What does negative percentage error indicate?

Answer 1

In a numerical analysis sense, it means you've made a mistake/forgotten to take the modulus, as the formula for error calculation involves taking modulus values:

Erel= |x-x*| / |x|, where x is the proper value, and x* an approximate value.

Percentage error is just the relative error (formula above) x100, so really if you calculate it correctly, its actually impossible to get a negative percentage error.

That aside, the only thing a negative error means, besides making a mistake, is that your approximation is larger/smaller than the real value, depending on which one you take away from, as it doesn't matter if you do x-x* or x*-x due to the modulus. The only thing that matters about any error value, is the size/number, which indicates by how much your approximation differs from the real value.