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Both the "compatibility" function STDEVP and the "consistency" function STDEV.P in Excel 2010 return the 0.5 population standard deviation for the given set of values. However, numerical inaccuracy still can be shown using this example by extending the existing figure to include 10 15 , whereupon the erroneous standard deviation found by Excel ...
Stability is a measure of the sensitivity to rounding errors of a given numerical procedure; by contrast, the condition number of a function for a given problem indicates the inherent sensitivity of the function to small perturbations in its input and is independent of the implementation used to solve the problem. [5] [6]
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
A seventh order polynomial function was fit to the training data. In the right column, the function is tested on data sampled from the underlying joint probability distribution of x and y. In the top row, the function is fit on a sample dataset of 10 datapoints. In the bottom row, the function is fit on a sample dataset of 100 datapoints.
Random variations are not predictable but they do tend to follow some rules, and those rules are usually summarized by a mathematical construct called a probability density function (PDF). This function, in turn, has a few parameters that are very useful in describing the variation of the observed measurements.
If the data exhibit a trend, the regression model is likely incorrect; for example, the true function may be a quadratic or higher order polynomial. If they are random, or have no trend, but "fan out" - they exhibit a phenomenon called heteroscedasticity. If all of the residuals are equal, or do not fan out, they exhibit homoscedasticity.
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