For x between 0 and 100, suppose the normal linear model holds with E(y) = 45 + 0.1x + 0.0005x2 + 0.0000005x3 + 0.0000000005x4

+0.0000000000005x5 and ???? = 10.0. Randomly generate 25 observations from the model, with x having a uniform distribution between 0 and 100. Fit the simple model E(y) = ????0 + ????1x and the “correct” model E(y) = ????0 + ????1x + ⋯ + ????5x5. Construct plots, showing the data, the true relationship, and the model fits. For each model, summarize the quality of the fit by the mean of | ̂????i − ????i|. Summarize, and explain what this exercise illustrates about model parsimony.