Skip to main content
$\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{{\not{\mid}}} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&}$

## 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: