Quadratic and Cubic Modeling

Section II: Quadratic and Cubic Modeling

        For section two, our group was assigned to use quadratic and cubic modeling to demonstrate which approach would provide closer predictions for equations dealing with the average wage earned from 1995 to 2012. First, we will find a polynomial equation of degree two that models the data, which will be labeled, Y1. Second, we will find a polynomial equation of degree three, which will be labeled, Y2. Thirdly, we will use both equations to find the value of four years after the starting year and interpret what this means. Fourthly, we will use both equations to find the value ten years after the starting year and see if the predictions are reasonable. Finally, we will graph both equation on a calculator and compare the two graphs.

Using the data set and scatter plot from section one, we first made an excel graph that models the data with a quadratic regression. Similarly, we made a second graph which also uses data and the scatter plot from section one, but uses a cubic regression in excel. Included in both of the graphs are a trendline to represent the regression equation chosen, the R2 value of each equation, and labeled axes. The following information and graphs demonstrate those equations.

Polynomial equation of degree
2 (quadratic regression): Y1

Y1 = -16.065*X^2 + 1395.2*X + 22331

Polynomial equation of degree

3 (cubic regression in Excel): Y2

Y2 = -0.0521*X^3 – 14.58*X^2 + 1383.6*X + 22351

[pic 1][pic 2]

[pic 3][pic 4]

Next, we used both equations, Y1 and Y2, to find the value four years after the starting year and interpreted what this mean in the real situation. In our data the actual figure for four years after the starting year is $29229.69. The “X” variable was replaced with a five to represent the change in time since from 1995 to 1999. For Y1, the equation came out to be $28905.38, while Y2 came out to be $28897.99.  Clearly, both equations are reasonably close to the data, but the quadratic regression better represents the actual data.  The following information demonstrates the use of both equations and how we came to that conclusion.