4. Simulate quadratic data using the previous formulation with the exception that sigma_2 <- 4.0.

[If you did exercise 3, ignore those instructions, use y_2 <- 7.1 + 2*x_2 + 20*x_2*x_2 + err_2 as in the original simulation].

(i) Simulate the data and fit the straight-line and quadratic models.

(ii) Form a table of model selection information for three models (one mean, a straight-line, and a quadratic fit).

(iii) Perform the two likelihood ratio tests and state an overall conclusion.

(iv) Use AIC and BIC to select the best model. Do these results agree with each other and with the conclusion in (iii)?

(v) Plot both x versus y and the residuals from the straight linear. Do these plots support the conclusion drawn in part (iii)?