If time is of the essence this is an easy and quick calculation to make but it is quite basic. Ggplot(df, aes(x=index, y=lstat, col = Outlier)) + geom_point() + scale_color_manual(values=c('black', 'red')) Outlier <- as.factor(sapply(bost$lstat, id_outlier)) The detected outliers are data points 8, 15 and the inserted outliers are data points 8, 15. Outliers_iqr <- which(sapply(bost$lstat, id_outlier) = 1) To calculate CookвЂ™s Distance the projection matrix is first calculated. # Residual standard error: 0.11 on 26 degrees of freedom SuppressPackageStartupMessages(library(gridExtra)) SuppressPackageStartupMessages(library(ggplot2)) suppressPackageStartupMessages(library(arm)) The Boston data set will be down sampled and some artificial outliers will be put in. This wonвЂ™t be the best model to fit the data just a useful one for explanation. Using the projection matrix, CookвЂ™s Distance is defined asДЄ simple example will be set up to demonstrate the calculation of CookвЂ™s distance. The observation with the largest change will be the observation that is most influential on the model fit. With this in mind it makes sense to evaluate how much the model changes when observation is removed from the data frame. Taking a step back, intuitively we want to know how influential any given point is. Leverage is defined as the measure of how far away the predictor values are from the response variable values.

The diagonal elements of are the leverage values. It can be shown the solution to the regression model which minimises the sum of squares isДЇollowing from this the predicted values of are given byДЇor CookвЂ™s Distance calculations the key component is the projection matrix. The paramter vector contains coefficients i.e. Data points with high influence can significantly skew results. CookвЂ™s DistanceД¬ookвЂ™s Distance is a measure of the influence of a point in regression analysis. In this post weвЂ™ll get a gentle introduction to a few methods of outlier detection, CookвЂ™s Distance, the interquartile range, and Mahalanobis distance. ThereвЂ™s no one way to detect and treat outliers and is unwise to blindly use an out-of-the-box procedure. They have the potential to distort and skew your data and depending on the problem could completely change the model that you build. Outliers are typically extraneous data points that may have occurred due to an error in measurement or they could be genuine only very unlikely to occur. Outlier detection and treatment is an important part of data analysis and one of the first things you should do with a new data set.

Dfind outliers in high dimension