Which of the following defines a residual in regression analysis?

• A. The difference between observed and predicted values.
• B. The squared error summed across observations.
• C. The predicted value.
• D. The slope of the regression line.

Answer: (A)

In regression, a residual is the difference between what was observed and what the model predicted for that observation. For each data point, you take the observed value and subtract the predicted value from the regression line. This residual can be positive (the point sits above the line) or negative (it sits below). It represents the prediction error for that case. The squared residuals are used to assess overall fit (forming the sum of squared errors), but the residual itself is simply the raw difference, not the predicted value or the slope of the line.