1. The problem asks to determine the standard error of the estimate, denoted as $S_{YX}$. 2. The standard error of the estimate measures the average distance that the observed values fall from the regression line. It is calculated using the formula: $$S_{YX} = \sqrt{\frac{\sum (Y_i - \hat{Y_i})^2}{n - 2}}$$ where $Y_i$ are the observed values, $\hat{Y_i}$ are the predicted values from the regression, and $n$ is the number of data points. 3. To compute $S_{YX}$, you need the sum of squared residuals $\sum (Y_i - \hat{Y_i})^2$ and the sample size $n$. 4. Substitute the values into the formula and simplify: $$S_{YX} = \sqrt{\frac{\text{sum of squared residuals}}{n - 2}}$$ 5. Round the result to four decimal places as required. Without the specific data or sum of squared residuals and $n$, the exact numeric answer cannot be computed here. Please provide these values to proceed with the calculation.