All questions pertain to the simple (two-variable) linear regression model for which the population
regression equation can be written in conventional notation as:
Yi = β0 + β1Xi + ui (1)
where Yi and Xi are observable variables, β0 and β1 are unknown (constant) regression coefficients, and ui
is an unobservable random error term. The Ordinary Least Squares (OLS) sample regression equation
corresponding to regression equation (1) is
ˆ ˆ
Yi = β0 + β1Xi + uˆi (i = 1, ..., N) (2)
ˆ
is the OLS estimator of the intercept coefficient β0
ˆ
where β0 , β1 is the OLS estimator of the
slope coefficient β1 , β
ˆ
1 is the OLS residual for the i-th sample observation, and N is sample size
(the number of observations in the sample).
10 Marks
1. Show that the OLS slope coefficient estimator βˆ
1 is a linear function of the Yi sample values.
Stating explicitly all required assumptions, prove that the OLS slope coefficient estimator βˆ
1 is an
unbiased estimator of the slope coefficient β1
(10 Marks)
2. Give a general definition of the F-distribution. Starting from this definition, derive the F-
statistic for the OLS slope coefficient estimator βˆ1. State all assumptions required for the
derivation.

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1 1 is an unb... View the full answer