EQ: How do I use data to model higher degree polynomials?
The above situation is a typical problem where a linear or quadratic regression model would not be as sufficient as a higher degree polynomial. In this example, a cubic model is the most appropriate with regards to shape and the R^2 value. If the problem includes data, plot the points in your calculator (use STAT, EDIT, L1 and L2) and then take a look at the scatterplot. Based on what the data is doing (is it just rising or is it rising and then falling?), decide whether linear, quadratic, cubic, or quartic is most appropriate. Make sure to turn on your diagnostics so that you can verify that it is a good fit using the R^2 value.
Work on these problems using your calculators and whiteboards. Check your answers by looking at the solutions below.
Unfortunately, few problems will include data. Other problems will simply present situations and you will have to decide the best way to approach those problems. Typical examples could include volume of figures and velocity. Try to do the following examples on your own, checking your solutions at the end.