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The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator.
The use of the MAPE as a loss function for regression analysis is feasible both on a practical point of view and on a theoretical ... actual value), given by ...
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 ...
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 percent yield is a comparison between the actual yield—which is the weight of the intended product of a chemical reaction in a laboratory setting—and the theoretical yield—the measurement of pure intended isolated product, based on the chemical equation of a flawless chemical reaction, [1] and is defined as,
A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one. [6]For example, if a house is worth $100,000 today and the year after its value goes up to $110,000, the percentage change of its value can be expressed as = = %.
In physics, a mass balance, also called a material balance, is an application of conservation of mass [1] to the analysis of physical systems.By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique.
Consider the equation of roasting lead(II) sulfide (PbS) in oxygen (O 2) to produce lead(II) oxide (PbO) and sulfur dioxide (SO 2): 2 PbS + 3 O 2 → 2 PbO + 2 SO 2. To determine the theoretical yield of lead(II) oxide if 200.0 g of lead(II) sulfide and 200.0 g of oxygen are heated in an open container: