Let's take a look at a few examples that should help to clarify the distinction between the two types of extreme values. 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. 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. Note that - for our purposes - we consider a data point to be an outlier only if it is extreme with respect to the other y values, not the x values.Ī data point is influential if it unduly influences any part of regression analysis, such as the predicted responses, the estimated slope coefficients, or the hypothesis test results. With multiple predictors, extreme x values may be particularly high or low for one or more predictors or may be "unusual" combinations of predictor values (e.g., with two predictors that are positively correlated, an unusual combination of predictor values might be a high value of one predictor paired with a low value of the other predictor). With a single predictor, an extreme x value is simply one that is particularly high or low. You are saying: 'go look in the ame ust for a variable called lm.res, and plot that as y' But you created lm.
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