Consider the following data:

x 1 4 5 7 8 12 11 14 19 20 y 1 54 125 324 512 5,530 5,331 5,740 7,058 7,945

a. Construct a scatter plot of the data. Determine the order of the polynomial that is represented by this data.

b. Obtain an estimate of the model identified in part a.

c. Conduct a test of hypothesis to determine if a thirdorder, as opposed to a first-order, polynomial is a better representation of the relationship between y and x. Use a significance level of 0.05 and the p-value approach.