Non-Ideal Gas Behavior I obtained measurements of temperature and pressure at various temperatures ($-10, 0, 20, \text{ and } 50^\circ \mathrm{C}$) and plotted them on a graph. Projecting backwards, the best-fit line predicts 0 pressure at significantly above $-273.15^\circ \mathrm{C}$(0 Kelvin). I am wondering why this is.

My understanding is that a true linear relation assumes "Ideal Gas Behavior", which is predicated on the false assumptions that molecules have no attraction for each other and that they take up no space. I know that at high/low temperatures and pressures the realities about volume and attraction begin to make a difference. But I don't understand how these account for my results.

The pressure for all measurements fell between $680$ and $820$ torr. My understanding is that that is not a significant amount of pressure. In terms of predicting pressures at lower temperatures, I understand that the less kinetic energy of the gas the more relevant the attractive forces are...but I would think that would lower the pressure which makes things worse--if the pressure actually falls faster and faster as temperature drops, then the predicted zero-pressure point would be even higher than the predicted values I got. I need it to be lower! 

I am under the (possibly incorrect) impression that both the realities of volume and attraction are supposed to be causing my incorrect prediction...but I don't understand how either does...

Thanks for any help!
There is little reality to such an extrapolation. Attaching much significance will just lead you astray. There are a number of real gas equations which purport to correct for this or that "problem" with the ideal gas equation. The greater truth is that the equations just add extra fitting coefficients which make the equation more accurate. Different equations will work for different gases in different ranges.