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
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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
Again, this method only uses one variable but shows us the best variable to use. If we use multiple regression models we would be able to get a more accurate result.
In this case, the independent variable is the gender and the dependent variable is the
15 In testing the hypotheses: H0 β1 ’ 0: vs. H1: β 1 ≠ 0 , the following statistics are available: n = 10, b0 = 1.8, b1 = 2.45, and Sb1= 1.20. The value of the test statistic is:
* Independent variable coefficient – This is the measured effect the independent variables have on the dependent variable. This is the main output of the regression analysis.
In the Private Sector, there are many choices to be made by Business managers regarding which “projects” to borrow for and which “projects” to invest in. These choices often contain a great deal of ______________________ as well as the potential for benefits (profits).
and report your results in the usual form. What is the (approx) predicted percentage increase in salary given one more year as a CEO?
The business literature involving human capital shows that education influences an individual’s annual income. Combined, these may influence family size. With this in mind, what should the real estate builder be particularly concerned with when analyzing the multiple regression model?
"There are several different kinds of relationships between variables. Before drawing a conclusion, you should first understand how one variable changes with the other. This means you need to establish how the variables are related - is the relationship linear or quadratic or inverse or logarithmic or something else" ("Relationship Between Variables ", n.d)
In the above table second column reports the OLS estimates. Dummy $Urban$ has positive coefficient, which indicates that child labor on an average work 0.4 hour more in
There are two hypotheses that were tested in relation to the overall fit of the model:
Computer Exercises C1.2 Use the data in BWGHT.RAW to answer this question. . summ Variable | Obs Mean Std. Dev.
Yi: Gross national income per capita (measured in US dollar). It can be defined as the sum of value added by all resident producers plus any product taxes (less subsidies) not included in the valuation of output plus net receipts of primary income (compensation of employees and property income) from abroad. In this model, we want to observe if gross national income per capita has a significant effect on total private domestic consumption as a percentage of GDP. If gross national income per capita increases, total private domestic consumption as a percentage of GDP is expected to increase because a rise in income encourages households to spend and consume more. Thus, β3 is expected to be positive.
For model II, the hypothesis that the coefficient is zero is rejected at the 5% significance level only for the three of the independent variables (log(Def), log(Educ), and log(Healt)).