QUESTION 4 We model energy use as follows: Intres.RS = Bo + B.Lnypcpenn + B2Lnypcpenn2+ B3LnGasprice + B.LnAnnualprecipo + BsTempGoldest + BoTempWarmest + B, FossilFuelRentsGDP + BgLnPop + B.LnLand + D_incomegroups + u The variables are defined as follows: Lntpes.Rc = log of total primary energy consumption per capita (ktoe) Lypsreon=log of GDP per capita (USD) Lnypcpenn2 = square of log of GDP per capita (USD) In gasprics - log of pump price for gasoline (USD/liter) LnAnnualprecir= log of annual precipitation (mm) Temp. soldest - average temperature for the coldest month in a year (in C) Temp. Warmest average temperature for the warmest month in a year (in C) ffrents Fossil Fuel Rents % of GDP) La Pop = log of population in millions) Inland -log of land area (in km2) LIncomegroun = refers to income groups "1","2" and "3", low, mid and high income countries. **Log" always refers to natural logs or "In" here. The output is as follows: Linear regression Number of obs F(11, 119) Prob > F R-squared Root MSE 131 143.13 0.0000 0.8941 .36402 Intpes_pc Coef. Robust Std. Err. t P>t (95% Conf. Intervall lnypcpenn inypcpenn2 In_gasprice temp_coldest tenp_warnest In annualprecip ffrents Inpop Inland _I inconegro_2 _Iinconegro_3 -cons -.9599562 .0954567 -.2392021 -.01857 .0166677 .006395 .0028204 -.0469675 .0546541 .1032733 -.0828519 0.303336 .4732335 0256192 .0566569 .605238 .016009 0539954 0028546 .638339 0328958 .2283648 .1007342 2.40965 3.73 -4.22 -3.55 1.04 0.12 0.99 -1.23 1.66 0.45 -0.82 3.45 0.045 0.000 0.000 0.001 0.300 0.906 0.325 0.223 0.999 0.652 0.412 0.001 -1.897006 .8447282 -.3513885 -.0289417 -.0150318 -1005213 -.0028319 - 1228807 -. 0104820 -.3489118 -.2823156 3.531989 - 0229066 . 1461852 -. 1270157 -.0881983 .0483671 . 1133114 .0084728 .6289456 .119791 .5554584 .1166118 13.07460 1) Interpret the constant and its p-value. 2) Interpret the coefficient on the gas price and carry out a t-test to determine the significance of the coefficient 3) Interpret the coefficient on annual precipitation and its p-value. 9 marks 4) Interpret the R-squared. 2 marks 5) The above model belongs to the class of nonlinear equations. Calculate the turning point of the nonlinear relationship. 3 marks 6) Is this a U-shaped or inverted U-shaped relationship? 1 marks 7) Please describe if MLR 4 is likely to hold or not? 3 marks (Total: 18 marks) QUESTION 4 We model energy use as follows: Intres.RS = Bo + B.Lnypcpenn + B2Lnypcpenn2+ B3LnGasprice + B.LnAnnualprecipo + BsTempGoldest + BoTempWarmest + B, FossilFuelRentsGDP + BgLnPop + B.LnLand + D_incomegroups + u The variables are defined as follows: Lntpes.Rc = log of total primary energy consumption per capita (ktoe) Lypsreon=log of GDP per capita (USD) Lnypcpenn2 = square of log of GDP per capita (USD) In gasprics - log of pump price for gasoline (USD/liter) LnAnnualprecir= log of annual precipitation (mm) Temp. soldest - average temperature for the coldest month in a year (in C) Temp. Warmest average temperature for the warmest month in a year (in C) ffrents Fossil Fuel Rents % of GDP) La Pop = log of population in millions) Inland -log of land area (in km2) LIncomegroun = refers to income groups "1","2" and "3", low, mid and high income countries. **Log" always refers to natural logs or "In" here. The output is as follows: Linear regression Number of obs F(11, 119) Prob > F R-squared Root MSE 131 143.13 0.0000 0.8941 .36402 Intpes_pc Coef. Robust Std. Err. t P>t (95% Conf. Intervall lnypcpenn inypcpenn2 In_gasprice temp_coldest tenp_warnest In annualprecip ffrents Inpop Inland _I inconegro_2 _Iinconegro_3 -cons -.9599562 .0954567 -.2392021 -.01857 .0166677 .006395 .0028204 -.0469675 .0546541 .1032733 -.0828519 0.303336 .4732335 0256192 .0566569 .605238 .016009 0539954 0028546 .638339 0328958 .2283648 .1007342 2.40965 3.73 -4.22 -3.55 1.04 0.12 0.99 -1.23 1.66 0.45 -0.82 3.45 0.045 0.000 0.000 0.001 0.300 0.906 0.325 0.223 0.999 0.652 0.412 0.001 -1.897006 .8447282 -.3513885 -.0289417 -.0150318 -1005213 -.0028319 - 1228807 -. 0104820 -.3489118 -.2823156 3.531989 - 0229066 . 1461852 -. 1270157 -.0881983 .0483671 . 1133114 .0084728 .6289456 .119791 .5554584 .1166118 13.07460 1) Interpret the constant and its p-value. 2) Interpret the coefficient on the gas price and carry out a t-test to determine the significance of the coefficient 3) Interpret the coefficient on annual precipitation and its p-value. 9 marks 4) Interpret the R-squared. 2 marks 5) The above model belongs to the class of nonlinear equations. Calculate the turning point of the nonlinear relationship. 3 marks 6) Is this a U-shaped or inverted U-shaped relationship? 1 marks 7) Please describe if MLR 4 is likely to hold or not? 3 marks (Total: 18 marks)
