When all the actual values of y and the predicted values of y are equal, the standard error of estimate will be:Group of answer choices2.0.0.0.1.0.–1.0.

Break Down the Problem

1. We need to determine what happens to the standard error of estimate when all actual values of $y$ are equal to their predicted values.

Relevant Concepts

2. The standard error of the estimate (SEE) measures the accuracy of predictions made with a regression line. It is calculated using the formula: $SEE = \sqrt{\frac{\sum (y_i - \hat{y}_i)^2}{n}}$ where $y_i$ are the actual values, $\hat{y}_i$ are the predicted values, and $n$ is the number of observations.

Analysis and Detail

3. If all actual values $y_i$ are equal to the predicted values $\hat{y}_i$, then the difference $(y_i - \hat{y}_i)$ for each observation will be $0$. Therefore, the squared differences will also be $0$: $(y_i - \hat{y}_i)^2 = 0 \quad \text{for all } i$ Consequently, the summation of squared differences: $\sum (y_i - \hat{y}_i)^2 = 0$ This leads to: $SEE = \sqrt{\frac{0}{n}} = 0$

Verify and Summarize

4. Since the calculated standard error of estimate is $0$, it confirms that there is no error between the actual and predicted values.

Final Answer

The standard error of estimate will be 0.