Ordinary least square estimation in regression analysis
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OLS estimates and coefficients. See attached file for full problem description.
I need help solving question #2. Please provide me with detailed explanations for #2.
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Solution Summary
Estimation of regression coefficients, Durbin Watson Statistic, Serial correlation in Ordinary least square estimation.
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Please see the attached file.
The following regression was fitted by OLS , using 32 annual observations on time series data:
Yt = 4.52 - 0.62 X1t, +0.93 X2t +0.61 X3t +0.16 X 4t Adjusted R2 = 0.638
S.E (1.23) (0.28) (0.38) (0.21) (0.12) DW=0.61
Note that Y = quantity of wheat exports from Canada
X1 = Price of Canadian wheat in international market
X2 = Quantity of Canadian wheat harvested
X3 = GNP per capita in countries importing Canadian wheat
X4 = price of barley in world market.
(a) Test at 5% level of significance the hypothesis that, all else equal, the coefficient on GNP per capita is less than 1.
Ans.
Here the null hypothesis can be written as
Vs
The test statistics is given by t =
where b is the regression coefficient, se(b) is the standard error of the regression coefficient, N is the number of subjects, and k is the number of predictor variables. The resulting t is on N - k - 1 degrees of freedom.
Here given that
b3 = 0.61
se(b3) ...
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