Consider the simple linear regression model where i 's are independent N(0, 2 ) random variables Therefore, Y i is a normal random variable with mean 0 1 x i and variance 2 Moreover, Y i 's are independent As usual, we have the observed data pairs (x 1 , y 1 ), (x 2 , y 2 ), , (x n , y n ) from whi...

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Consider the simple linear regression model where i 's are independent N(0, 2 ) random variables.

Question:

Consider the simple linear regression model Y = Bo + Bixi + i,

where ϵ_i's are independent N(0,σ²) random variables. Therefore, Y_i is a normal random variable with mean β₀ +β₁x_i and variance σ². Moreover, Y_i's are independent. As usual, we have the observed data pairs (x₁, y₁), (x₂, y₂), ⋯, (x_n, y_n) from which we would like to estimate β₀ and β₁. In this chapter, we found the following estimators where Sxx = Sxy = Sxy B = 8/7/2012 S xx Bo =Y B2. n (x - x), i=1 n i=1 (x - x)(Yi - Y).