In Chapter 1 you first made sense of your data by determining what the results from each small test market could tell you about your product's demand in the large nationwide market. The next step, then, is to go beyond your short list of data points to model the overall trend those data points suggest. After all, chances are that the "best" price point to set for your product will not exactly be one of the prices you tested, but something in between. But how do we read in between our data points?
Proposition2.0.1Construct a function that models national market demand
Use technology to find a quadratic function \(p = D(q)\) that best fits your national market demand data. This demand function will model the relationship between all possible quantities \(q\) that could sell in the market and the unit price \(p\) at which that many could be sold.
The key quantitative method in this process is regression, the statistical process of varying the parameters in a formula so as to minimize the mean-square error inherent in how that formula's predicted data points differ from your actual data points. In other words, it is the process of finding a "curve of best fit" of a given type for a set of data points. The statistical details of regression analysis are beyond the scope of this course, but the result provides the crucial link between real-world data and idealized mathematical models we can analyze using the tools of algebra and calculus.