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High-leverage points, if any, are outliers with respect to the independent variables. That is, high-leverage points have no neighboring points in R p {\displaystyle \mathbb {R} ^{p}} space, where p {\displaystyle {p}} is the number of independent variables in a regression model.
[6] [7] A high-leverage point are observations made at extreme values of independent variables. [8] Both types of atypical observations will force the regression line to be close to the point. [2] In Anscombe's quartet, the bottom right image has a point with high leverage and the bottom left image has an outlying point.
The calculated regression is offset by the one outlier, which exerts enough influence to lower the correlation coefficient from 1 to 0.816. Finally, the fourth graph (bottom right) shows an example when one high-leverage point is enough to produce a high correlation coefficient, even though the other data points do not indicate any relationship ...
Previously when assessing a dataset before running a linear regression, the possibility of outliers would be assessed using histograms and scatterplots. Both methods of assessing data points were subjective and there was little way of knowing how much leverage each potential outlier had on the results data.
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
In statistics, Cook's distance or Cook's D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. [1] In a practical ordinary least squares analysis, Cook's distance can be used in several ways: to indicate influential data points that are particularly worth checking for validity; or to indicate regions of the design space where it ...
Graph of points and linear least squares lines in the simple linear regression numerical example. The 0.975 quantile of Student's t-distribution with 13 degrees of freedom is t * 13 = 2.1604, and thus the 95% confidence intervals for α and β are
For linear models, the trace of the projection matrix is equal to the rank of , which is the number of independent parameters of the linear model. [8] For other models such as LOESS that are still linear in the observations y {\displaystyle \mathbf {y} } , the projection matrix can be used to define the effective degrees of freedom of the model.