# stat331-pracsol1 - STAT 331 SYDE 334 Applied Linear Models...

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STAT 331 - SYDE 334: Applied Linear ModelsMidterm 1: Practice Question Solutionsversion: 2015-02-10·23:52:50Q1.Consider the simple linear regression modelyi|xiind∼ N(β0+β1xi, σ2),i= 1, . . . , n.a. Write down expressionsˆβ0andˆβ1for the MLEs ofβ0andβ1.
n,ˆσc. Suppose thatn= 50 andSxx= 180,¯x= 4.8,Sxy= 353,nsummationdisplayi=1xiyi= 3378.Calculate the values of the MLEsˆβ0andˆβ1.
Q2.Consider the simple linear regression modelyi|xiind∼ N(β0+β1xi, σ2),i= 1, . . . , n.Suppose thatn= 10 andˆβ1= 5,ˆβ0=2,Sxx= 16,
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Midterm 1: Practice Question SolutionsValue ofqαsuch thatP(T < qα) =αTt(ν)α= 0.9α= 0.925α= 0.95α= 0.975ν= 81.41.591.862.31ν= 101.371.561.812.23ν= 121.361.541.782.18a. Calculate a two-sided 95% confidence interval forβ1.
b. Calculate an upper 95% prediction bound fory0=β0+β1x0+ǫ0at the value ofx0= 5.