Vaccination Investigation.

     One thing that I'm definitely going to be an expert by the end of this STP is reading graphs! 

So for this experiment, we had to figure out the best type of model that fit our data. We talked about three different models; linear, proportional, and inverse proportional.

A linear model is basically a line graph, where if positive, as the x value goes up, the y value also goes up. These type of models usually have a y-intercept and are mathematically written as y=mx+b. For our experiments, the y value is our dependent variable, the x is our independent variable, m is the slope of the model, and b is the y-intercept. So whenever the independent variable increases, so does the dependent variable plus whatever that initial amount. Sometimes, for our experiments, we really want to only observe the relationship between our dependent and our independent variable, and not worry about that initial amount. That's where a proportional model comes in.

A proportional model, much like a linear model, also has it's dependent variable increase as the independent variable increases. But as the name implies, that increase is much more proportional. The equation looks more like y=kx in which k is a constant. If the value of the independent variable is doubled, then the value of the dependent variable also doubles. There is no initial value to add into the proportion, so it is better at accurately predicting data.

An inverse proportional model is much the same as a proportional model except that if the independent variable increases, then the dependent variable decreases and vice versa . What's important though is that the constant remains.

For our "Vaccination Investigation" we looked into the relationship between volume and pressure using a syringe, and this is what our data looks like.

 

We can see that the relationship between pressure and volume is an inverse. As the values of our independent variable (the volume inside the syringe) increases, the dependent variable (pressure inside the syringe) decreases. The linear model is there just to compare and help decide which model fits the data better. With this inverse model though, it would be really difficult to be able to predict anything about the relationship between the volume and pressure, which is why we created a proportional model.

 

 

By making a inversely proportional model, we can now have a constant and really see how in average as the inverse of the volume increases, the pressure increases. This also shows us that it is impossible to have a inverse volume of 0, as 0 does not have an inverse value. 

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