hw1fall11sol - STAT5044: Regression and ANOVA Homework #1:...

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STAT5044: Regression and ANOVA Homework #1: solution 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? The implication of the model is that the regression line always goes through the origin. The model only depends on slope. 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? This means that the line is horizontal line passing (0,¯ y ). 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 ˆ β = x i y i x 2 i ˆ σ 2 = i ( y i - ˆ βx i ) 2 n - 1 = Y t ( I - H ) Y n - 1 where, H = X ( X t X ) - 1 X t
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hw1fall11sol - STAT5044: Regression and ANOVA Homework #1:...

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