Influential observation
In statistics, an influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regression analysis an influential observation is one whose deletion has a large effect on the parameter estimates. Assessment. Various methods have been proposed for measuring influence. Assume an estimated regression formula_1, where formula_2 is an "n"×1 column vector for the response variable, formula_3 is the "n"×"k" design matrix of explanatory variables (including a constant), formula_4 is the "n"×1 residual vector, and formula_5 is a "k"×1 vector of estimates of some  population parameter formula_6. Also define formula_7, the projection matrix of formula_3. Then we have the following measures of influence: Outliers, leverage and influence. An outlier may be defined as a data point that differs significantly from other observations. A high-leverage point are observations made at extreme values of independent variables. Both types of atypical observations will force the regression line to be close to the point. In Anscombe's quartet, the bottom right image has a point with high leverage and the bottom left image has an outlying point.