Question

The temperature coefficient of resistance for carbon at 0oC is -0.0048/oC. What is the significance of the minus sign?

Answer 1

This means that the standard temperature at which the carbon resistance is equal to the standard resistance of 0 degrees when the temperature increases, the resistance drops due to the minus sign

Everyone knows that 

$R=R_0\times(1+\alpha\times t);\\$

Therefore, if the tcr is negative, then as the temperature increases, the resistance decreases, i.e.

$R\lt R_0;\\$