Why outliers are called influential observations

For this discussion, you will assess the use of various support decision tools and explain why outliers are sometimes called influential observations. Discuss what could happen to the slope of a regression of Y versus a single X when an outlier is included versus when it is not included. Will this necessarily happen when a point is an outlier? You are required to give at least two examples in your response.

Sample Solution

What is an outlier?

Albright & Winston, (2017) describe an outlier as an observation that has an extreme value for at least one variable.

Albright & Winston, (2017) describe an outlier as an observation that has an extreme value for at least one variable. An outlier lies at an abnormal distance from the rest of the observations. Usually, an outlier contains one or more characteristics: for example, its value of the dependent variable can be larger or smaller than forecasted by the XY regression line, and as well, its residual can be extremely large in magnitude (p.512). Sometimes outliers can be called influential observations since they can significantly tilt a regression line towards them. When an outlier is included in a regression of Y versus a single X, the slope of the line is greatly tilted towards the outlier. This change in slope normally leads to a shift in the y-intercept. When an outlier is not included, the y-intercept does not change, instead, it remains in its original position. Besides, without the outlier, the XY regression line has a slope though not prevalent as it is when an outlier is included. These changes can take place upon inclusion of another point that is not necessarily an outlier but they become pronounced if the point is an outlier.
Examples are attached below:
Albright, S. C, & Winston, W. L. (2017). Business analytics: Data analysis and decision making (6th ed.). Retrieved from https://redshelf.com/

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