Examples of root-mean-square error in the following topics:
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- Root-mean-square (RMS) error, also known as RMS deviation, is a frequently used measure of the differences between values predicted by a model or an estimator and the values actually observed.
- Root-mean-square error serves to aggregate the magnitudes of the errors in predictions for various times into a single measure of predictive power.
- RMS error is the square root of mean squared error (MSE), which is a risk function corresponding to the expected value of the squared error loss or quadratic loss.
- MSE measures the average of the squares of the "errors. " The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator and its bias.
- RMS error is simply the square root of the resulting MSE quantity.
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- Bias leads to a sample mean that is either lower or higher than the true mean .
- The mean squared error (MSE) of $\hat { \theta }$ is defined as the expected value of the squared errors.
- In this case, high MSE means the average distance of the arrows from the bull's-eye is high, and low MSE means the average distance from the bull's-eye is low.
- This generalized error in the mean is the square root of the sample variance (treated as a population) times $\frac{1+(N-1)\rho}{(N-1)(1-\rho)}$.
- The $\rho = 0$ line is the more familiar standard error in the mean for samples that are uncorrelated.
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- It is therefore more useful to have a quantity that is the square root of the variance.
- Next, compute the average of these values, and take the square root:
- This quantity is the population standard deviation, and is equal to the square root of the variance.
- Using the uncorrected estimator (using $N$) yields lower mean squared error.
- We can obtain this by determining the standard deviation of the sampled mean, which is the standard deviation divided by the square root of the total amount of numbers in a data set:
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- In regression analysis, the term "standard error" is also used in the phrase standard error of the regression to mean the ordinary least squares estimate of the standard deviation of the underlying errors.
- As mentioned, the standard error of the mean (SEM) is the standard deviation of the sample-mean's estimate of a population mean.
- It can also be viewed as the standard deviation of the error in the sample mean relative to the true mean, since the sample mean is an unbiased estimator.
- SEM is usually estimated by the sample estimate of the population standard deviation (sample standard deviation) divided by the square root of the sample size (assuming statistical independence of the values in the sample):
- Paraphrase standard error, standard error of the mean, standard error correction and relative standard error.
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- The standard error of the mean is the standard deviation of the sample mean's estimate of a population mean.
- The standard error of the mean (i.e., standard error of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population.
- As mentioned, the standard error of the mean (SEM) is the standard deviation of the sample-mean's estimate of a population mean.
- It can also be viewed as the standard deviation of the error in the sample mean relative to the true mean, since the sample mean is an unbiased estimator.
- Generally, the SEM is the sample estimate of the population standard deviation (sample standard deviation) divided by the square root of the sample size:
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- The root-mean-square speed measures the average speed of particles in a gas, defined as $v_{rms}=\sqrt{\frac{3RT}{M}}$ .
- The root-mean-square speed is the measure of the speed of particles in a gas, defined as the square root of the average velocity-squared of the molecules in a gas.
- The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
- What is the root-mean-square speed for a sample of oxygen gas at 298 K?
- Recall the mathematical formulation of the root-mean-square velocity for a gas.
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- The root-mean-square, also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity, or set of numbers.
- Its name comes from its definition as the square root of the mean of the squares of the values.
- The root-mean-square is always greater than or equal to the average of the unsigned values.
- Physical scientists often use the term "root-mean-square" as a synonym for standard deviation when referring to the square root of the mean squared deviation of a signal from a given baseline or fit.
- $G$ is the geometric mean, $H$ is the harmonic mean, $Q$ is the quadratic mean (also known as root-mean-square).
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- The mean of the distribution of differences between sample means is equal to the difference between population means.
- which says that the mean of the distribution of differences between sample means is equal to the difference between population means.
- Recall that the standard error of a sampling distribution is the standard deviation of the sampling distribution, which is the square root of the above variance.
- The difference between means comes out to be 10, and the standard error comes out to be 3.317.
- Standard error equals the square root of (60 / 10) + (70 / 14) = 3.317.
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- Expected value and standard error can provide useful information about the data recorded in an experiment.
- The standard error is the standard deviation of the sampling distribution of a statistic.
- The standard error of the mean (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples of a given size drawn from the population.
- The standard error of the sum can be calculated by the square root of number of draws multiplied by the standard deviation of the box: $\sqrt{25} \cdot \text{SD of box} = 5\cdot 1.17 = 5.8$.
- Solve for the standard error of a sum and the expected value of a random variable
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- There is no such value such that when squared it results in a negative value; we therefore classify roots of negative numbers as "imaginary."
- What does it mean, then, if the value under the radical is negative, such as in $\displaystyle \sqrt{-1}$?
- This means that there is no real value of $x$ that would make $x^2 =-1$ a true statement.
- Specifically, the imaginary number, $i$, is defined as the square root of -1: thus, $i=\sqrt{-1}$.
- We can write the square root of any negative number in terms of $i$.