What is the name of the distance captured by the purple dotted line (shown below)?

Question

BlackTom AI · Accepted Answer

Question restatement: What is the name of the distance captured by the purple dotted line (shown below)?

Available answer option:
- A negative residual.

Analysis of the option:
- Correct-looking rationale: In regression analysis, a residual is the vertical distance from a data point (dot) to the regression line. If the dot lies below the regression line, the residual is negative. The purple dotted line, as described, likely represents that vertical distance between the point and the model’s predicted value. Therefore, labeling this distance as a negative residual is consistent with the standard definition of residuals in regression.

Considerations about missing other options: The prompt provides only one answer choice. If other competing options existed (e.g., positive residual, distance to the line in a horizontal sense, or a regression coefficient), they would need to be evaluated against the same definition. However, with the single option given, the statement that the distance is a negative residual aligns with the residual concept for a point below the regression line.

Pedagogical note: A residual is not the slope or the regression coefficient; it is specifically the vertical difference between observed values and their predicted values on the regression line. Positive residuals indicate points above the line, while negative residuals indicate points below the line. This aligns with the general interpretation of residuals in least-squares regression.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 1B

What is the name of the distance captured by the purple dotted line (shown below)?

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