What is a residual in regression analysis?

• A. actual y - predicted y
• B. predicted y - actual y
• C. the average of y-values
• D. the slope of the regression line

Answer: (A)

In regression, a residual is how far off the model’s prediction is from what was actually observed. It’s the vertical difference between the actual y value and the predicted y value from the regression line: residual = y − ŷ. If a data point sits above the line, the residual is positive (the model underestimates that observation); if it sits below, the residual is negative (the model overestimates it). The larger the residual, the bigger the error for that point.

This is why the correct description is actual minus predicted. The reverse order would give the negative of the residual, which isn’t the standard definition. The average of y-values is just the mean, not a residual, and the slope is a property of the line, not an error term.