1. (a) You are given a simple linear regression model Yi =B + Bxi +8, i=1,...,n,...

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1. (a) You are given a simple linear regression model Yi =B₁ + B₂xi +8₁, i=1,...,n, where B₁ and ₂ are unknown parameters, & are the random error terms and n is the sample size. Let b₁ and b₂ be the best linear unbiased estimators of P₁ and ₂, respec- tively. Let rxy be the correlation coefficient, let R² be the coefficient of determination and let y be the fitted values of y. (i) Prove that r = R². Give appropriate details. (ii) Prove that ²2=2. Give appropriate details. (1) [5] [5] 1. (a) You are given a simple linear regression model Yi =B₁ + B₂xi +8₁, i=1,...,n, where B₁ and ₂ are unknown parameters, & are the random error terms and n is the sample size. Let b₁ and b₂ be the best linear unbiased estimators of P₁ and ₂, respec- tively. Let rxy be the correlation coefficient, let R² be the coefficient of determination and let y be the fitted values of y. (i) Prove that r = R². Give appropriate details. (ii) Prove that ²2=2. Give appropriate details. (1) [5] [5]