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Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
The RMSD of predicted values ^ for times t of a regression's dependent variable, with variables observed over T times, is computed for T different predictions as the square root of the mean of the squares of the deviations:
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of one parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size ...
The general regression model with n observations and k explanators, the first of which is a constant unit vector whose coefficient is the regression intercept, is = + where y is an n × 1 vector of dependent variable observations, each column of the n × k matrix X is a vector of observations on one of the k explanators, is a k × 1 vector of true coefficients, and e is an n× 1 vector of the ...
Peak values can be calculated from RMS values from the above formula, which implies V P = V RMS × √ 2, assuming the source is a pure sine wave. Thus the peak value of the mains voltage in the USA is about 120 × √ 2, or about 170 volts. The peak-to-peak voltage, being double this, is about 340 volts.
If, for example, the out-of-sample mean squared error, also known as the mean squared prediction error, is substantially higher than the in-sample mean square error, this is a sign of deficiency in the model. A development in medical statistics is the use of out-of-sample cross validation techniques in meta-analysis.
When a dynamical system fluctuates about some well-defined average position, the RMSD from the average over time can be referred to as the RMSF or root mean square fluctuation. The size of this fluctuation can be measured, for example using Mössbauer spectroscopy or nuclear magnetic resonance , and can provide important physical information.
This page was last edited on 25 March 2005, at 21:16 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...