Final answer:
An outlier is a data point that significantly deviates from other points in a data set, either in regression analysis or within a distribution. Evaluation involves checking if the point is a statistical anomaly or provides significant information. Proper investigation of outliers is essential as they can influence the results and understanding of the data.
Step-by-step explanation:
What is an Outlier?
An outlier is an observed value in a data set that is significantly different from the other data points. It can be an extreme value at either end of a distribution. In the context of regression analysis, an outlier may be far from the least squares regression line, potentially more than two standard deviations of the residuals from its predicted value. Outliers can have large errors and not lie close to the best-fit line. It's important to determine whether the outlier is due to an error or if it provides valuable information about the population under study. Unlike outliers, influential points are determined by their horizontal distance from other values and can have a significant effect on the slope of the regression line.
When using a box-and-whisker plot, outliers may be marked with dots if the whiskers do not extend to these points. Careful examination is crucial to decide whether to include or exclude an outlier from analysis, as this can affect the interpretation of data.