Solutions_to_Assignment_5

# Solutions_to_Assignment_5 - Stat 332/322 Short Solutions to...

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Stat 332/322 Short Solutions to Assignment 5 1. (a) ˆ μ ( y ) ratio = ˆ θμ ( x ) = 2 . 70, where ˆ θ = ˆ μ ( y ) / ˆ μ ( x ). The estimated variance of the cor- responding estimator is d V ar μ ( y ) ratio ) = (1 - n/N σ 2 /n = 0 . 0034 where ˆ σ 2 = i s ( y i - ˆ θx i ) 2 / ( n - 1) = 0 . 037. 1. (b) ﬁt a linear model Y i = α + β ( x i - ¯ x ) + R i , then we have ˆ α = 3 . 2 and ˆ β = 1 . 02. Then the regression estimate is ˆ μ ( y ) reg = ˆ α + ˆ β * ( μ ( x ) - ¯ x ) = 3 . 2 + 1 . 02 * (2 . 43 - 2 . 88) = 2 . 74 and the estimated variance is d V ar μ ( y ) reg ) = (1 - n/N ) * ˆ σ 2 /n = 0 . 0021, where ˆ σ 2 = i s ( y i - ¯ y - ˆ β * ( x i - ¯ x )) 2 / ( n - 1) = 0 . 023. 1. (c) For the particular data we have here, the sample size is a bit of too small, and both ratio and regression estimators can be unreliable. If we pass this issue, then the general guideline in choosing between ratio and regression estimator is to look at the scatter plot: if a ﬁtted regression line has a close-to-zero intercept, then ratio estimator is preferred, due to its simplicity; otherwise the regression estimator should be used. The regression estimator

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## This note was uploaded on 01/12/2012 for the course STAT 332 taught by Professor Xu(sunny)wang during the Fall '09 term at Waterloo.

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Solutions_to_Assignment_5 - Stat 332/322 Short Solutions to...

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