root mean-square error

简明释义

均方根误差

英英释义

例句

1.The root mean-square error was calculated to assess the forecasting accuracy of our time series model.

计算了均方根误差以评估我们时间序列模型的预测准确性。

2.By comparing the root mean-square error across different models, we selected the one with the best predictive performance.

通过比较不同模型的均方根误差，我们选择了预测性能最佳的模型。

3.To improve accuracy, we aimed to minimize the root mean-square error in our regression analysis.

为了提高准确性，我们的目标是在回归分析中尽量减少均方根误差。

4.The model's performance was evaluated using the root mean-square error, which measures the average magnitude of the errors between predicted and observed values.

该模型的性能通过使用均方根误差进行评估，该指标测量预测值与观察值之间误差的平均大小。

5.In machine learning, a lower root mean-square error indicates a better fit of the model to the data.

在机器学习中，较低的均方根误差表示模型与数据的拟合程度更好。

作文

In the world of data analysis and statistical modeling, understanding various metrics is crucial for evaluating model performance. One such important metric is root mean-square error, often abbreviated as RMSE. This metric provides a clear indication of how well a model's predictions align with the actual observed values. Essentially, the root mean-square error (均方根误差) quantifies the difference between predicted values and actual values, offering insights into the accuracy of predictive models.To calculate the root mean-square error, one must first determine the residuals, which are the differences between the observed values and the predicted values. Once these residuals are calculated, they are squared to eliminate any negative signs, ensuring that larger errors have a more significant impact on the final result. The next step involves averaging these squared residuals, which gives us the mean square error (MSE). Finally, by taking the square root of this average, we arrive at the root mean-square error. This process not only provides a single number that summarizes the model's predictive accuracy but also emphasizes larger errors due to the squaring step.The significance of the root mean-square error cannot be overstated. It serves as a key performance indicator in various fields, including finance, engineering, and environmental science. For instance, in finance, RMSE can be used to assess the accuracy of stock price predictions made by different models. A lower RMSE indicates a better fit, meaning the model's predictions are closer to the actual market behavior. In engineering, RMSE might be employed to evaluate the precision of measurements taken from sensors against known standards. Here, a smaller RMSE signifies that the sensors are providing reliable data, which is crucial for safety and efficiency.Moreover, the root mean-square error is particularly useful because it is expressed in the same units as the original data, making it easier for analysts and stakeholders to interpret. Unlike other metrics, such as mean absolute error (MAE), RMSE penalizes larger errors more heavily, which can be advantageous in situations where large deviations are particularly undesirable. This characteristic makes RMSE a preferred choice in many applications where accuracy is paramount.However, it is essential to note that while the root mean-square error is a powerful tool, it is not without its limitations. For example, RMSE can be sensitive to outliers, which may skew the results and provide a misleading picture of model performance. Therefore, it is often recommended to use RMSE in conjunction with other metrics, such as MAE or R-squared, to gain a more comprehensive understanding of a model's effectiveness.In conclusion, the root mean-square error (均方根误差) is an invaluable metric in the realm of data analysis and model evaluation. Its ability to quantify prediction accuracy and highlight larger errors makes it a critical component of model assessment. By understanding and utilizing RMSE alongside other performance indicators, analysts can make informed decisions that lead to more accurate predictions and ultimately better outcomes in their respective fields.