
4403:
4400:
4398:
4395:
4380:
4378:
4377:
4372:
4367:
4362:
4361:
4358:
4346:
4345:
4342:
4340:
4337:
4327:
4325:
4324:
4319:
4314:
4309:
4308:
4305:
4293:
4292:
4289:
4287:
4284:
4271:
4269:
4268:
4263:
4261:
4260:
4258:
4257:
4254:
4252:
4249:
4246:
4245:
4242:
4240:
4237:
4234:
4222:
4221:
4164:
4158:
4148:
4142:
4136:
4126:
4113:
4107:
4100:
4014:
4012:
4011:
4006:
4004:
4002:
3985:
3974:
3969:
3968:
3941:
3940:
3935:
3934:
3926:
3905:
3881:
3830:
3828:
3827:
3822:
3820:
3819:
3817:
3816:
3815:
3812:
3810:
3807:
3804:
3799:
3798:
3795:
3785:
3784:
3783:
3780:
3778:
3775:
3772:
3767:
3766:
3763:
3753:
3741:
3740:
3735:
3734:
3726:
3709:. The adjusted
3707:Mordecai Ezekiel
3695:
3693:
3692:
3687:
3684:
3679:
3676:
3663:
3661:
3660:
3655:
3652:
3647:
3644:
3631:
3629:
3628:
3623:
3621:
3620:
3615:
3614:
3606:
3512:
3510:
3509:
3504:
3502:
3501:
3473:calculation for
3468:
3466:
3465:
3460:
3458:
3457:
3452:
3438:
3436:
3435:
3430:
3428:
3427:
3411:
3409:
3408:
3403:
3401:
3400:
3384:
3382:
3381:
3376:
3374:
3373:
3357:
3355:
3354:
3349:
3347:
3346:
3330:
3328:
3327:
3322:
3320:
3319:
3314:
3297:
3295:
3294:
3289:
3280:
3279:
3267:
3266:
3254:
3253:
3241:
3240:
3228:
3227:
3202:
3200:
3199:
3194:
3192:
3173:
3171:
3170:
3165:
3156:
3155:
3143:
3142:
3130:
3129:
3074:
3072:
3071:
3066:
3064:
3063:
3060:
3030:depends only on
3029:
3027:
3026:
3021:
3019:
3018:
2982:
2980:
2979:
2974:
2934:
2932:
2931:
2926:
2923:
2922:
2910:
2909:
2897:
2896:
2883:
2873:
2852:
2851:
2848:
2838:
2710:
2708:
2707:
2702:
2700:
2699:
2691:
2677:
2675:
2674:
2669:
2618:
2616:
2615:
2610:
2608:
2607:
2589:
2588:
2568:
2566:
2565:
2560:
2558:
2557:
2542:regressors, and
2537:
2535:
2534:
2529:
2527:
2526:
2502:
2501:
2479:
2477:
2476:
2471:
2469:
2468:
2467:
2443:
2441:
2440:
2435:
2430:
2429:
2417:
2416:
2401:
2400:
2390:
2385:
2367:
2366:
2354:
2353:
2256:. In this case,
2198:
2182:
2180:
2179:
2174:
2162:
2160:
2159:
2154:
2131:
2129:
2128:
2123:
2121:
2120:
2105:
2104:
2074:
2072:
2071:
2066:
2061:
2059:
2058:
2057:
2056:
2048:
2041:
2040:
2039:
2031:
2023:
2022:
2018:
2017:
2016:
2008:
2002:
2001:
1993:
1978:
1973:
1972:
1971:
1970:
1962:
1956:
1955:
1947:
1922:
1920:
1919:
1914:
1902:
1900:
1899:
1894:
1882:
1880:
1879:
1874:
1857:
1856:
1833:
1831:
1830:
1825:
1813:
1811:
1810:
1805:
1789:
1787:
1786:
1781:
1764:
1763:
1731:
1729:
1728:
1723:
1717:
1716:
1708:
1702:
1701:
1693:
1673:
1671:
1670:
1665:
1663:
1662:
1654:
1644:
1642:
1641:
1636:
1634:
1633:
1625:
1581:
1579:
1578:
1573:
1571:
1570:
1561:
1560:
1552:
1546:
1545:
1537:
1531:
1530:
1491:
1478:
1447:
1445:
1444:
1439:
1437:
1435:
1431:
1426:
1425:
1422:
1412:
1408:
1403:
1402:
1399:
1389:
1384:
1382:
1381:
1380:
1377:
1367:
1366:
1365:
1362:
1352:
1347:
1346:
1316:
1314:
1313:
1308:
1306:
1305:
1302:
1290:
1289:
1286:
1274:
1273:
1270:
1240:
1238:
1237:
1232:
1230:
1229:
1220:
1219:
1211:
1205:
1204:
1191:
1179:
1178:
1175:
1157:, is defined as
1152:
1134:
1132:
1131:
1126:
1124:
1121:
1110:
1109:
1075:
1068:
1062:
1055:
1053:
1052:
1047:
1039:
1038:
1035:
1017:
1015:
1014:
1009:
1007:
1005:
1004:
1003:
1002:
982:
981:
980:
979:
959:
948:
947:
928:
926:
925:
920:
918:
917:
908:
907:
899:
893:
892:
879:
867:
866:
863:
837:
835:
834:
829:
825:
820:
810:
798:
797:
788:
787:
775:
774:
761:
749:
748:
745:
717:
715:
714:
709:
707:
706:
696:
691:
676:
668:
663:
662:
654:
644:
642:
641:
636:
634:
633:
625:
606:
482:
480:
479:
474:
472:
469:
468:
467:
464:
452:
451:
450:
447:
436:
425:
424:
337:) vs. measured (
139:
133:
107:
106:|topic=
104:, and specifying
89:Google Translate
70:
67:(September 2019)
66:
49:
48:
41:
21:
8183:
8182:
8178:
8177:
8176:
8174:
8173:
8172:
8148:
8147:
8146:
8141:
8128:
8102:
8079:
8070:Inception score
8058:
8035:
8013:Computer Vision
8007:
7979:
7916:
7848:
7780:
7774:
7700:
7662:
7656:
7632:
7626:
7607:
7601:
7587:Porter, Dawn C.
7581:
7578:
7576:Further reading
7573:
7559:
7558:
7554:
7545:
7541:
7534:
7521:
7520:
7516:
7490:
7489:
7485:
7471:
7470:
7466:
7459:
7442:
7441:
7432:
7425:Cross Validated
7419:
7418:
7414:
7382:
7377:
7376:
7367:
7349:
7345:
7299:
7298:
7294:
7258:
7257:
7253:
7215:
7214:
7203:
7163:
7154:
7153:
7149:
7124:
7123:
7119:
7077:
7076:
7069:
7062:
7051:
7044:
7043:
7039:
7026:
7025:
7021:
7006:10.2307/2683704
6991:
6990:
6986:
6979:
6966:
6965:
6961:
6954:
6941:
6940:
6936:
6906:
6905:
6901:
6863:
6862:
6858:
6812:
6811:
6807:
6785:
6784:
6780:
6773:
6757:
6756:
6752:
6745:
6732:
6731:
6724:
6717:
6704:
6703:
6699:
6692:
6684:. McGraw-Hill.
6679:
6678:
6674:
6660:
6659:
6655:
6651:
6608:Goodness of fit
6594:
6582:
6497:
6468:
6460:
6459:
6401:
6383:
6382:
6368:
6361:
6319:
6271:
6270:
6225:
6224:
6198:Nico Nagelkerke
6152:
6055:
6036:
6031:
6030:
5980:
5979:
5947:
5946:
5885:
5867:
5861:
5860:
5841:
5836:
5835:
5809:In the case of
5807:
5774:
5769:
5768:
5747:
5742:
5741:
5707:
5706:
5672:
5671:
5650:
5645:
5644:
5623:
5618:
5617:
5598:
5597:
5576:
5571:
5570:
5545:
5540:
5539:
5518:
5513:
5512:
5491:
5486:
5485:
5460:
5455:
5454:
5433:
5402:
5397:
5396:
5366:
5347:
5309:
5298:
5287:
5268:
5260:
5235:
5227:
5211:
5206:
5205:
5183:
5182:
5163:
5162:
5141:
5136:
5135:
5103:
5098:
5097:
5076:
5071:
5070:
5029:
5009:
4999:
4986:
4959:
4943:
4922:
4917:
4916:
4894:
4893:
4872:
4867:
4866:
4847:
4846:
4802:
4801:
4739:
4704:
4700:
4689:
4673:
4669:
4662:
4661:
4628:
4624:
4619: res, full
4613:
4597:
4593:
4586:
4585:
4563:
4557:
4476:
4458:
4453:
4452:
4411:
4393:
4388:
4387:
4353:
4335:
4330:
4329:
4300:
4282:
4277:
4276:
4247:
4235:
4213:
4208:
4207:
4160:
4154:
4144:
4138:
4132:
4122:
4109:
4102:
4096:
4041:, the adjusted
3986:
3975:
3960:
3923:
3918:
3917:
3899:
3893:
3887:
3871:
3865:
3855:
3849:
3839:
3805:
3790:
3786:
3773:
3758:
3754:
3723:
3718:
3717:
3666:
3665:
3634:
3633:
3603:
3598:
3597:
3590:
3584:
3576:
3527:
3487:
3479:
3478:
3447:
3442:
3441:
3419:
3414:
3413:
3392:
3387:
3386:
3365:
3360:
3359:
3338:
3333:
3332:
3309:
3304:
3303:
3271:
3258:
3245:
3232:
3219:
3208:
3207:
3183:
3182:
3147:
3134:
3121:
3110:
3109:
3055:
3047:
3046:
3004:
2996:
2995:
2992:
2965:
2964:
2958:
2943:
2914:
2901:
2888:
2843:
2825:
2824:
2808:
2766:
2684:
2683:
2660:
2659:
2639:
2599:
2580:
2575:
2574:
2569:is a mean zero
2549:
2544:
2543:
2512:
2487:
2482:
2481:
2459:
2453:
2452:
2447:where, for the
2421:
2402:
2392:
2358:
2345:
2340:
2339:
2329:
2255:
2212:goodness of fit
2205:
2197:
2185:
2165:
2164:
2145:
2144:
2109:
2096:
2088:
2087:
2042:
2025:
2024:
1990:
1986:
1979:
1940:
1935:
1934:
1905:
1904:
1885:
1884:
1848:
1843:
1842:
1816:
1815:
1796:
1795:
1755:
1750:
1749:
1738:
1686:
1685:
1647:
1646:
1618:
1617:
1615:
1606:
1593:
1562:
1522:
1517:
1516:
1503:
1486:
1480:
1473:
1467:
1417:
1413:
1394:
1390:
1372:
1368:
1357:
1353:
1338:
1333:
1332:
1297:
1281:
1265:
1257:
1256:
1221:
1196:
1170:
1162:
1161:
1147:
1140:
1101:
1096:
1095:
1088:
1082:
1070:
1064:
1057:
1030:
1022:
1021:
987:
983:
964:
960:
939:
934:
933:
909:
884:
858:
850:
849:
789:
779:
766:
740:
732:
731:
720:sums of squares
698:
647:
646:
618:
617:
605:
596:
587:
579:
564:
556:, or sometimes
555:
546:
537:
525:or as a vector
524:
515:
506:
483:
459:
442:
416:
411:
410:
404:
397:
390:
383:
376:
365:
354:
343:
336:
259:. When only an
156:
155:
154:
137:
131:
73:
50:
46:
39:
28:
23:
22:
15:
12:
11:
5:
8181:
8179:
8171:
8170:
8165:
8160:
8150:
8149:
8143:
8142:
8140:
8139:
8133:
8130:
8129:
8127:
8126:
8121:
8116:
8110:
8108:
8104:
8103:
8101:
8100:
8095:
8089:
8087:
8081:
8080:
8078:
8077:
8072:
8066:
8064:
8060:
8059:
8057:
8056:
8051:
8045:
8043:
8037:
8036:
8034:
8033:
8028:
8023:
8017:
8015:
8009:
8008:
8006:
8005:
8000:
7995:
7989:
7987:
7981:
7980:
7978:
7977:
7972:
7967:
7962:
7957:
7952:
7947:
7942:
7940:Davies-Bouldin
7937:
7932:
7926:
7924:
7918:
7917:
7915:
7914:
7909:
7904:
7899:
7894:
7889:
7884:
7879:
7874:
7869:
7864:
7858:
7856:
7854:Classification
7850:
7849:
7847:
7846:
7841:
7836:
7831:
7826:
7821:
7816:
7811:
7806:
7801:
7796:
7790:
7788:
7782:
7781:
7775:
7773:
7772:
7765:
7758:
7750:
7744:
7743:
7713:(e623): e623.
7698:
7660:
7654:
7630:
7624:
7605:
7599:
7577:
7574:
7572:
7571:
7552:
7539:
7532:
7514:
7483:
7464:
7457:
7430:
7412:
7393:(3): 691–692.
7365:
7343:
7292:
7271:(1): 201–211.
7251:
7224:(2): 387–407.
7201:
7174:(2): 203–224.
7147:
7145:, pp. 208–211.
7117:
7090:(4): 291–305.
7067:
7060:
7037:
7019:
7000:(4): 279–285.
6984:
6977:
6959:
6952:
6934:
6899:
6872:(1): 233–241.
6856:
6825:(e623): e623.
6805:
6778:
6771:
6750:
6743:
6722:
6715:
6697:
6690:
6672:
6652:
6650:
6647:
6646:
6645:
6640:
6635:
6630:
6625:
6620:
6610:
6605:
6600:
6593:
6590:
6581:
6578:
6565:change), then
6552:
6551:
6548:
6547:
6544:
6541:
6538:
6535:
6532:
6528:
6527:
6524:
6521:
6518:
6515:
6512:
6495:
6471:
6467:
6439:
6438:
6427:
6424:
6421:
6418:
6415:
6404:
6400:
6395:
6367:
6364:
6359:
6334:
6330:
6326:
6322:
6318:
6315:
6312:
6307:
6302:
6299:
6296:
6293:
6288:
6283:
6279:
6254:
6248:
6245:
6239:
6234:
6221:
6220:
6217:
6214:
6211:
6208:
6205:
6184:
6183:
6170:
6166:
6162:
6159:
6155:
6151:
6148:
6145:
6140:
6137:
6131:
6128:
6122:
6117:
6112:
6109:
6106:
6103:
6100:
6097:
6094:
6091:
6086:
6081:
6078:
6075:
6072:
6067:
6064:
6058:
6054:
6051:
6048:
6043:
6039:
6010:
6004:
6001:
5995:
5990:
5967:
5964:
5961:
5956:
5943:
5942:
5929:
5925:
5921:
5916:
5910:
5904:
5901:
5895:
5890:
5883:
5880:
5877:
5872:
5864:
5859:
5856:
5853:
5848:
5844:
5806:
5800:
5781:
5777:
5754:
5750:
5727:
5722:
5719:
5715:
5692:
5687:
5684:
5680:
5657:
5653:
5630:
5626:
5605:
5583:
5579:
5569:value between
5552:
5548:
5521:
5498:
5494:
5467:
5463:
5440:
5436:
5432:
5429:
5426:
5423:
5418:
5411:
5408:
5393:
5392:
5381:
5376:
5373:
5369:
5363:
5356:
5353:
5345:
5341:
5334:
5331:
5324:
5319:
5316:
5312:
5308:
5304:
5301:
5297:
5293:
5290:
5284:
5277:
5274:
5266:
5263:
5259:
5256:
5251:
5244:
5241:
5233:
5230:
5226:
5223:
5218:
5214:
5190:
5170:
5148:
5144:
5110:
5106:
5083:
5079:
5059:
5058:
5047:
5041:
5036:
5032:
5028:
5025:
5022:
5019:
5015:
5012:
5006:
5002:
4998:
4995:
4992:
4989:
4984:
4981:
4978:
4975:
4972:
4969:
4965:
4962:
4958:
4955:
4952:
4949:
4946:
4940:
4937:
4934:
4929:
4925:
4901:
4879:
4875:
4854:
4839:
4838:
4827:
4824:
4821:
4818:
4815:
4812:
4809:
4738:
4732:
4731:
4730:
4719:
4707:
4703:
4692:
4688:
4685:
4676:
4672:
4655:
4654:
4643:
4631:
4627:
4616:
4612:
4609:
4600:
4596:
4556:
4553:
4505:
4502:
4499:
4496:
4493:
4489:
4479:
4475:
4472:
4440:
4437:
4434:
4431:
4428:
4424:
4414:
4410:
4407:
4370:
4366:
4356:
4352:
4349:
4317:
4313:
4303:
4299:
4296:
4273:
4272:
4232:
4229:
4225:
4220:
4216:
4016:
4015:
4001:
3998:
3995:
3992:
3989:
3984:
3981:
3978:
3972:
3967:
3963:
3959:
3956:
3953:
3950:
3947:
3944:
3939:
3932:
3929:
3895:
3883:
3867:
3864:in the model,
3851:
3845:
3835:
3832:
3831:
3803:
3793:
3789:
3771:
3761:
3757:
3751:
3748:
3744:
3739:
3732:
3729:
3713:is defined as
3683:
3674:
3651:
3642:
3619:
3612:
3609:
3583:
3577:
3575:
3572:
3571:
3570:
3567:
3564:
3557:
3554:
3547:
3541:
3526:
3523:
3500:
3497:
3494:
3490:
3486:
3456:
3451:
3426:
3422:
3399:
3395:
3372:
3368:
3345:
3341:
3318:
3313:
3299:
3298:
3286:
3283:
3278:
3274:
3270:
3265:
3261:
3257:
3252:
3248:
3244:
3239:
3235:
3231:
3226:
3222:
3218:
3215:
3191:
3175:
3174:
3162:
3159:
3154:
3150:
3146:
3141:
3137:
3133:
3128:
3124:
3120:
3117:
3058:
3054:
3017:
3014:
3011:
3007:
3003:
2990:
2972:
2956:
2941:
2936:
2935:
2921:
2917:
2913:
2908:
2904:
2900:
2895:
2891:
2887:
2882:
2878:
2872:
2868:
2864:
2861:
2858:
2855:
2846:
2842:
2837:
2833:
2804:
2765:
2759:
2697:
2694:
2667:
2635:
2606:
2602:
2598:
2595:
2592:
2587:
2583:
2556:
2552:
2525:
2522:
2519:
2515:
2511:
2508:
2505:
2500:
2497:
2494:
2490:
2466:
2462:
2445:
2444:
2433:
2428:
2424:
2420:
2415:
2412:
2409:
2405:
2399:
2395:
2389:
2384:
2381:
2378:
2374:
2370:
2365:
2361:
2357:
2352:
2348:
2335:, of the form
2328:
2325:
2253:
2204:
2203:Interpretation
2201:
2193:
2172:
2152:
2119:
2116:
2112:
2108:
2103:
2099:
2095:
2076:
2075:
2064:
2054:
2051:
2045:
2037:
2034:
2028:
2021:
2014:
2011:
2005:
1999:
1996:
1989:
1985:
1982:
1976:
1968:
1965:
1959:
1953:
1950:
1943:
1912:
1892:
1872:
1869:
1866:
1863:
1860:
1855:
1851:
1823:
1803:
1779:
1776:
1773:
1770:
1767:
1762:
1758:
1737:
1734:
1733:
1732:
1720:
1714:
1711:
1705:
1699:
1696:
1660:
1657:
1631:
1628:
1611:
1602:
1589:
1583:
1582:
1569:
1565:
1558:
1555:
1549:
1543:
1540:
1534:
1529:
1525:
1499:
1484:
1471:
1449:
1448:
1434:
1430:
1420:
1416:
1411:
1407:
1397:
1393:
1387:
1375:
1371:
1360:
1356:
1350:
1345:
1341:
1318:
1317:
1300:
1296:
1293:
1284:
1280:
1277:
1268:
1264:
1242:
1241:
1228:
1224:
1217:
1214:
1208:
1203:
1199:
1195:
1190:
1186:
1182:
1173:
1169:
1139:
1136:
1119:
1116:
1113:
1108:
1104:
1084:Main article:
1081:
1078:
1045:
1042:
1033:
1029:
1001:
998:
995:
990:
986:
978:
975:
972:
967:
963:
957:
954:
951:
946:
942:
930:
929:
916:
912:
905:
902:
896:
891:
887:
883:
878:
874:
870:
861:
857:
848:of the data):
838:
824:
819:
815:
809:
805:
801:
796:
792:
786:
782:
778:
773:
769:
765:
760:
756:
752:
743:
739:
705:
701:
695:
690:
687:
684:
680:
674:
671:
666:
660:
657:
631:
628:
601:
592:
583:
565:, as a vector
560:
551:
542:
535:
520:
511:
504:
500:values marked
462:
458:
445:
441:
434:
431:
428:
423:
419:
403:
400:
395:
388:
381:
374:
363:
352:
341:
334:
279:are included,
169:regression of
158:
157:
153:
152:
145:
134:
112:
109:
97:adding a topic
92:
81:
74:
55:
54:
53:
51:
44:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
8180:
8169:
8168:Least squares
8166:
8164:
8161:
8159:
8156:
8155:
8153:
8138:
8135:
8134:
8131:
8125:
8122:
8120:
8117:
8115:
8112:
8111:
8109:
8105:
8099:
8096:
8094:
8091:
8090:
8088:
8086:
8082:
8076:
8073:
8071:
8068:
8067:
8065:
8061:
8055:
8052:
8050:
8047:
8046:
8044:
8042:
8038:
8032:
8029:
8027:
8024:
8022:
8019:
8018:
8016:
8014:
8010:
8004:
8001:
7999:
7996:
7994:
7991:
7990:
7988:
7986:
7982:
7976:
7973:
7971:
7968:
7966:
7963:
7961:
7958:
7956:
7955:Jaccard index
7953:
7951:
7948:
7946:
7943:
7941:
7938:
7936:
7933:
7931:
7928:
7927:
7925:
7923:
7919:
7913:
7910:
7908:
7905:
7903:
7900:
7898:
7895:
7893:
7890:
7888:
7885:
7883:
7880:
7878:
7875:
7873:
7870:
7868:
7865:
7863:
7860:
7859:
7857:
7855:
7851:
7845:
7842:
7840:
7837:
7835:
7832:
7830:
7827:
7825:
7822:
7820:
7817:
7815:
7812:
7810:
7807:
7805:
7802:
7800:
7797:
7795:
7792:
7791:
7789:
7787:
7783:
7778:
7771:
7766:
7764:
7759:
7757:
7752:
7751:
7748:
7740:
7736:
7731:
7726:
7721:
7716:
7712:
7708:
7704:
7699:
7695:
7691:
7687:
7683:
7679:
7675:
7674:
7669:
7665:
7661:
7657:
7651:
7647:
7642:
7641:
7635:
7631:
7627:
7625:0-201-03021-7
7621:
7617:
7613:
7612:
7606:
7602:
7596:
7592:
7588:
7584:
7580:
7579:
7575:
7567:
7563:
7556:
7553:
7549:
7543:
7540:
7535:
7529:
7525:
7518:
7515:
7510:
7506:
7502:
7498:
7494:
7487:
7484:
7479:
7475:
7468:
7465:
7460:
7454:
7450:
7446:
7439:
7437:
7435:
7431:
7426:
7422:
7416:
7413:
7408:
7404:
7400:
7396:
7392:
7388:
7381:
7374:
7372:
7370:
7366:
7362:
7361:
7356:
7355:
7347:
7344:
7339:
7335:
7330:
7325:
7320:
7315:
7311:
7307:
7303:
7296:
7293:
7288:
7284:
7279:
7274:
7270:
7266:
7262:
7255:
7252:
7247:
7243:
7239:
7235:
7231:
7227:
7223:
7219:
7212:
7210:
7208:
7206:
7202:
7197:
7193:
7189:
7185:
7181:
7177:
7173:
7169:
7162:
7160:
7151:
7148:
7143:
7139:
7135:
7131:
7127:
7121:
7118:
7113:
7109:
7105:
7101:
7097:
7093:
7089:
7085:
7081:
7074:
7072:
7068:
7063:
7061:9781584884255
7057:
7050:
7049:
7041:
7038:
7033:
7029:
7023:
7020:
7015:
7011:
7007:
7003:
6999:
6995:
6988:
6985:
6980:
6978:9788131503942
6974:
6970:
6963:
6960:
6955:
6949:
6945:
6938:
6935:
6930:
6926:
6922:
6918:
6914:
6910:
6903:
6900:
6895:
6891:
6887:
6883:
6879:
6875:
6871:
6867:
6860:
6857:
6852:
6848:
6843:
6838:
6833:
6828:
6824:
6820:
6816:
6809:
6806:
6801:
6797:
6794:(2): 1790–2.
6793:
6789:
6782:
6779:
6774:
6772:90-247-3502-5
6768:
6764:
6760:
6754:
6751:
6746:
6740:
6736:
6729:
6727:
6723:
6718:
6712:
6708:
6701:
6698:
6693:
6687:
6683:
6676:
6673:
6668:
6664:
6657:
6654:
6648:
6644:
6641:
6639:
6636:
6634:
6631:
6629:
6626:
6624:
6621:
6618:
6614:
6611:
6609:
6606:
6604:
6601:
6599:
6596:
6595:
6591:
6589:
6587:
6586:Sewall Wright
6579:
6577:
6575:
6570:
6568:
6564:
6560:
6556:
6545:
6542:
6539:
6536:
6533:
6530:
6529:
6525:
6522:
6519:
6516:
6513:
6510:
6509:
6506:
6505:
6504:
6502:
6498:
6491:
6488:term acts to
6469:
6465:
6457:
6452:
6448:
6447:least squares
6444:
6425:
6419:
6413:
6402:
6398:
6393:
6381:
6380:
6379:
6377:
6373:
6365:
6363:
6358:
6354:
6350:
6332:
6328:
6324:
6313:
6297:
6294:
6291:
6286:
6277:
6268:
6246:
6243:
6218:
6215:
6212:
6209:
6206:
6203:
6202:
6201:
6199:
6195:
6193:
6189:
6168:
6164:
6160:
6157:
6153:
6149:
6146:
6143:
6129:
6126:
6107:
6104:
6101:
6092:
6076:
6073:
6065:
6062:
6056:
6052:
6049:
6046:
6041:
6037:
6029:
6028:
6027:
6025:
6002:
5999:
5962:
5927:
5923:
5919:
5914:
5902:
5899:
5878:
5862:
5857:
5854:
5851:
5846:
5842:
5834:
5833:
5832:
5830:
5825:
5823:
5822:
5816:
5812:
5804:
5801:
5799:
5797:
5779:
5775:
5752:
5748:
5725:
5720:
5717:
5713:
5690:
5685:
5682:
5678:
5655:
5651:
5628:
5624:
5603:
5581:
5577:
5568:
5550:
5546:
5519:
5496:
5492:
5483:
5465:
5461:
5438:
5434:
5430:
5427:
5424:
5421:
5416:
5406:
5379:
5374:
5371:
5361:
5351:
5343:
5339:
5329:
5317:
5314:
5306:
5302:
5299:
5291:
5282:
5272:
5264:
5261:
5249:
5239:
5231:
5228:
5221:
5216:
5212:
5204:
5203:
5202:
5188:
5168:
5146:
5142:
5133:
5128:
5126:
5108:
5104:
5081:
5077:
5068:
5064:
5045:
5034:
5030:
5026:
5023:
5020:
5013:
5004:
5000:
4996:
4993:
4990:
4979:
4976:
4973:
4970:
4963:
4956:
4953:
4950:
4947:
4938:
4935:
4932:
4927:
4923:
4915:
4914:
4913:
4899:
4877:
4873:
4852:
4844:
4825:
4822:
4819:
4816:
4813:
4810:
4807:
4800:
4799:
4798:
4796:
4792:
4788:
4784:
4780:
4776:
4768:
4763:
4759:
4757:
4752:
4748:
4744:
4737:
4733:
4717:
4705:
4701:
4690:
4686:
4683:
4674:
4670:
4660:
4659:
4658:
4641:
4629:
4625:
4614:
4610:
4607:
4598:
4594:
4584:
4583:
4582:
4580:
4576:
4572:
4567:
4562:
4554:
4552:
4550:
4546:
4542:
4538:
4534:
4533:John W. Pratt
4530:
4526:
4522:
4517:
4500:
4497:
4494:
4487:
4477:
4473:
4470:
4435:
4432:
4429:
4422:
4412:
4408:
4405:
4385:
4368:
4364:
4354:
4350:
4347:
4315:
4311:
4301:
4297:
4294:
4230:
4227:
4223:
4218:
4214:
4206:
4205:
4204:
4202:
4198:
4193:
4191:
4187:
4183:
4179:
4175:
4170:
4168:
4163:
4157:
4152:
4147:
4141:
4135:
4130:
4125:
4119:
4115:
4112:
4106:
4099:
4093:
4089:
4085:
4083:
4079:
4075:
4071:
4068:The adjusted
4062:
4058:
4056:
4052:
4048:
4044:
4040:
4036:
4032:
4029:The adjusted
4027:
4025:
4021:
3999:
3996:
3993:
3990:
3987:
3982:
3979:
3976:
3965:
3961:
3957:
3954:
3948:
3945:
3942:
3937:
3927:
3916:
3915:
3914:
3912:
3907:
3903:
3898:
3891:
3886:
3879:
3875:
3870:
3863:
3859:
3854:
3848:
3843:
3838:
3801:
3791:
3787:
3769:
3759:
3755:
3749:
3746:
3742:
3737:
3727:
3716:
3715:
3714:
3712:
3708:
3704:
3699:
3681:
3672:
3649:
3640:
3617:
3607:
3595:
3589:
3582:
3578:
3573:
3568:
3565:
3562:
3558:
3555:
3552:
3548:
3545:
3542:
3539:
3535:
3534:
3533:
3531:
3524:
3522:
3520:
3516:
3498:
3495:
3492:
3488:
3484:
3476:
3470:
3454:
3424:
3420:
3397:
3393:
3370:
3366:
3343:
3339:
3316:
3284:
3281:
3276:
3272:
3268:
3263:
3259:
3255:
3250:
3246:
3242:
3237:
3233:
3229:
3224:
3220:
3216:
3213:
3206:
3205:
3204:
3180:
3160:
3157:
3152:
3148:
3144:
3139:
3135:
3131:
3126:
3122:
3118:
3115:
3108:
3107:
3106:
3099:
3095:
3093:
3088:
3086:
3082:
3078:
3056:
3052:
3044:
3039:
3037:
3033:
3015:
3012:
3009:
3005:
3001:
2993:
2986:
2970:
2961:
2959:
2952:
2948:
2944:
2919:
2911:
2906:
2902:
2898:
2893:
2889:
2880:
2876:
2870:
2856:
2844:
2840:
2835:
2823:
2822:
2821:
2818:
2816:
2812:
2807:
2803:
2799:
2795:
2791:
2787:
2783:
2779:
2775:
2771:
2770:least squares
2764:
2761:Inflation of
2760:
2758:
2756:
2752:
2748:
2744:
2740:
2735:
2733:
2729:
2725:
2720:
2718:
2714:
2692:
2681:
2665:
2657:
2653:
2649:
2647:
2643:
2638:
2634:
2630:
2626:
2622:
2621:least squares
2604:
2600:
2596:
2593:
2590:
2585:
2581:
2572:
2554:
2550:
2541:
2523:
2520:
2517:
2513:
2509:
2506:
2503:
2498:
2495:
2492:
2488:
2464:
2460:
2450:
2431:
2426:
2422:
2418:
2413:
2410:
2407:
2403:
2397:
2393:
2387:
2382:
2379:
2376:
2372:
2368:
2363:
2359:
2355:
2350:
2346:
2338:
2337:
2336:
2334:
2326:
2324:
2322:
2318:
2314:
2310:
2306:
2302:
2298:
2294:
2293:
2286:
2284:
2279:
2275:
2271:
2267:
2263:
2259:
2252:
2248:
2243:
2241:
2237:
2232:
2231:least-squares
2228:
2223:
2221:
2217:
2213:
2209:
2202:
2200:
2196:
2192:
2188:
2170:
2150:
2142:
2138:
2133:
2117:
2114:
2106:
2101:
2097:
2085:
2081:
2062:
2052:
2049:
2043:
2035:
2032:
2026:
2019:
2012:
2009:
2003:
1997:
1994:
1987:
1983:
1980:
1974:
1966:
1963:
1957:
1951:
1948:
1941:
1933:
1932:
1931:
1930:, defined as
1929:
1924:
1910:
1890:
1867:
1864:
1861:
1853:
1849:
1840:
1835:
1821:
1801:
1793:
1774:
1771:
1768:
1760:
1756:
1747:
1743:
1735:
1718:
1709:
1703:
1694:
1684:
1683:
1682:
1680:
1675:
1658:
1655:
1629:
1626:
1614:
1610:
1607: =
1605:
1601:
1597:
1592:
1588:
1567:
1563:
1556:
1553:
1547:
1541:
1538:
1532:
1527:
1523:
1515:
1514:
1513:
1511:
1507:
1502:
1498:
1493:
1490:
1483:
1477:
1470:
1465:
1461:
1458:In this form
1456:
1454:
1432:
1428:
1418:
1414:
1409:
1405:
1395:
1391:
1385:
1373:
1369:
1358:
1354:
1348:
1343:
1339:
1331:
1330:
1329:
1327:
1323:
1298:
1294:
1291:
1282:
1278:
1275:
1266:
1262:
1255:
1254:
1253:
1251:
1247:
1226:
1212:
1206:
1201:
1197:
1188:
1184:
1180:
1171:
1167:
1160:
1159:
1158:
1156:
1150:
1145:
1137:
1135:
1117:
1114:
1111:
1106:
1102:
1093:
1087:
1079:
1077:
1073:
1067:
1060:
1043:
1040:
1031:
1027:
1018:
988:
984:
965:
961:
955:
952:
949:
944:
940:
914:
900:
894:
889:
885:
876:
872:
868:
859:
855:
847:
843:
839:
822:
817:
813:
807:
803:
799:
794:
784:
780:
776:
771:
767:
758:
754:
750:
741:
737:
729:
725:
724:
723:
721:
703:
699:
693:
688:
685:
682:
678:
672:
669:
664:
655:
626:
614:
612:
611:
604:
600:
595:
591:
586:
582:
577:
572:
570:
569:
563:
559:
554:
550:
545:
541:
534:
530:
529:
523:
519:
514:
510:
503:
499:
495:
487:
460:
456:
443:
439:
432:
429:
426:
421:
417:
408:
401:
399:
394:
387:
380:
373:
369:
362:
358:
351:
347:
340:
333:
328:
326:
322:
318:
314:
310:
306:
301:
298:
293:
288:
286:
282:
278:
274:
270:
266:
262:
258:
254:
250:
246:
241:
239:
235:
231:
227:
222:
220:
216:
212:
208:
200:
196:
192:
188:
183:
176:
172:
168:
164:
150:
146:
143:
135:
129:
125:
121:
117:
113:
110:
103:
102:main category
99:
98:
93:
90:
86:
82:
79:
76:
75:
69:
63:
61:
56:You can help
52:
43:
42:
37:
33:
19:
7833:
7710:
7706:
7677:
7671:
7667:
7639:
7610:
7590:
7565:
7561:
7555:
7542:
7523:
7517:
7503:(3): 250–3.
7500:
7496:
7492:
7486:
7477:
7474:Snell, E. J.
7472:Cox, D. D.;
7467:
7448:
7424:
7415:
7390:
7386:
7358:
7353:
7346:
7329:1887/3161248
7309:
7305:
7295:
7268:
7264:
7254:
7221:
7217:
7171:
7167:
7158:
7157:"Estimating
7150:
7129:
7120:
7087:
7083:
7047:
7040:
7031:
7022:
6997:
6993:
6987:
6968:
6962:
6943:
6937:
6915:(1): 33–45.
6912:
6908:
6902:
6869:
6865:
6859:
6822:
6818:
6808:
6791:
6787:
6781:
6762:
6753:
6734:
6706:
6700:
6681:
6675:
6662:
6656:
6583:
6571:
6566:
6558:
6554:
6553:
6500:
6493:
6455:
6450:
6442:
6440:
6369:
6356:
6352:
6348:
6266:
6222:
6196:
6187:
6185:
6023:
5944:
5828:
5826:
5820:
5808:
5802:
5566:
5481:
5394:
5131:
5129:
5124:
5066:
5062:
5060:
4842:
4840:
4794:
4774:
4772:
4766:
4755:
4750:
4742:
4740:
4735:
4656:
4578:
4570:
4568:
4564:
4548:
4544:
4540:
4535:derived the
4529:Ingram Olkin
4524:
4520:
4518:
4274:
4200:
4196:
4194:
4185:
4181:
4177:
4173:
4171:
4166:
4161:
4155:
4150:
4145:
4139:
4133:
4128:
4123:
4120:
4116:
4110:
4104:
4101:, the term (
4097:
4091:
4087:
4086:
4081:
4077:
4069:
4067:
4054:
4050:
4046:
4042:
4038:
4034:
4030:
4028:
4023:
4019:
4017:
3910:
3908:
3901:
3896:
3889:
3884:
3877:
3873:
3868:
3861:
3857:
3852:
3846:
3836:
3833:
3710:
3702:
3697:
3593:
3591:
3580:
3561:collinearity
3549:the correct
3529:
3528:
3518:
3514:
3474:
3471:
3300:
3176:
3104:
3091:
3089:
3084:
3080:
3076:
3042:
3040:
3035:
3031:
2988:
2984:
2962:
2954:
2950:
2946:
2939:
2937:
2819:
2814:
2810:
2805:
2801:
2797:
2781:
2777:
2773:
2767:
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2186:
2163:and modeled
2136:
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1065:
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214:
210:
204:
198:
189:(black) and
174:
124:edit summary
115:
95:
65:
57:
7680:: 153–171.
7634:Kmenta, Jan
6667:McGraw Hill
4165:instead of
2728:correlation
1508:. A milder
574:Define the
402:Definitions
8152:Categories
8107:Similarity
8049:Perplexity
7960:Rand index
7945:Dunn index
7930:Silhouette
7922:Clustering
7786:Regression
7568:: 557–585.
7387:Biometrika
7142:Q120123877
4781:– such as
4559:See also:
4386:versions:
3586:See also:
3574:Extensions
3551:regression
2987:th row is
2225:Values of
1585:where the
722:formulas:
547:(known as
366:+ b). The
277:regressors
238:hypotheses
234:prediction
213:, denoted
207:statistics
171:Okun's law
7877:Precision
7829:RMSE/RMSD
7338:2474-7394
7287:0003-4851
7238:1094-4281
7196:121614674
7188:0022-0973
7112:122308344
7104:0146-6216
6894:128417849
6563:SI prefix
6490:normalize
6449:analysis
6423:‖
6417:‖
6298:−
6247:^
6244:θ
6158:−
6150:−
6130:^
6127:θ
6108:
6102:−
6077:
6053:−
6003:^
6000:θ
5903:^
5900:θ
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5780:⊗
5753:⊗
5726:⊗
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5551:⊗
5493:β
5466:⊗
5435:β
5428:−
5410:~
5372:−
5355:~
5333:~
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5243:~
5217:⊗
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5105:β
5078:β
5031:β
5024:−
5001:β
4994:−
4974:−
4951:−
4939:−
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4823:ε
4817:β
4684:−
4608:−
4498:−
4433:−
4231:−
4037:. Unlike
3997:−
3991:−
3980:−
3958:−
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3579:Adjusted
3559:there is
3553:was used;
3367:β
3340:β
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3269:⋅
3260:β
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3234:β
3221:β
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3145:⋅
3136:β
3123:β
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2877:∑
2863:⇒
2696:¯
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2594:…
2582:β
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2507:…
2451:th case,
2423:ε
2394:β
2373:∑
2360:β
2290:adjusted
2115:−
2053:^
2050:β
2044:σ
2036:^
2033:α
2027:σ
2013:^
2010:β
1998:^
1995:α
1984:
1967:^
1964:β
1952:^
1949:α
1942:ρ
1850:ρ
1757:ρ
1713:¯
1698:¯
1679:residuals
1659:^
1656:β
1630:^
1627:α
1557:^
1554:β
1542:^
1539:α
1216:¯
1207:−
1185:∑
1118:−
956:−
904:¯
895:−
873:∑
804:∑
777:−
755:∑
679:∑
659:¯
630:¯
576:residuals
433:−
261:intercept
226:statistic
142:talk page
94:Consider
62:in German
8093:Coverage
7872:Accuracy
7739:34307865
7694:23317769
7636:(1986).
7589:(2009).
7476:(1989).
7246:55098407
7138:Wikidata
7128:(1930),
6851:34307865
6592:See also
5344:′
5303:′
5292:′
5265:′
5232:′
5014:′
4964:′
4384:unbiased
3834:where df
2809:, where
2678:, while
846:variance
494:data set
224:It is a
195:outliers
118:provide
7985:Ranking
7975:SimHash
7862:F-score
7730:8279135
7646:240–243
7616:344–348
7407:2337038
7014:2683704
6917:Bibcode
6874:Bibcode
6842:8279135
6580:History
6458:is the
5819:pseudo-
5127:again.
3840:is the
3546:exists;
3525:Caveats
1748:equals
538:, ...,
507:, ...,
271:(i.e.,
140:to the
122:in the
64:.
7882:Recall
7737:
7727:
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7622:
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6688:
6186:where
5945:where
5395:where
5181:times
4747:F-test
4275:where
4018:where
2938:where
2786:F-test
1451:where
1248:, the
1151:= 0.49
315:, and
251:where
209:, the
7887:Kappa
7804:sMAPE
7690:JSTOR
7403:JSTOR
7383:(PDF)
7242:S2CID
7192:S2CID
7164:(PDF)
7134:Wiley
7108:S2CID
7052:(PDF)
7010:JSTOR
6890:S2CID
6649:Notes
6441:Both
5796:lasso
4791:lasso
4575:ANOVA
2644:) in
2571:error
1837:In a
325:SMAPE
85:DeepL
8054:BLEU
8026:SSIM
8021:PSNR
7998:NDCG
7819:MSPE
7814:MASE
7809:MAPE
7735:PMID
7650:ISBN
7620:ISBN
7595:ISBN
7528:ISBN
7453:ISBN
7334:ISSN
7283:ISSN
7234:ISSN
7184:ISSN
7100:ISSN
7056:ISBN
6973:ISBN
6948:ISBN
6847:PMID
6767:ISBN
6739:ISBN
6711:ISBN
6686:ISBN
6574:RMSE
6546:9.6
6372:norm
5643:and
5596:and
4531:and
4451:and
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3882:. df
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1056:and
840:The
496:has
396:pred
391:= 1·
382:pred
377:and
364:pred
335:pred
317:RMSE
309:MAPE
116:must
114:You
78:View
8075:FID
8041:NLP
8031:IoU
7993:MRR
7970:SMC
7902:ROC
7897:AUC
7892:MCC
7844:MAD
7839:MDA
7824:RMS
7799:MAE
7794:MSE
7725:PMC
7715:doi
7682:doi
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7395:doi
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7324:hdl
7314:doi
7273:doi
7226:doi
7176:doi
7092:doi
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6925:doi
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6882:doi
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6827:doi
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319:in
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1028:S
1000:t
997:o
994:t
989:S
985:S
977:s
974:e
971:r
966:S
962:S
953:1
950:=
945:2
941:R
915:2
911:)
901:y
890:i
886:y
882:(
877:i
869:=
860:S
856:S
823:2
818:i
814:e
808:i
800:=
795:2
791:)
785:i
781:f
772:i
768:y
764:(
759:i
751:=
742:S
738:S
704:i
700:y
694:n
689:1
686:=
683:i
673:n
670:1
665:=
656:y
627:y
610:e
603:i
599:f
594:i
590:y
585:i
581:e
568:f
562:i
558:ŷ
553:i
549:f
544:n
540:f
536:1
533:f
528:y
522:i
518:y
513:n
509:y
505:1
502:y
498:n
486:R
461:S
457:S
444:S
440:S
430:1
427:=
422:2
418:R
393:Y
386:Y
379:Y
372:Y
368:R
361:Y
359:·
357:m
350:Y
346:R
339:Y
332:Y
297:R
292:R
281:R
273:r
265:r
257:R
253:r
245:R
219:r
215:R
201:.
199:R
175:R
151:.
144:.
38:.
20:)
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