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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 ...
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g. The relevant equation [ 1 ] for an idealized simple pendulum is, approximately,
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 ...
The following example illustrates this by applying the second SMAPE formula: Over-forecasting: A t = 100 and F t = 110 give SMAPE = 4.76% Under-forecasting: A t = 100 and F t = 90 give SMAPE = 5.26%.
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 ...
For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters.
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Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics , which uses experimental tools to probe these phenomena.