The formula to calculate the RMS Error is:
\[ \text{RMS Error} = \sqrt{\frac{\sum (\text{observed} - \text{predicted})^2}{n}} \]
Where:
RMS Error is a measure used to evaluate the differences between values predicted by a model or an estimator and the actual values observed. The RMS Error represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. It is commonly used in forecasting and regression analysis to verify experimental results.
Example 1:
Step 1: Calculate the RMS Error:
\[ \text{RMS Error} = \sqrt{\frac{(10-11)^2 + (12-13)^2 + (14-15)^2}{3}} = \sqrt{\frac{1 + 1 + 1}{3}} = \sqrt{1} = 1 \]
Example 2:
Step 1: Calculate the RMS Error:
\[ \text{RMS Error} = \sqrt{\frac{(5-4)^2 + (6-6)^2 + (7-8)^2}{3}} = \sqrt{\frac{1 + 0 + 1}{3}} = \sqrt{\frac{2}{3}} \approx 0.8165 \]
