mean squared error

USAGE SUMMARY

“mean squared error” is a correct and usable phrase in written English.
You can use it when referring to the mathematical concept of calculating the average of the squares of the errors. For example, “The mean squared error of our model was 0.02, indicating a good degree of accuracy.”.

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

50 human-written examples

What was the root mean squared error?

Harvard Business Review

Thereby, the proposed estimator reduces the mean squared error.

Journal of Econometrics

The results achieved a mean squared error of 0.07.

International Journal of Applied Earth Observation and Geoinformation

The training was performed on each class to minimize the mean squared error value.

Nature

The root mean squared error of calibration (RMSEC) is 0.0503 and the root mean squared error of validation (RMSEV) is 0.0485.

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy

The efficacy of the ANFIS models has been judged through the correlation coefficient (R), mean squared error (MSE) and root mean squared error (RMSE).

Journal of Environmental Chemical Engineering

Human-verified similar examples from authoritative sources

Similar Expressions

9 human-written examples

The algorithm employs iterative mean squared error minimization using least squares curve fitting [64].

Plosone

The training phase minimizes the mean-squared error on the training set.

Computers & Geosciences

Finally, the fine time adjustment based on the minimum mean-squared error criterion is performed.

Physical Communication

Learning is achieved by stochastic gradient-descent using a mean-squared error training objective.

Neural Networks

root-mean-squared error.

Earth, Planets and Space

Expert writing Tips

Best practice

Use "mean squared error" to evaluate the performance of models or estimators in regression tasks. It helps quantify the average squared difference between predicted and actual values, providing a measure of model accuracy.

Common error

Avoid using "mean squared error" (MSE) and root mean squared error (RMSE) interchangeably. RMSE is the square root of MSE and is expressed in the same units as the target variable, making it more interpretable. Choose the appropriate metric based on your reporting needs.

Linguistic Context

The phrase "mean squared error" functions as a noun phrase within the context of statistical analysis and machine learning. It serves as a technical term that describes a specific method for quantifying the difference between predicted and actual values. Ludwig AI indicates it's correct and usable.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

The phrase "mean squared error" is a grammatically correct and highly prevalent term in statistics and machine learning, serving as a key metric for evaluating model performance. As Ludwig AI confirms, it's a valid and usable phrase, primarily found within scientific contexts. It quantifies the average squared difference between predicted and actual values. Related phrases include "root mean squared error", "average squared deviation", and "least squares error". When using "mean squared error", it's crucial to specify the context and units of measurement. Be mindful of the distinction between MSE and RMSE. This comprehensive analysis provides a solid foundation for accurately interpreting and applying "mean squared error" in your work.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

average squared deviation

Focuses on deviation rather than error, implying a broader statistical dispersion measure.

root mean squared deviation

Adds a square root, scaling the error back to the original units of measurement, providing interpretability.

expected squared error

Emphasizes the probabilistic nature of the error, considering it as an expected value.

residual sum of squares

Considers the sum of squared differences between observed and predicted values, without averaging.

sum of squared residuals

This alternative focuses on the summation rather than the averaging of the squared residuals.

least squares error

Highlights the minimization aspect, often used in optimization problems.

quadratic loss

Frames the error as a loss function, common in machine learning and optimization.

L2 loss

A more concise, mathematical representation of the same concept of quadratic loss.

prediction error variance

Focuses on the variance of the prediction errors, rather than the mean of the squared errors.

model discrepancy

This expresses the difference between the model and observed values in a broader, less mathematical way.

FAQs

How is the "mean squared error" calculated?

The "mean squared error" is calculated by taking the average of the squares of the differences between the predicted values and the actual values. This provides a measure of the overall accuracy of a model.

What does a low "mean squared error" indicate?

A low "mean squared error" indicates that the model's predictions are close to the actual values, suggesting high accuracy. However, it's important to consider the context and scale of the data when interpreting the MSE value.

How does "mean squared error" differ from "mean absolute error"?

While both measure prediction accuracy, "mean squared error" squares the errors, penalizing larger errors more heavily than "mean absolute error". This makes MSE more sensitive to outliers.

When should I use the root "mean squared error" (RMSE) instead of the "mean squared error" (MSE)?

RMSE is often preferred over MSE because it is in the same units as the original data, making it easier to interpret. RMSE is also more sensitive to outliers because it squares the errors before taking the square root.