Explanation

In simple linear regression, the standard error of the estimate (SEE) is also known as the root mean square error (RMSE).

Key Concepts:

1. Standard Error of the Estimate (SEE): Measures the standard deviation of the residuals (errors) in a regression model. It represents the average distance that the observed values fall from the regression line.

2. Root Mean Square Error (RMSE): This is calculated as:

   $$RMSE = \sqrt{\frac{\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}{n-k-1}}$$

   where:

   • $y_i$ = actual values
   • $\hat{y}_i$ = predicted values
   • $n$ = number of observations
   • $k$ = number of independent variables (for simple linear regression, k=1)

3. Why not the other options:

   • Mean Square Error (MSE): This is the average of the squared errors, not the standard error. MSE = SEE²
   • Sum of Squares Error (SSE): This is the total of squared errors, not the standard error. SSE = Σ(y_i - ŷ_i)²

Formula Relationship:

Therefore, the correct answer is C. root mean square error.