Free Essay On Regression Graphics And The Durban Watson Test
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This assignment will be performed with the barro.csv and the top incomes data.csv files that we have used before in other assignments.
As the Barro dataset consists of cross-sectional data, I do not expect to find autocorrelation in the sense that autocorrelation means serial correlation of a variable with itself over time, and thus it could only be seen in prospective data. Another name for autocorrelation is serial correlation (because it involves time). However, it is possible to find spatial autocorrelation in cross-sectional data, which is similar concept, but applied to regions geographically correlated (Cliff and Ord, 268). This concept means that an event that affects economic activity in one region might have repercussions in other areas because they have economic ties.
A regression consisting of political instability (pol2) and public consumption / GDP (gcony2) as independent variables, and annual change per capita GDP (y.net) was performed. Furthermore, a Durban Watson test was run, with H0: there is no correlation among residuals and H1: the residuals are autocorrelated, and resulted in a DW statistic of 1.6311 and a p-value of 0.0082, which rejects the null hypothesis. Therefore, there is spatial autocorrelation between the variables (see Figure 1 for a plot of the residuals in this model).
Figure 1. Residuals plot from the first regression model (y.net~pol2+gcony2).
In the top income data, it is expected to find autocorrelation in the sense of serial correlation, because it consists of prospective data. Therefore, a regression model was performed to predict Top1PercentE as dependent variable from Year as independent variable. The results show a DW statistic of 0.1584 and a p-value of < 2.2e-16, which allows us to reject the null hypothesis of independence of residuals. Hence, there is also autocorrelation in the residuals of these variables (see Figure 2 for a plot of the residuals in this model).
Figure 2. Residuals plot from the second regression model (Top1PercentE~Year).
This is how the first graphic should look like, but with your name instead of “Name”:
This is how the second graphic should look like, but with your name instead of “Name”:
Cliff, A., & Ord, K. (1972). Testing for spatial autocorrelation among regression residuals. Geographical Analysis, 4(3), 267-284.
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