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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 ...
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.
x erf x 1 − erf x; 0: 0: 1: 0.02: 0.022 564 575: 0.977 435 425: 0.04: 0.045 111 106: 0.954 888 894: 0.06: 0.067 621 594: 0.932 378 406: 0.08: 0.090 078 126: 0.909 ...
For a value that is sampled with an unbiased normally distributed error, ... The following expressions can be used to calculate the upper and lower 95% confidence ...
One can then also calculate the mean square of the model by dividing the sum of squares of the model minus the degrees of freedom, which is just the number of parameters. Then the F value can be calculated by dividing the mean square of the model by the mean square of the error, and we can then determine significance (which is why you want the ...
where the average values (bars) and estimated standard deviations s are shown, as are the respective sample sizes. In principle, by using very large n the RE of the estimated g could be driven down to an arbitrarily small value.
It is defined as chi-square per degree of freedom: [8] [9] [10] [11]: 85 [12] [13] [14] [15] =, where the chi-squared is a weighted sum of squared deviations: = with ...