Leverage Versus Influence in Regression
In an agricultural experiment, researchers examined how varying amounts of fertilizer (in kg) affected plant growth (in cm). After plotting the data and computing a regression line, a student noted an extreme data point with a very high fertilizer amount that lay close to the regression line. The student labeled this point as an influential outlier. What mistake did the student make in classifying this point?
They confused high leverage with high influence, not recognizing that a point with an extreme x-value (high leverage) but a small residual does not necessarily distort the regression line.
They removed the point from the analysis, mistakenly believing it was erroneous.
They correctly identified the point as influential because any point with an extreme x-value must affect the regression.
They ignored the fact that this extreme point had a large residual and should be treated as an outlier.
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