Linear Unbiased Estimator Assignment PDF

Added on - 31 May 2021

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735263Question 1a)According to Gauss Markow Theorem, OLS is the Best Linear Unbiased Estimator when thevariance is the least among the forecasted values or calculated values of Regressions and theactual values of the co-efficients of regressions.(Wooldridge, 2015)The Gauss Markow is also, true , only if the assumptions that the regression is linear and errors arehomoskedascistic.(Wooldridge, 2015)b)Statistically, Null Hypothesis is that Beta values are equal and all are equal to zero. Thestatistical interpretation is that the Co-efficients of Regression of the log of lot size, the numberof bathrooms, the dummy variable that the house has 3 bedrooms, dummby variables that thehouse has 4 bedrooms, and dummy variable that the house has 5 bedrooms is zero. This impliesthat the variable are not regressors of the independent variable or they have a negligible impactof changes in the dependent variable, here lprice is higher.(Lambert, 2013)In terms of economics, this indicates that the increase in house price is autonomous. Thisimplies that the house price and an increase in house price is exogenous and is not related to the lotsize, the number of bedrooms or bathrooms. The supply is either artificially fixed or completelyinelastic to these factors.c)If the null hypothesis is true, thenβ2=β3=β4= 0, then (lprice)=β0+β1llotsize +β2bathrooms+β3bd2+β4bd3+β5bd4 +u =δ(lprice)=β0+β1llotsize +β2bathrooms+uThe partial regression is not equal to the full equation. Hence, the null hypothesis is rejected.The size of the bedroom has an effect on the price of the house.d)R-Square measures the Goodness of Fit of regression or how close the estimated values are tothe actual values. The goodness of It is computed as{n∑xy – (x)(y)}/√{(nx2– (x)2}{(ny2– (y)2}(Wooldridge, 2015)The R-Square and the Adjusted R-Square for the second model are higher, implying, this model is abetter fit than the first one. Hence, based on the goodness of the fit, the second model is preferred.e)The results for variable bd2 were possibly eliminated due to the presence of collinearity orsimilarity.(Lamber, 2013)f)The new equation will be:(lprice)=β0+β1llotsize +β2(good)+uThe co-efficient will indicate the extent to which being located in a good area would be aregressor of house price.Question 2a)i) In the given equation, RSS stands for residual Sum of Squares or the Sum of Squared Errors ofPrediction. It is the sum of squared residuals. An Equation is homoskedastic (there is noheteroskedascity) if the RSS is within a range for all values i.e for observations 1- 100. However,
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