Question

[tex]4. The following sample moment for = [1, 1, 2, 3
\ \textless \ br /\ \textgreater \ ] were computed from 100 observations
\ \textless \ br /\ \textgreater \ produced using a random number generator:
\ \textless \ br /\ \textgreater \
\ \textless \ br /\ \textgreater \ ′ = [
\ \textless \ br /\ \textgreater \ 100 123
\ \textless \ br /\ \textgreater \ 123 252
\ \textless \ br /\ \textgreater \ 96 109
\ \textless \ br /\ \textgreater \ 125 189
\ \textless \ br /\ \textgreater \ 96 125
\ \textless \ br /\ \textgreater \ 109 189
\ \textless \ br /\ \textgreater \ 167 146
\ \textless \ br /\ \textgreater \ 146 168
\ \textless \ br /\ \textgreater \ ],
\ \textless \ br /\ \textgreater \ ′ = [
\ \textless \ br /\ \textgreater \ 460
\ \textless \ br /\ \textgreater \ 810
\ \textless \ br /\ \textgreater \ 615
\ \textless \ br /\ \textgreater \ 712
\ \textless \ br /\ \textgreater \ ].
\ \textless \ br /\ \textgreater \ ′ = 3924.
\ \textless \ br /\ \textgreater \ The true model underlying these data is = 1 + 2 + 3 + .
\ \textless \ br /\ \textgreater \ a) Compute the OLS coefficients in the regression of on a constant, 1, 2 and 3.
\ \textless \ br /\ \textgreater \ b) Examine whether the estimated model can be considered as a good representative of true
\ \textless \ br /\ \textgreater \ model? [Hint: Test for significance of the coefficients using appropriate null hypothesis.]
\ \textless \ br /\ \textgreater \ c) Compute coefficient of determination for the mode[/tex]
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