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Bonus Questions how that for a set of design points such as x| , x2, design points are different then Σ(x-x) >0 , en f at least two of the (3 points) Q2). Show that for the linear regression model y-A, +B x + ε, the point estimate β, s an unbiased estimator for Po (5 points) Derive the upper one-sided 1000-α)% confidence interval for B. (3 points) Q3). Q4). Suppose that you are drawing a sample of random observations y,y ..., y , from a population that is normally distributed with a mean-μ and variance-σ 2 . Derive the two-sided likelihood ratio test for testing Ho : μ Ho versus H, : μ where μο. (5 points) Q5). Show that in the context of a linear regression model y-A, + B x + ε , i-l i-1 4 points) is| is|

Question 3 with all work please. This is an upper-sided confidence interval for slope of a regression line, not a two-sided confidence interval.

Answer 1

Q3

(β

follow t-distribution with n-2 degree of freedom

P(T < t) = 1-0

t -ta,n-2

hence

< ta,n-2 se(A )

BBtan-2* se(31)

upper one sided confidence interval

co, 01

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