A residual is the remaining _______________ after we have calculated the regression line.

Question

BlackTom AI · Accepted Answer

The question asks about what a residual represents in the context of a regression line.
In regression analysis, after fitting a line (the regression line), each observed value has a corresponding predicted value on that line, often denoted ŷ.
A residual is the difference between the observed value y and its predicted value ŷ for a given data point: residual = y − ŷ.
This difference reflects how far off the regression line is from the actual observation for that point, i.e., the prediction error for that observation.
Common misconceptions include confusing residuals with the entire scatter in the data (which relates to variability) or with the standardized error; residuals are simple raw prediction errors, not squared or standardized forms unless specifically transformed.
If a question offered distractors, they might include terms like “variance,” “bias,” or “forecast value,” which do not precisely define the residual as the remaining prediction error after fitting the regression line.

STAT 1450.02 SP2025 (28132) Checkpoint 5.5

A residual is the remaining _______________ after we have calculated the regression line.

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