mean squared errors

USAGE SUMMARY

The phrase "mean squared errors" is correct and usable in written English.
It is typically used in statistical analysis and machine learning to refer to the average of the squares of the errors between predicted and actual values. Example: "The model's performance was evaluated using mean squared errors to determine its accuracy in predictions."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

55 human-written examples

The models' R2 ranged from 0.71 to 0.88, and their root mean squared errors (RMSEs) ranged from 3.07 to 6.95.

Rangeland Ecology & Management

Overall, root mean squared errors for runoff were reduced by 22.2% when hydrological model calibration is performed with WRF precipitation.

Journal of Hydrology

The model has to be retrained every 10 20 days to retain estimation mean squared errors below 0.35 V2.

Electric Power Systems Research

The performance of different ANN architectures was obtained as error (mean squared errors: MSE) and goodness of fit (determination coefficient: R2) parameters.

Engineering in Agriculture, Environment and Food

The Aquarius soil moisture data showed higher root mean squared errors in areas where there were more frequent wetting and drying cycles.

International Journal of Applied Earth Observation and Geoinformation

Results indicated that the root mean squared errors (RMSEs) of horizontal residual errors calculated from 30 check points were less than 10 m.

ISPRS Journal of Photogrammetry and Remote Sensing

Human-verified similar examples from authoritative sources

Similar Expressions

5 human-written examples

In addition, for assessing estimator of the nonparametric component g, we study the square root of mean-squared errors (RMSE) based on 1000 repetitions.

Journal of Inequalities and Applications

All the parameters in the models were estimated by minimizing mean-squared errors between the model predictions and experimental data.

Biochemical Engineering Journal

Optimized models had the root mean-squared errors of 26.1 nm/min and 0.103 nm for the etch rate and surface roughness, respectively.

Microelectronic Engineering

Also an artificial neural network was designed in order to model the experimental data, R-squared and mean-squared errors of this model were 0.9972 and 0.000037887 respectively.

Journal of Molecular Liquids

Root mean-squared errors (RMSE), mean-absolute errors (MAE) and determination coefficient (R2) were used for the evaluation of the models' performances.

Journal of Hydrology

Expert writing Tips

Best practice

When reporting the results of a model, always specify whether you are presenting "mean squared errors" or root mean squared error (RMSE), as they represent different scales of error.

Common error

Avoid using "mean squared errors" interchangeably with other error metrics like mean absolute error (MAE). MSE penalizes larger errors more heavily due to the squaring operation, making it sensitive to outliers, while MAE treats all errors equally.

Linguistic Context

The phrase "mean squared errors" functions as a noun phrase in statistical analysis and machine learning. It quantifies the average squared difference between predicted and actual values, serving as a measure of a model's predictive accuracy. As Ludwig AI confirms, it's a correct and usable term.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, "mean squared errors" (MSE) is a fundamental concept in statistics and machine learning used to evaluate the performance of predictive models. As confirmed by Ludwig AI, the term is grammatically correct and widely used, particularly in scientific contexts. It quantifies the average squared difference between predicted and actual values, with lower values indicating better model accuracy. Alternatives include "average squared errors" or MSE. When writing about MSE, ensure you differentiate it from RMSE and other error metrics and specify the metric when reporting results. In conclusion, understand the proper scope of the phrase and remember that "root mean squared error" can be more appropriate at times depending on the goal.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

MSE (Mean Squared Error)

This provides the abbreviation, which is commonly used in technical writing and presentations.

average squared errors

This alternative uses simpler language by replacing "mean" with "average", which is more accessible to a broader audience.

root mean squared error (RMSE)

This related metric is the square root of the MSE, providing error in the original unit of measurement, often easier to interpret.

mean squared deviation

This phrase replaces "errors" with "deviation", focusing on the spread of data points around the mean rather than the difference between predictions and actual values.

average of squared residuals

This option focuses on the residuals, which are the differences between observed and predicted values, and then averages their squares.

sum of squared errors divided by n

This alternative provides the mathematical definition of mean squared error, clarifying how it's calculated.

expected squared error

This highlights the expected value of the squared error, emphasizing the probabilistic nature of the measurement.

L2 loss

This option uses a term commonly used in machine learning. It refers to a loss function based on the square of the Euclidean distance.

quadratic loss

This term describes the error calculation method, emphasizing the squaring of differences.

variance of the errors

Focuses on the spread of errors, not the actual error measure, implying a slightly different statistical focus.

FAQs

How do I interpret "mean squared errors"?

The "mean squared errors" represent the average of the squared differences between predicted and actual values. A lower MSE indicates better model performance, with values closer to zero suggesting more accurate predictions.

What's the difference between "mean squared errors" and root mean squared error (RMSE)?

The RMSE is the square root of the "mean squared errors". RMSE is often preferred because it expresses the error in the same units as the target variable, making it easier to interpret. For example, "root mean squared error" can be more intuitive to understand in the original scale of the data.

When should I use "mean squared errors" versus other metrics?

"Mean squared errors" are useful when large errors are particularly undesirable, as the squaring amplifies their impact. However, if you want a metric that is less sensitive to outliers, consider using the mean absolute error (MAE) instead. It's also worth noting that for interpretability, the "root mean squared error" is better.

What are some alternatives to saying "mean squared errors"?

Depending on the context, you could use phrases like "average squared errors", "mean squared deviation", or simply refer to it as MSE. In a machine learning context, one may also use the term "L2 loss".