Covering chapter 10 in BVD3 this week, we have been spending some time straightening data. I'm sure I've read over it again and again, but perhaps I am missing the big picture with this...why are we straightening data? Does it come down to being able to understand the residual plots better when the scatterplot creating them is linear?
A few follow up questions prompted by one of my students...
* Using the example in the teacher's guide on US pop vs. year, the model needed ends up being a quadratic. That said, when we straighten the data and get a linear model for (year, sqrt(pop)), we get a different r^2 value than if we just generate a quadratic regression for (year, pop). Why? * Further, if we use our model that we found for sqrt(pop) and square both sides, it doesn't match the model the calculator generates for the quadratic regression. Why? Is it in how the calculator generates the regression (how is this done)? * If it's important for the students to straighten the data during their analysis, why are there so many regression options available to us on the calculators? If it's sound mathematics to straighten, these options seem like unnecessary distractors.
Thanks for the guidance from a newbie trying to learn the ropes.