In econometrics and other applications of multivariate time series analysis, a "'variance decomposition "'or "'forecast error variance decomposition "'( FEVD ) is used to aid in the interpretation of a vector autoregression ( VAR ) model once it has been fitted.
22.
Where q represents the Studentized range value, \ bar { X } _ A and \ bar { X } _ B are the largest and smallest sample means within a range, MSE is the error variance taken from the ANOVA table, and n is the sample size ( number of observations within a sample ).
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Methods for estimating this exponent from data can use type-2 regressions, such as major axis regression or reduced major axis regression, as these account for the variation in both variables, contrary to least squares regression, which does not account for error variance in the independent variable ( e . g ., log body mass ).
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Where df " t " is the degrees of freedom " n " 1 of the estimate of the population variance of the dependent variable, and df " e " is the degrees of freedom " n " " p " 1 of the estimate of the underlying population error variance.
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The more general formulation of effective degree of freedom would result in a more realistic estimate for, e . g ., the error variance ? 2, which in its turn scales the unknown parameters "'a posteriori " standard deviation; the degree of freedom will also affect the expansion factor necessary to produce an error ellipse for a given confidence level.
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Regardless of whether the error variance is tiny or huge, if the p-value for the slope is, say, . 0086, then if you ran such regressions from the same data generating process numerous times and if the null of no effect were true, then you would only get a result for the estimated slope so far away from zero 0.86 % of the time . talk ) 20 : 46, 26 February 2013 ( UTC)
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First, the squared residuals from the original model serve as a proxy for the variance of the error term at each observation . ( The error term is assumed to have a mean of zero, and the variance of a zero-mean random variable is just the expectation of its square . ) The independent variables in the auxiliary regression account for the possibility that the error variance depends on the values of the original regressors in some way ( linear or quadratic ).
