ECON 2206 assignment 2
ECON2206 ASSIGNMENT 1
Question 1
MLR 1 (Linear in Parameters) – From observation of equation (2) we can see that the model in the population can be written in the form y = β0 + β1X1 + …+ βkXk + u. In the model β1, β2 …βk are the unknown parameters of interest and u is an unobserved random error. log(TCi) = β1+ β2log(Qi) + β3log(pi1) + β4log(pi2) + β5log(pi3) + ui (2)
MLR 2 (Random Sampling) – This assumption assumes a random samples of n observations. We deduce that it would be infeasible to collect the entire population of observations and thus one would assume that random sampling was applied to obtain a random sample of n observations.
MLR 3 (No Perfect Collinearity) – This assumption requires that in the sample, none of the independent variables is constant, and there are no exact linear relationships among the independent variables. To determine if this is satisfied we must look at relationships between all the independent variables (output, plabor, pfuel, pkap). For MLR 3 to be violated independent variables cannot be perfectly correlated. We can tell that two independent variables are perfectly correlated when one variable is a constant multiple of another. This clearly does not exist in our equation (2). Also there are no same explanatory variables that are measured in different units in our equation. Also in our equation (2) we have at least k+1 observations. Thus we can conclude that MLR 3 stands.
MLR 4 (Zero Conditional Mean) – This assumption requires that the error u has an expected value of 0 given any values of the independent variables. From the given information we can deduce the following things: that there is no misspecification of the functional form, we have no omitted variable bias, there is no measurement error in the explanatory values, Xj is not correlated with the error term. Thus MLR 4 holds.
Question 2
i) Units of measurement – Total Cost: Million US$, Output: billion KwH, wage: $/hr, price of fuel: cent/btu, price capital:
Question 1
MLR 1 (Linear in Parameters) – From observation of equation (2) we can see that the model in the population can be written in the form y = β0 + β1X1 + …+ βkXk + u. In the model β1, β2 …βk are the unknown parameters of interest and u is an unobserved random error. log(TCi) = β1+ β2log(Qi) + β3log(pi1) + β4log(pi2) + β5log(pi3) + ui (2)
MLR 2 (Random Sampling) – This assumption assumes a random samples of n observations. We deduce that it would be infeasible to collect the entire population of observations and thus one would assume that random sampling was applied to obtain a random sample of n observations.
MLR 3 (No Perfect Collinearity) – This assumption requires that in the sample, none of the independent variables is constant, and there are no exact linear relationships among the independent variables. To determine if this is satisfied we must look at relationships between all the independent variables (output, plabor, pfuel, pkap). For MLR 3 to be violated independent variables cannot be perfectly correlated. We can tell that two independent variables are perfectly correlated when one variable is a constant multiple of another. This clearly does not exist in our equation (2). Also there are no same explanatory variables that are measured in different units in our equation. Also in our equation (2) we have at least k+1 observations. Thus we can conclude that MLR 3 stands.
MLR 4 (Zero Conditional Mean) – This assumption requires that the error u has an expected value of 0 given any values of the independent variables. From the given information we can deduce the following things: that there is no misspecification of the functional form, we have no omitted variable bias, there is no measurement error in the explanatory values, Xj is not correlated with the error term. Thus MLR 4 holds.
Question 2
i) Units of measurement – Total Cost: Million US$, Output: billion KwH, wage: $/hr, price of fuel: cent/btu, price capital: