What is defined as an outlier in regression analysis?

In regression analysis, an outlier is characterized as any observation that does not conform to the trend exhibited by the majority of the data points. This means that it stands apart from the pattern that the regression model is trying to capture, either by being unusually high or low relative to the other observations. Identifying outliers is critical because they can significantly affect the results of regression analysis, potentially skewing the relationship being studied and leading to misleading conclusions.

Observations that fit the predicted trend contribute to the overall pattern without disrupting it, whereas those with a significant standard deviation might not necessarily be outliers in the context of regression if they still align with the trend. Correlation, meanwhile, refers to the degree of relationship between two variables and does not directly define an outlier. Thus, the correct definition focuses specifically on how an observation relates to the overall trend of the data set, which is why the identification of any observation that does not align with this trend is crucial in regression analysis.