hw1fall11 - i is following normal distribution. What ar the...

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STAT5044: Regression and ANOVA Homework #1 Problem# 1. Refer to regression model. Assume that X = 0 is within the scope of the model. What is the implication for the regression function if β 0 = 0 so that the model is Y i = β 1 X i + ± i ? How would the regression function plot on a graph? Problem#2. Refer to regression model. What is the implication for the regression function if β 1 = 0 so that the model is Y i = β 0 + ± i ? How would the regression function plot on a graph? Problem# 3. Consider the following model: Y i = βX i + ± i where i = 1 ,...,n , ± i are i.i.d with mean 0, variance σ 2 . (a) What estimator would you use to estimate β and σ 2 ?. Please Justify your answer (b) Denote by ˆ β , the estimator of β you suggest in (a). Are ˆ β and r 1 uncorrelated, where r 1 = Y 1 - X 1 ˆ β ?. Are they independent of each other ? (c) Denote by ˆ σ 2 , the estimator of σ 2 you suggest in (a). Are ˆ β and ˆ σ 2 independent of each other ? (d) Let us assume that
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Unformatted text preview: i is following normal distribution. What ar the distribution of and 2 ? Why? Problem# 4. Consider the following model: Y i = + i where i = 1 ,...,n , i are i.i.d with mean 0, variance 2 . (a) What estimator would you use to estimate and 2 ? Why? (b) Are these estimators independent each other? Why? (c) Let us assume that i is following normal distribution. What ar the distribution of and 2 ? Why? Problem# 5. Y 1 ,Y 2 ,...,Y n are iid Normal with mean and variance 2 . Let Y and S 2 denote the sample mean and the sample variance of Y s , respectively. (a) Show that Y and S 2 are independent (b) Under what condition(s) that n i =1 a i Y i and n i =1 b i Y i are independent and why?. 1...
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This note was uploaded on 01/02/2012 for the course STAT 5044` taught by Professor Staff during the Fall '11 term at Virginia Tech.

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