Bob is carrying out a cross-country analysis on the relationship between population and GDP. The following...

 

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Bob is carrying out a cross-country analysis on the relationship between population and GDP. The following regression is considered: GDP=0+√popu+as (popu) + u (3) where GDP and popu denote the GDP (in million USD) and population (in million) of a given country, respectively. To detect the presence of heteroskedasticity, Bob also ran the following auxiliary regression ²6 +5√popu+6; (popu) + v, (4) where û is the residual from regression (3). The following information was extracted from the ANOVA table associated with the auxiliary regression (4): Regression R²: 0.35 Number of observations: 50 Sum of squared residuals: 6.81 (a) [6 marks] Based on the auxiliary regression (4), carry out a test for heteroskedastic errors in regression (3) at the 5% significance level. Show all your steps. (b) [4 marks] Suppose the errors are heteroskedastic in regression (3). Comment on the accuracy of the OLS estimates of ag, an and a2 and their OLS standard. orrore (a) [6 marks] Based on the auxiliary regression (4), carry out a test for heteroskedastic errors in regression (3) at the 5% significance level. Show all your steps. (b) [4 marks] Suppose the errors are heteroskedastic in regression (3). Comment on the accuracy of the OLS estimates of a, a, and as and their OLS standard errors. (c) [6 marks] Bob thought that it is reasonable to assume that sd(u/popu= ax popu for the errors in regression (3). Suppose this assumption is correct. Explain how Bob can transform regression (3) so that the regression errors become homoskedastic. (d) [4 marks] Describe an alternative method which Bob may use to conduct valid statistical inference for regression (3). Bob is carrying out a cross-country analysis on the relationship between population and GDP. The following regression is considered: GDP=0+√popu+as (popu) + u (3) where GDP and popu denote the GDP (in million USD) and population (in million) of a given country, respectively. To detect the presence of heteroskedasticity, Bob also ran the following auxiliary regression ²6 +5√popu+6; (popu) + v, (4) where û is the residual from regression (3). The following information was extracted from the ANOVA table associated with the auxiliary regression (4): Regression R²: 0.35 Number of observations: 50 Sum of squared residuals: 6.81 (a) [6 marks] Based on the auxiliary regression (4), carry out a test for heteroskedastic errors in regression (3) at the 5% significance level. Show all your steps. (b) [4 marks] Suppose the errors are heteroskedastic in regression (3). Comment on the accuracy of the OLS estimates of ag, an and a2 and their OLS standard. orrore (a) [6 marks] Based on the auxiliary regression (4), carry out a test for heteroskedastic errors in regression (3) at the 5% significance level. Show all your steps. (b) [4 marks] Suppose the errors are heteroskedastic in regression (3). Comment on the accuracy of the OLS estimates of a, a, and as and their OLS standard errors. (c) [6 marks] Bob thought that it is reasonable to assume that sd(u/popu= ax popu for the errors in regression (3). Suppose this assumption is correct. Explain how Bob can transform regression (3) so that the regression errors become homoskedastic. (d) [4 marks] Describe an alternative method which Bob may use to conduct valid statistical inference for regression (3).

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a sHeteroskedasticity Inferences regarding the model parameters may be made incorrectly when heteroskedasticity is present in a regression model The O... View the full answer