# Hat Matrix Leverage Values

### Leverage considered large if it is bigger than.

Hat matrix leverage values. The cooks distance is given by the formula. Y j i is the fitted value for the j observation without including the i-th observation in the data that will generate the model. Yˆ is fitted value and e is residual the elements hii of H may be interpreted as the amount of leverage excreted by the ith observation yi on the ith fitted value ˆ yi.

The predicted values ybcan then be written as by X b XXT X 1XT y. Leverage Values Outliers in X can be identified because they will have large leverage values. The hat matrix provides a measure of leverage.

TrH p 1 17 But the trace of any matrix is the sum of its diagonal entries trH Xn i1 H ii 18 so the trace of the hat matrix is the sum of each points leverage. The leverage h i i is a measure of the distance between the x value for the i t h data point and the mean of the x values for all n data points. 3 Draw a histogram stem-and-leaf or other plot of h ii.

The leverage h i i is a number between 0 and 1 inclusive. Where H XXT X 1XT is an n nmatrix which puts the hat on y and is therefore. The function returns the diagonal values of the Hat matrix used in linear regression.

It is useful for investigating whether one or more observations are outlying with regard to their X values and therefore might be excessively influencing the regression results. 2 Moderate leverage if h ii20205 and high leverage if h ii2051. D i j 1 n Y j Y j i 2 p M S E.

The invocation hatvalues vglmObject should return a n times M matrix of the diagonal elements of the hat projection matrix of a vglm object. A vector with the diagonal Hat matrix values the leverage of each observation. It is useful for investigating whether one or more observations are outlying with regard to their X values and therefore might be excessively influencing the regression results.

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