Answer: the difference between the observed value of Y and the estimated value of Y

## Explanation In simple linear regression, the residual (also called error term) for an observation is defined as: **Residual = Observed value of Y - Predicted/Estimated value of Y** Mathematically: \( e_i = Y_i - \hat{Y}_i \) Where: - \( Y_i \) = actual observed value of the dependent variable - \( \hat{Y}_i \) = predicted value from the regression equation **Why option C is correct:** - This is the standard definition of a residual in regression analysis - Residuals represent the vertical distance between actual data points and the regression line - They measure the unexplained portion of the variation after accounting for the relationship with the independent variable **Why other options are incorrect:** - **Option A**: This describes a ratio, not a residual. Residuals are differences, not ratios. - **Option B**: This describes a ratio of unexplained to explained variation, which is related to R-squared concepts but not the definition of an individual residual. **Key Points:** - Residuals should sum to zero in ordinary least squares regression - Analysis of residuals is crucial for checking regression assumptions (linearity, homoscedasticity, normality) - Residuals represent the error or unexplained variation for each observation

Author: LeetQuiz .