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3008 Q - STAT3008 Applied Regression Analysis(2011-2012 1st...

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STAT3008 Applied Regression Analysis (2011-2012 1 st Semester) Revision on Mid-term Examination Exercises: Question 1 1 2 1 2 1 2 ( , ) 1.5 3.2 0.5 1.1 E Y X X X X X X = + + For the above fitted model, one unit increase in 1 X will lead to an increase of 3.2 units in Y . Is that true? Why? Question 2 In a medical study, several measurements are taken for each patient, including the length of right arm( 1 X ) and the length of left leg( 2 X ). Benjamin claimed that including both 1 X and 2 X in the regression model as the predictors can get the greatest amount of information from the patients. Comment. Question 3 Suppose we know the true model: 1 1 2 2 Y X X e β β = + + However, we fit the following model: 1 1 Y X e β = For both models, assume 2 ( ) 0, ( ) E e Var e I σ = . (a) Find 1 ( ) E β . (b) Find 1 ( ) Var β . (c) Find ( ) E Y . Question 4 Consider the following regression model, 2 , ( ) 0, ( ) i i i i i y x e E e Var e β σ =+ = = a) Find the least square estimate β for β .
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