The correct answer is option 4: the square root of the absolute temperature. The average speed of molecules in a gas is directly proportional to the square root of the absolute temperature.

Let`s look at the other options to understand why they are not correct:

Option 1: Temperature - While temperature does affect the average speed of gas molecules, it is not directly proportional. The relationship between temperature and average speed is actually expressed as the square root of the temperature.

Option 2: Square of the temperature - This option is incorrect because the relationship between average speed and temperature is not directly proportional to the square of the temperature. It is proportional to the square root of the temperature.

Option 3: Pressure - The average speed of molecules in a gas is actually inversely proportional to the square root of the pressure. So, pressure does affect the average speed, but it does not have a direct proportionality relationship.

To summarize, the correct answer is the square root of the absolute temperature.