Step 1: Write the resistance formula to check each claim against it. \[ R = \rho \frac{l}{A} \]
Step 2: Test the claims about length and area.
Since $R$ is directly proportional to length $l$, resistance clearly does depend on length, ruling out the first option, and since $R$ is inversely proportional to the area $A$, a thicker wire, having a larger area, actually offers less resistance, not more, ruling out the second option. Resistance also depends on the ratio $l/A$, not their product, so the last option is wrong too.
Step 3: Look at the term $\rho$ left in the formula.
The resistivity $\rho$ is a constant that depends purely on the material the wire is made of, copper and iron, for instance, have very different resistivities even in wires of identical shape and size.
Step 4: State the correct statement.
Since $\rho$, and hence resistance, changes from material to material, resistance genuinely does depend on the nature of the material.
\[ \boxed{\text{Resistance depends on the nature of the material}} \]