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Calibration of Gasoline Flow Meters
Published in Donald B. Owen, Subir Ghosh, William R. Schucany, William B. Smith, Statistics of Quality, 2020
Conrad D. Krueger, Jerome P. Keating, Nandini Kannan, Robert L. Mason
Table 5 indicates that several other observations have unusual diagnostic values. For example, observations 2 and 11 have the highest leverage values, which are values that indicate which observations have the most influence on the estimates of the parameters. Belsley et al. (1990) recommend a cutoff value of 2(p + l)/n = 0.75 for identification of influential points. Observations 2 and 11 are the only two that meet this criterion in the data set. However, the leverage values of these two points are not unexpected, as they have the largest total volumes of the 24 observations and, more importantly, are combinations of data collected over a two-day period rather than a one-day period. In this analysis, these points carry more weight than the one-day observations to reflect this influence.
Residual-diagnostics Plots
Published in Przemyslaw Biecek, Tomasz Burzykowski, Explanatory Model Analysis, 2021
Przemyslaw Biecek, Tomasz Burzykowski
The bottom-left panel of Figure 19.1 presents the plot of standardized residuals in the function of leverage. Leverage is a measure of the distance between xi and the vector of mean values for all explanatory variables (Kutner et al., 2005). A large leverage value for the i-th observation, say 1,, indicates that xi is distant from the center of all observed values of the vector of explanatory variables. Importantly, a large leverage value implies that the observation may have an important influence on predicted/fitted values. In fact, for the classical linear-regression model, it can be shown that the predicted sum-of-squares, defined in (15.5), can be written as PRESS=∑i=1n(y^i(−i)−yi)2=∑i=1nri2(1−li)2.
Classification, Comparison, and Correlation
Published in F. Brent Neal, John C. Russ, Measuring Shape, 2017
For determining whether points in a regression analysis may be outliers, Cook’s distance (Cook, 1977) measures the effect of deleting a given observation on the remainder of the data. An observation whose omission changes the shape of the distribution of the remaining points is considered more likely to be one that does not belong. Data points with large residuals or high leverage might distort the outcome and accuracy of a regression or other analysis.
Knowledge Reduction in Formal Contexts through CUR Matrix Decomposition
Published in Cybernetics and Systems, 2019
K. Sumangali, Ch. Aswani Kumar
The computation of ‘leverage/importance’ scores plays a vital role in the construction process of CUR matrix decomposition. In statistics, leverage score denotes the distance measure of the observations of an independent variable from those of the remaining observations. From linear algebraic point of view, it measures the degree of correlation between the singular vectors of any matrix to its standard basis. High leverage scores are attributed to the high level of importance. Leverage scores can be computed for each column/row of any given matrix. In the CUR decomposition process of a matrix A, the matrices C and R, respectively, denote the randomly selected columns and rows of the original matrix A based on their high leverage scores. The matrix U is chosen such that Let us next outline about the process of leverage score computation.
Risk factors for work-related musculoskeletal disorders among workers in the footwear industry: a cross-sectional study
Published in International Journal of Occupational Safety and Ergonomics, 2021
Wilza Karla dos Santos Leite, Anísio José da Silva Araújo, Jonhatan Magno Norte da Silva, Leila Amaral Gontijo, Elamara Marama de Araújo Vieira, Erivaldo Lopes de Souza, Geraldo Alves Colaço, Luiz Bueno da Silva
Outliers were detected in the regression models; however, they were only excluded when they behaved as high-leverage points. According to Cordeiro and Demétrio [38], a point is considered to have high leverage when it is inconsistent and influences the regression model; thus, its inconsistency is ensured when the standardized residual is outside the [−2;2] interval, and its influence is ensured when its value is greater than 2p/n, where p = number of independent variables; n = sample size [39]. High-leverage points are observations made in a study that may change OR estimates by deviating them from the general trend (concerning the relationship between the dependent and independent variables) identified for the largest part of the dataset.