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Unformatted text preview: STAT5044: Regression and ANOVA, Fall 2009 Exam 1 on Nov 5 Solution Please make sure to specify all of your notations in each problem GOOD LUCK! 1 Problem# 1. • (a) Write down a simple linear regression model. Specify each term as random or fixed. Specify each term as unknown term or known term. y i = β + β 1 x i + ε i , i = 1 ,..., n where E ( ε i ) = 0, Var ( ε i ) = 0, and cov ( ε i , ε j ) = – y i : random and known – ε i : random and unknown. – x i : fixed and known – β , β 1 , σ 2 : unknown and fixed • (b) In simple linear regression, what assumptions do we have? How do you check each assumption? What tests and plots are you going to use for checking assumption? – Linearity: use R 2 , scatter plot – Randomness/independence: Run, Dwtest, scatter plot – Constant variance: BF, BP, Residual, Abs residual, scatter plot – Normality: Shapiro, KS, Anderson-Darling, Normal QQ • (b) After I fit the simple linear regression, I obtain the residual plot and normal QQ plot which are shown in Figures 1-2. Using these plots, do you think what assumption is violated? Why? If so, how can you revise the model? Residual plot shows “v” shaped pattern. This means nonconstant. Normal QQ plots shows that points are far from the 45 line. So normality assumption is violated. We can revise the model by using box cox transformation of y. We can also use bootstrap for nonnormality....
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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.
- Fall '11
- Linear Regression