Complete the question to practice graphing data and determining the polynomial regression model for the data.

Click here to check your answer.

      1. Find the quadratic regression that best models the number of diagonals of a polygon with n sides.
Number of sides (n)
3
4
5
6
Number of diagonals

0

2

5

9

L1 = x-values =

L2 = y-values =

Quadratic regression:

Examples 1 and 2 state explicitly the type of regression model to use. In most problems, this information is not given. Typically, you must plot the given data, view the scatter plot, and use your knowledge of polynomials to select the regression model that best fits the data points. Use a linear function when the points appear to lie in a straight line. If the scatter plot is curved but has no inflection point, a quadratic function might be used. If the scatter plot has an inflection point or two turning points, a cubic model might be appropriate.

Ideally, you want to reason beyond it fits well to choose a model for real life data. However, when no basis exists for choosing a model, look for a balance between fit and simplicity. For polynomials, try to choose a model with the lowest possible degree that has a reasonably good fit. Also, use polynomial functions for models only when they apply. (In Units 6, 7, and 8, you will see data for which a polynomial function is inappropriate.)