What is the difference between outliers influential points and high leverage points?
In this section, we learn the distinction between outliers and high leverage observations. In short: An outlier is a data point whose response y does not follow the general trend of the rest of the data. A data point has high leverage if it has “extreme” predictor x values.
What is a high influence point?
An influential point is an outlier that greatly affects the slope of the regression line. One way to test the influence of an outlier is to compute the regression equation with and without the outlier.
What is an influential point in statistics?
An influential point is an outlier that greatly affects the slope of the regression line. One way to test the influence of an outlier is to compute the regression equation with and without the outlier. This type of analysis is illustrated below.
What is leverage points in statistics?
Leverage points are those observations, if any, made at extreme or outlying values of the independent variables such that the lack of neighboring observations means that the fitted regression model will pass close to that particular observation.
Can a high leverage data point be influential?
Outliers and high leverage data points have the potential to be influential, but we generally have to investigate further to determine whether or not they are actually influential. One advantage of the case in which we have only one predictor is that we can look at simple scatter plots in order to identify any outliers and influential data points.
What is an outlier, leverage, and influential point?
However, rather than calling them x- or y-unusual observations, they are categorized as outlier, leverage, and influential points according to their impact on the regression model. Outlier – an outlier is defined by an unusual observation with respect to either x-value or y-value.
How is the leverage of a point determined?
A leverage point is determined by a point whose x-value is an outlier, while the y -value is on the predicted line ( y -value is not an outlier). Therefore, this point is undetected by the y -outlier detection statistics, including the RESI, SRES, and TRES.
When does a person have high leverage and high influence?
And although he has the potential of high influence, he will not be able to impact the regression line significantly because his force is exerted almost parallel to the line. At [10,10], he has both high leverage and high influence, since he stands far from the rest of the observations in X and Y.