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Applied Econometrics BE5103 Tutorial 1 Q1 a) In the simple OLS regression estimation it is not possible that all actual independent Yi values lie above the estimated regression line. This is because OLS minimizes SUM ê2 , the residual , ê, is the difference between the actual Yi and the predicted Yi and has zero mean. In other words, OLS calculates the slope coefficient so that the difference between the predicted Yi and actual Yi is minimized. The OLS estimates of the βs: Are unbiased – the βs are centred around the true population values of βs Have minimum variance – the distribution of the β estimates around the true βs are as tight as possible Are consistent – as the sample size(n) approaches infinity, the estimated βs…show more content…
The closer that R2 is to 1, the better the fit meaning the group of independent variable could explain better what happens to the dependent variable. R2 may not be the best estimate at times because if we add another independent variable to the model the R2 would increase but it does not say necessary the model becomes better. Therefore some would prefer to look at the adjusted R2 as it would only increase if the variable used are relevant to the model. Addition of independent variable to the model would not result in an increase in adjusted R2 if the variables does not improve the model. We can then look at the T-Statistics to see how individual variable can explain the dependent variable, by doing a T-test comparing it with the Critical value T. By doing a 10%,5% or 1% test. We could also look at the model as a whole by looking at the F-Statistics and doing a F-test. With Eviews regression we can simply look at the P-Values to see at which level of confidence we can reject the Hypothesis, From the above 3models, it seems that R2 is highest in model 3, and the adjusted R2 is also the highest in the model which tells us that the independent variable are better in explaining the dependent variable. Model 3 is a better regression model. Income per person is a better independent variable rather than income and population as a variable. Again this goes in line with economic theory, as income per person increases it would result increase
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