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Section2.1Motivation 2

Our goal is to determine a demand function, a mathematical mode \(p = D(q)\) which best explains the relationship between the quantity sold in the national market \(q\) and the unit price we'd charge to sell that quantity, \(q\text{.}\)

To get there, take every data scientist's recommendation for a first step in any data project: make a scatter plot. Then, use technology to fit an equation to that data. For our project, we'll choose a quadratic equation (a polynomial of degree 2). That means we'll get a demand function equation that matches the template

\begin{align} y\amp = Ax^2 +Bx+C \amp \text{or, in context,}\tag{2.1.1}\\ p = D(q) \amp = Aq^2 + Bq+C\tag{2.1.2} \end{align}

The question is, what values of the coefficients \(A,B,C\) will give us an equation that best matches the data?

Do it with Excel:

Do it with Desmos: