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II year Management

Econometrics Final Project

I took the data set about the wealth of nations and in particular the dependence between the population and total wealth of the country (nation).

Source: http://data.worldbank.org/data-catalog/wealth-of-nations

2011 WSB-NLU

Professor: Jacek Leskow

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- 1. Aleksey Narko II year Management Econometrics Final Project I took the data set about the wealth of nations and in particular the dependence between the population and total wealth of the country (nation). Source: http://data.worldbank.org/data-catalog/wealth-of-nations Step 1: Anova analysis A) Anova The first factor (independent variable) is the income(low, lower middle, upper middle,high) P value is less than 5 % so we reject the null hypothese at 5 % level. That means that Income is different among different groups. Hypotheses of One-Way Anova Analysis: Reject Ho H1: not all the Income means are the same H1 : Not all μ i are the same Conclusion: Not all the Income means are the same among different groups. B) Checking homoskedasticity Hartley Statistic H= (max{s12…sk2})/(min{s12…sk2}) In my case H = 28775,7 which seems to be bad
- 2. Bartlett test My p-value is much less than 5%. After these two tests I can draw a conclusion that I have a very serious problem with heteroskedasticity. I don’t need to use Anova. Step 2: Regression A) Regression analysis • R2=7,1% and it is very low, which means that the dividing line between small and big Total Wealth is not well coincided with the line between the big and small population of the countries. • The standard error is equal to 1, 94E+13 of total wealth which is quiet big, compared with the smallest amount of population among the countries. • Slope=36787-unitary increase by one mean in the population gives us 36787 dollars in Total Wealth more • Y =3,34E+12 (intercept) +36787*X (population) • T stat=Slope/Standard error=3,28
- 3. • P value=0,0013< 5%-reject, there is a significance between cylinders and displacement. • [14618; 58956] The first number is the least in total wealth we can get by increase in one unit of population(man), and the second is the maximum we can get by increase in one unit. • F test : H0: R2=0- reject, model significant Ha: R2>0 • After sorting the studentized residuals I got two King Kongs: 71 and 135, which are >3 • After eliminating these King Kongs we get R2=12,2% which means that our result improved a little bit more than for 5% as previous R2 before elimination was 7,1%,which means that we need to make another elimination process. Regression Statistics Multiple R 0,349702 R Square 0,122292 Adjusted R Square 0,115932 Standard Error 6,7E+12 Observations 140 • After sorting the studentized residuals I got 4 King Kongs: 69,47,133,51,which are bigger than 3. 69 47 133 51 • 3,889923198 4,856760879 5,488564929 6,213019657 After eliminating these King Kongs we get R2=22,1% which means that our result improved for more than 5% as previous R2 before elimination was 12,2%,which means that we need to make another elimination process. Regression Statistics Multiple R 0,47065427
- 4. R Square Adjusted R Square Standard Error Observations • After sorting the studentized residuals I got 3 King Kongs: 24, 110 and 129 which are bigger than 3. 24 110 129 • 0,221515442 0,215705856 4,46825E+12 136 3,448344982 3,480936339 8,403463852 After eliminating these King Kongs we get R2=23,4% which means that our result improved for less than 5% as previous R2 before elimination was 22,1%, which means that at this time elimination process didn’t improve the model a lot and we can stop it. Regression Statistics Multiple R 0,488095929 R Square 0,238237636 Adjusted R Square 0,232422656 Standard Error 4,31091E+12 Observations 133 Significance F 2,53083E-09 • Our P value is equal to 2,53E-09 and it means that it is not significant, which means that the pour fit of the model is definitely not due to the presence of outliers. B) Checking Normality Here we don’t have any problems, because our sample size is much bigger than 30. C) Checking Homoscedasticity In our case we got Heteroskedasticity, because the growing number of residuals means growing spread of percentage.
- 5. Fact: Total wealth study produces simple regression model with heteroskedastic outliers. This is the most likely reason for the poor fit of the model. D) Checking autocorrelation lag ACF 1 2 PACF 0,009747857 0,085140888 0,009747857 0,085244009 1.96/sqrt(n) -1.96/sqrt(n) 0,169953554 -0,169953554 0,169953554 -0,169953554 My ACF is between U and L, which means that I don’t have autocorrelation. STEP 3: Final Interpretation All these results that I got tell me that even with the problems of heteroscedasticity and these King Kongs my model is significant and because of the lack of the problem with autocorrelation there is a powerful relation between the Population and Total Wealth of the country.
- 6. Fact: Total wealth study produces simple regression model with heteroskedastic outliers. This is the most likely reason for the poor fit of the model. D) Checking autocorrelation lag ACF 1 2 PACF 0,009747857 0,085140888 0,009747857 0,085244009 1.96/sqrt(n) -1.96/sqrt(n) 0,169953554 -0,169953554 0,169953554 -0,169953554 My ACF is between U and L, which means that I don’t have autocorrelation. STEP 3: Final Interpretation All these results that I got tell me that even with the problems of heteroscedasticity and these King Kongs my model is significant and because of the lack of the problem with autocorrelation there is a powerful relation between the Population and Total Wealth of the country.

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