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where A t is the actual value and F t is the forecast value. The absolute difference between A t and F t is divided by half the sum of absolute values of the actual value A t and the forecast value F t. The value of this calculation is summed for every fitted point t and divided again by the number of fitted points n.
where is the actual value of the quantity being forecast, is the forecast, and is the number of different times for which the variable is forecast. Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result, the formula can be used as a ...
Excel's storage of numbers in binary format also affects its accuracy. [3] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number
This little-known but serious issue can be overcome by using an accuracy measure based on the logarithm of the accuracy ratio (the ratio of the predicted to actual value), given by (). This approach leads to superior statistical properties and also leads to predictions which can be interpreted in terms of the geometric mean.
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 statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...
Best rational approximants for π (green circle), e (blue diamond), ϕ (pink oblong), (√3)/2 (grey hexagon), 1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values (black dashes)
In this case, no variation in Y can be accounted for, and the FVU then has its maximum value of 1. More generally, the FVU will be 1 if the explanatory variables X tell us nothing about Y in the sense that the predicted values of Y do not covary with Y. But as prediction gets better and the MSE can be reduced, the FVU goes down.