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Definition and basic properties. The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
For a value that is sampled with an unbiased normally distributed error, ... , leading the following formula for standard error: (¯) = + ...
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The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.
where represents the standard deviation of the function , represents the standard deviation of , represents the standard deviation of , and so forth.. It is important to note that this formula is based on the linear characteristics of the gradient of and therefore it is a good estimation for the standard deviation of as long as ,,, … are small enough.
This t-statistic can be interpreted as "the number of standard errors away from the regression line." Regressions. In regression analysis, the distinction between errors and residuals is subtle and important, and leads to the concept of studentized residuals. Given an unobservable function that relates the independent variable to the dependent ...
It is a variant of MAPE in which the mean absolute percent errors is treated as a weighted arithmetic mean. Most commonly the absolute percent errors are weighted by the actuals (e.g. in case of sales forecasting, errors are weighted by sales volume).. Effectively, this overcomes the 'infinite error' issue. Its formula is:
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