The correct answer is C. $u=Y-y$.
An error term, disturbance term, or residual term is the difference between the observed value of a dependent variable and the value predicted by a regression model. It is often denoted by $u$ or $\varepsilon$.
The error term is a random variable that is assumed to have zero mean and constant variance. It is used to account for the fact that there will always be some error in the data, even if the model is perfectly specified.
The error term can be used to calculate the standard error of the estimate, which is a measure of the precision of the model. It can also be used to test the significance of the model’s coefficients.
Here is a brief explanation of each option:
- Option A: $U=A-b$ is not the correct formula for the error term. The error term is calculated as the difference between the observed value of the dependent variable and the value predicted by the model, not as the difference between two constants.
- Option B: $u=A-a$ is not the correct formula for the error term. The error term is calculated as the difference between the observed value of the dependent variable and the value predicted by the model, not as the difference between two constants.
- Option C: $u=Y-y$ is the correct formula for the error term. The error term is calculated as the difference between the observed value of the dependent variable and the value predicted by the model.
- Option D: $u=X-x$ is not the correct formula for the error term. The error term is calculated as the difference between the observed value of the dependent variable and the value predicted by the model, not as the difference between two constants.