PS5_solution

# PS5_solution - 1 Problem Set 5 Solutions by Edson Severnini...

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1 Problem Set 5 – Solutions by Edson Severnini 1. Using the GRETL prepackaged data set Ramathan data 7.14, Homicide across States, complete the following. Variables are those as defined by the GRETL descriptive label. a. Estimate and report OLS parameter estimates for the equation Mr i = α + β 1 exec i + β 2 south i + β 3 ue i + β 5 capital i + β 6 pcy i + ε i Present your estimated coefficients and t-statistics in a table. Answer : Model 1: OLS estimates using the 51 observations 1-51 Dependent variable: mr Coefficient Std. Error t-ratio p-value const -35.008 9.41774 -3.7172 0.00056 *** exec -0.145459 0.494027 -0.2944 0.76978 south 9.76824 2.89803 3.3706 0.00155 *** ue 1.27828 0.86191 1.4831 0.14502 capital 2.44452 3.39044 0.7210 0.47464 pcy 1.92023 0.521169 3.6845 0.00061 *** Mean dependent var 8.727451 S.D. dependent var 10.71758 Sum squared resid 3403.760 S.E. of regression 8.697075 R-squared 0.407353 Adjusted R-squared 0.341504 F(5, 45) 6.186115 P-value(F) 0.000192 Log-likelihood -179.4865 Akaike criterion 370.9731 Schwarz criterion 382.5640 Hannan-Quinn 375.4023 b. Plot the fitted values for mr on exec, mr on ue, and mr on pcy. Answer :

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2 mr on exec: -10 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 14 16 mr exec Actual and fitted mr versus exec fitted actual mr on ue: -10 0 10 20 30 40 50 60 70 80 3 4 5 6 7 8 9 10 11 ue Actual and fitted mr versus ue fitted actual
3 mr on pcy: -10 0 10 20 30 40 50 60 70 80 12 14 16 18 20 22 mr pcy Actual and fitted mr versus pcy fitted actual c. Plot the errors for errors on exec, errors on ue, and errors on pcy. Answer :

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4 residuals on exec: -20 -10 0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 residual exec Regression residuals (= observed - fitted mr) residuals on ue: -20 -10 0 10 20 30 40 50 3 4 5 6 7 8 9 10 11 ue Regression residuals (= observed - fitted mr)
residuals on pcy: -20 -10 0 10 20 30 40 50 12 14 16 18 20 22 residual pcy Regression residuals (= observed - fitted mr) d. Do these errors on exec, ue, and pcy indicate homo or hetroskecastic error terms? Answer : The graphs of residuals on exec and on pcy indicate homoskedasticity, because the variance of the residuals seems to be constant all over exec- and pcy-axis, respectively. However, the graph of residuals on ue indicates heteroskedasticity, because the variance of the residuals seems to vary over the values of ue (larger for bigger values of ue). e. Propose and implement a test for homoskedastic error terms. What is the name of the test, and are OLS errors homoskedastic or hetroskedastic from your test? You can use GRETL to implement the test. Answer : White test: White's test for heteroskedasticity OLS estimates using the 51 observations 1-51 Dependent variable: uhat^2 Omitted due to exact collinearity: X2_X5 X3_X5 coefficient std. error t-ratio p-value ---------------------------------------------------------- const 4535.81 791.379 5.732 1.92e-06 *** exec 348.784 396.466 0.8797 0.3852 south -2077.69 291.572 -7.126 3.10e-08 *** ue -333.321 128.870

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PS5_solution - 1 Problem Set 5 Solutions by Edson Severnini...

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