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Variance analysis, in budgeting or management accounting in general, is a tool of budgetary control and performance evaluation, assessing any variances between the budgeted, planned, or standard amount, and the actual amount realized. Variance analysis can be carried out for both costs and revenues.
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
Firstly, while the sample variance (using Bessel's correction) is an unbiased estimator of the population variance, its square root, the sample standard deviation, is a biased estimate of the population standard deviation; because the square root is a concave function, the bias is downward, by Jensen's inequality.
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
which is an unbiased estimator of the variance of the mean in terms of the observed sample variance and known quantities. If the autocorrelations are identically zero, this expression reduces to the well-known result for the variance of the mean for independent data. The effect of the expectation operator in these expressions is that the ...
Performance-based budgeting is the practice of developing budgets based on the relationship between program funding levels and expected results from that program. The performance-based budgeting process is a tool that program administrators use to manage budget outlays more cost-efficiently and effectively.
where R 2 is the coefficient of determination and VAR err and VAR tot are the variance of the residuals and the sample variance of the dependent variable. SS err (the sum of squared predictions errors, equivalently the residual sum of squares ), SS tot (the total sum of squares ), and SS reg (the sum of squares of the regression, equivalently ...
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