all error value are suppose to be prefixed by a +/- symbol to show that they can be either + or -. As everybody understands this they just forget about it.
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No, the absolute error cannot be negative. Absolute error is defined as the absolute value of the difference between the measured value and the true value, which ensures that it is always non-negative. It is calculated as |measured value - true value|, and since absolute values are always positive or zero, the absolute error itself will also never be negative.
Because that is the definition of absolute values
There is no answer - it is an error: negative numbers do not have logarithms. The log if a number tells to what power the (positive) base must be raised to get the number. Raising any positive number to any power will never result in a negative number, so it is an error to try and take the log of a negative number.
An exponential function can have negative y-values. However, a real-world exponential decay model will never have negative values. Think of it this way... If you divide a positive number by 2 (or take half of it) and then divide that next number by 2, you will never reach or go below 0. For Example: 20, 10, 5, 2.5, 1.25, 0.625, 0.3125, etc. (Each number is half of the number before it.)
No, it's not a probability since it's not set in terms of ratio of two values, such that the second value is greater than the first. For instance: 1 to 2 or 1 / 2. Also, probability is never negative.