As you add to the degree of a polynomial function that models data, the value of the coefficient of determination, R2, will increase. But increasing the degree of a polynomial doesn't necessarily significantly improve how well a function fits data. The formula below adjusts for the increase in accuracy that comes from increasing the degree of a polynomial function. The adjusted value of R2, R2A, allows you to judge whether the model has a significant improvement. The variable n represents the number of data points, and p represents the number of parameters in the model. There are two parameters in a linear, exponential, or power model (a and b), there are three in a quadratic model (a, b, and c), four in a cubic model (a, b, c, and d), and so on.

Consider these data, the depth of water in a leaking bucket at various times.

Find several polynomial equations to model these data, state the value of R2 that your calculator gives for each model, and use the formula to find R2A for each model. What is the best model to describe these data?

R2 = 1-0-R*)() Time (s) 1020 30 40 50 60 70 80 90 Depth (cm) 15 12.5 10.5 8.5 6.5 5.03.5 2.5 1.5 1.5