What tells you that the relation is best fit by a linear model? Use principles about what kinds of functions have consistency in which types of rates of change?

Question

Suppose a set of data about the spread (in hundreds of acres) of a food-borne bacteria (after t weeks) in lettuce has the following percentage rates of change: 0.9%, 1.3%, 1.1%, 1.0%, 1.3%, 1.0%; and the following average rates of change: 2.9, 2.4, 3.7, 3.1, 3.6, 3.2. Based only on the information given, and without doing any calculations, what type of model would you use? Why? (NOTE THAT the information given is not the actual data set. I have calculated the two types of rate of change for you. You should NOT BE CALCULATING ANYTHING!) 

Answer 1

Hi Sutton,

Firstly, I will say I might have misunderstood your intentions with the question, but if it is how I interpreted it, it's a great question.

The rate of change seems to follow a sin^2(x)+1.15 (ish) pattern. The average rate of change looks to me somewhat like the definite integral of this derivative equation (albeit with an outlier), which would be required when calculating the average.

At least, when modeling it, that would be the first pairing I would try (just by inspection).

BR,

Omar