Firework Plot as a Graphical Exploratory Data Analysis Tool for Evaluating the Impact of Outliers in Data Exploration and Regression

Outliers can distort many measures for data analysis. We propose a new set of graphical summaries, called firework plots, as simple tools for evaluating the impact of outliers in data exploration and regression assessment. One variation of the plot focuses on the impact of extreme observations on the mean and standard deviation by using curves that trace the relative contribution to the overall summary as weights for individual observations are changed from 1 to 0 in a univariate data set. Similarly, other variations for bivariate data allow examination of the impact of changing weights on combinations of the correlation coefficient and mean with two‐ or three‐dimensional firework plots. One variation of the plot focuses on the impact on the estimated intercept, the estimated slope, and the estimated standard deviation by using curves based on the relative contribution to the overall summary as weights for individual observations are changed from 1 to 0 in a simple linear regression analysis. Similarly, other variations for a multiple regression allow the practitioner to examine the impact of changing weights on combinations of the estimated regression coefficients and the standard error with the pairwise firework plot matrix.