Meteorologists, financial analysts, and sociologists are just three examples of the many people who try to make predictions by using models. To do this, they collect the relevant data and plot it. Then they ask, “Is there a linear relationship in the data?” That is, do the data points fall on or near a line, such as in the figure below? Maybe the data increases then decreases and so could best be modeled by a quadratic function?

Meteorologists, financial analysts, and sociologists are just three examples of the many people who try to make predictions by using models.
To do this, they collect the relevant data and plot it. Then they ask, “Is there a linear relationship in the data?” That is, do the data points fall on or near a line, such as in the figure below? Maybe the data increases then decreases and so could best be modeled by a quadratic function?
Oftentimes, neither a line nor quadratic function is a good fit for the data, and so a higher order polynomial function is needed (as in the tiger population example illustrated in the overview of this module). This is one of the main applications of polynomials, to use them to find a curve that best fits the data, in what is called the “least squares” sense. This line of best fit is also called a regression line.
The model obtained can be used not only to make predictions but also to illustrate behavior between the independent and dependent variables. While the idea is essentially the same no matter what order of polynomial is used, in this activity, we will focus on the simplest case, the linear function, y = mx + b, which is a 1st -degree polynomial.