Consider the simple regression model ? = ?0 + ?1? + ?) In the following cases,...

Consider the simple regression model ? = ?0 + ?1? + ?)

In the following cases, verify if the ‘zero conditional mean’ and ‘homoscedasticity in errors’ assumptions are satisfied:

a. If ? = 9? where ?(?⁄?) = 0, ???(?⁄?) = ? 2

b. If ? = 5.6 + ? where ?(?⁄?) = 0, ???(?⁄?) = 3? 2

c. If ? = 3?? where ?(?⁄?) = 0, ???(?⁄?) = ? 2 2)

D. In which of the cases above are we likely to get biased estimates of ?1?

Solutions

Expert Solution

Zero Conditional Mean -The error u has an expected value of zero given any values of the independent variables.

Homoskedasticity - The conditional variance of the error term in a regression equation is constant for all values of the independent variables.

An estimator is unbiased if E(b) =
That’s just saying if the expected value of estimator equals the parameter, then it’s an unbiased estimator.

Unbiased estimate

Biased estimate

Unbiased estimate

(Homoskedasticity is not required for unbiasedness of estimator)

Rahul Sunny answered 1 year ago

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