Reflections 4: "Vaccination"

In this week's experiment we investigated the correlation between volume and pressure. Volume is our independent variable and pressure is our dependent variable. Through our experiment we mainly focused on graphing our data points and choosing which model best represents the data: linear, proportional, or inverse proportional model. 

For a linear model we can mathematically represent this change as Y=mx+b. This means that the equation has an intercept otherwise meaning that at 0, y is already has constant value. Over time, or over increments of x, y will increase linearly by a value determined by the slope m. This can be represented in a straight line. In our experiment, we tried modeling Pressure v. volume through this formula, however the RMSE is 24.49kPs (for both adjusted and unadjusted volume). The RMSE is pretty large so there might be a better model that might represent the data better.

To represent our data better we used an inversely proportional model to get a more accurate prediction of the trend of the nature of pressure over volume. A formula that can represent this is y=a/x. This formula represent a proportionality between y and x such that if you were to double x, you would half y (hence the inverse proportionality). This model fit our data much better with an RMSE of 1.545kPs of the adjusted volume (6.128kPs for unadjusted). Therefore our inversely proportional model was a better fit for describing and predicting missed data of pressure over that volume.

For a proportional model, we can thing of y=Ax. What this model essentially means is that whatever you do to x it will directly correlate with y. For example, if you double x, y also gets doubled. In our experiment, we were able to use this model on the Pressure v. 1/ adjusted volume. If you look at the RMSE, they are the same as the inversely proportional model. That is because essentially what we did is we inverted the volume and graphed it in a proportional linear model. So essentially what you are graphing is P = a*1/V or x=1/V --> P=Ax. 

If we look at the graphs, on thing to note is that the unadjusted volume graph has a volume of 0mL and it tells us that at 0 volume there is 0 pressure. However, as we know zero volume does not evidently exist in nature or is yet observed (there are theories of zero volumes such as at the creation of the universe or theoretical thermodynamics). Therefore it is important that we adjusted our volume. In the syringe that we used, if we fully pushed out all the air from it, there is still a 0.8 mL of volume at the tip of the syringe which contains some volume in this enclosed system. By adjusting the volume, we have been able to receive a more accurate model of the system.