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Assume that a bioengineer wants to develop a mathematical model to predict the weight of the brain of mammals based on the weight of their bodies. She will be using the data at mammwmmmrmmm WWW In this data le, the rst column is an index or identier for each of the 62 mammals, the second number is brain weight in kilograms, and the third number is body weight in kilograms. I. Using Minitab, t the following regression models to the data: tY = Br: + [3: X aY = [10+ [51X + Bax: c. (My) = 50+ parse) d. Ln'r' = 39+ B: Ln): 2. According to each of these models, what would be the weight of the brain of a particular pig weighting 300 pounds? ._ For each of these models, use Minitalr to construct a 95% prediction interval for the weight of the brain of a particular pig weighting 300 pounds. Explain why some of these intervals predict negative values for the weight of the brain. aFor each of these models, if the weight of a given mammal increases by one kilogram, by how much is the weight of its brain is expected to change? Justify your answers. 3. Develop a linear regression model that is superior to all the models listed in [l]. .. Show your model equation and show the standard Minitab output for this model. aConstruct a normal probability plot of the residuals of this model. i. For this model, use Minitab to construct a 95% prediction interval for the weight of the brain of a particular pig weighting 300 pounds. .tFor this model, if the weight of a given mammal increases by one kilogram, by how much is the weight of its brain is expected to change? Justify your answers. 4. Complete the summary table on the following page; based on this summary, how can you justify that your model is the best? Make sure that your table does not exceed one page. \fY = Bo+ BIX Y =Bo+BIX+BzX3|(1/y)=ButBi(1/Vx)| LnY =Bo+BiLnX Your model Root MSE RZ Adjusted R Interval for the brain weight of a pig. Proportion of the variability of the mammal's brain weights that is explained by the model. Comments on the normality assumption of the residuals Comments on the residuals' constant- variance assumption. Comments on the independence of the residuals