Stat 136 Le 1 Samplex 001
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S136-LE1-001Statistics 135 Introduction to Regression Analysis
Sample First Long Exam
1.
a. If the regression equation is given by i o i i iY X ,2~ (0, )
i N i . Derive the
least-squares estimator of o and i .
b. If the regression equation is given by i i iY X , 2~ (0, )
i N i . Derive the least-
squares estimator of .
2. In the model, i o iY , i = 1,2,…,n
a. What is the least-squares estimator of o ?
b. What is the fitted or estimated value of Yi, i = 1,2,…,n?
c. Will the sum of the residuals equals zero in this model? Support your answer.
3. Prove the Gauss-Markov Theorem.
4. Show that:
a. E(MSE) =2
b.
E(MSR) = 2 +' '
1
X C X
p
, where p = number of parameters
5. Given the model Y X , where2~ ( , ) N , 0 . Solve for:
a. Least-squares estimator of .
b. ˆ( ) E
c. ˆ( )Var
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