Consider a simple linear model: yi = β1 + β2xi + εi, where εi ∼ N...

Consider a simple linear model:

yi = β1 + β2xi + εi, where εi ∼ N (0, σ2)

Derive the maximum likelihood estimators for β1 and β2. Are these the same as the estimators obtained from ordinary least squares? Is there a reason to prefer ordinary least squares or maximum likelihood in this case?

Expert Solution

orchestra answered 1 year ago

Consider a simple linear model Yi = β1 + β2Xi + ui . Suppose that we...

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1. Consider the linear regression model for a random sample of size n: yi = β0...

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Consider the model: yi = βxi + ei, i = 1,...,n where E(ei) = 0 and...

Consider the model: yi = βxi + ei, i = 1,...,n where E(ei) = 0 and Variance(ei) = σ2 and ei(s) are non-correlated errors. a) Obtain the minimum-square estimator for β and propose an unbiased estimator for σ2. b) Specify the approximate distribution of the β estimator. c) Specify an approximate confidence interval for the parameter β with confidence coefficient γ, 0 < γ < 1.

Consider the simple linear regression: Yi = β0 + β1Xi + ui whereYi and Xi...

Consider the simple linear regression: Yi = β0 + β1Xi + ui where Yi and Xi are random variables, β0 and β1 are population intercept and slope parameters, respectively, ui is the error term. Suppose the estimated regression equation is given by: Yˆ i = βˆ 0 + βˆ 1Xi where βˆ 0 and βˆ 1 are OLS estimates for β0 and β1. Define residuals ˆui as: uˆi = Yi − Yˆ i Show that: (a) (2 pts.) Pn i=1...

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