1. Plant scientists have developed varieties of corn that have increased amounts of the essential amino acid lysine. In a test of the protein quality of this corn, an experimental group of 20 one-day-old male chicks was fed a ration containing the new corn. A control group of another 20 chicks received a ration that was identical except that it contained normal corn. The weight gains (in grams) after 20 days are in the data set chicks.data. Determine whether the mean chick weight gain increases when fed the new high lysine corn.
2. Your benevolent professor despises the cold. This is why he moved from the mountains in Virginia to the balmy clime of Texas. Several times during the winter of 2009/2010, it snowed in Tyler, Texas. Al Gore notwithstanding, this should be taken as a call to all responsible, thinking, caring men and women to increase the rate of global warming, before your benevolent professor freezes to death. Consider the data set carmileage.data (from the EPA) relating miles per gallon (MPG) of passenger automobiles to the passenger cabin volume (VOL), the engine horsepower (HP), the top speed (SP), and the vehicle weight (WT).
   1. Fit the model with MPG as the y and the rest of the variables as predictors. What is the interpretataion for the slope for the HP variable?
   2. Suppose GM decides to create a new model, the Bureaucrat, with VOL = 150, HP = 40, SP = 70, and WT = 31. Using the model above give a 95% confidence interval for the MPG for the GM Bureaucrat.
   3. Are there any outliers according to this model? If so, discuss which and why you think they are outliers.
   4. Construct an added variable plot for SP.
   5. Construct a partial plus residual plot for HP.
   6. Are there any influential points? If so, discuss which and how and why you think they are influential?
   7. Are there any high leverage points? If so, discuss which and why you think they are high leverage points.
   8. Build appropriate model(s) and discuss the effects of each of these x-variables on vehicle miles per gallon. Be alert for any transformations of the variables that might be appropriate here.
3. Consider the data set quarterback.data giving quarterback salaries and total team salaries for NFL teams. Let TOTAL be the y variable. Is there a different relationship between QB (quarterback salary) and TOTAL (total team salary) for NFC and AFC teams?