Please help
QUESTION 2 We want model energy use as follows: Lntpes pc = Bo + BiLnypcpenn + B2Lnypcpenn2+ B3LnGasprice + B4LnAnnualprecip+ B5TempColdest + B6 TempWarmest + Byffrents + BgLnPop + B.LnLand + D_incomegroups +u The variables are defined as follows: Lntpes pc = log of total primary energy consumption per capita (ktoe) Lnypcpenn =log of GDP per capita (USD) Lnypcpenn2 = square of log of GDP per capita (USD) Ln gasprice = log of pump price for gasoline (USD/liter) LnAnnualprecip= log of annual precipitation (mm) Temp coldest = 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) Ln Pop = log of population (in millions) Ln Land = log of land area (in km2) I Incomegroup = refers to income groups "1","2" and 3, low, mid and high income countries. *"'Log" always refers to natural logs or "In" here. Linear regression Number of obs F(11, 119) Prob > F R-squared Root MSE 131 143.13 0.0000 0.8941 .36402 Robust Std. Err. intpes_pc Coef. t P>It! [95% Conf. Intervall -2.03 3.73 -4.22 -3.55 1.04 0.12 Inypcpenn Inypcpenn2 in_gasprice temp_coldest temp_warmest In_annualprecip ffrents Inpop inland _Iincomegro_2 _Iincomegro_3 cons -.9599562 .0954567 -.2392021 -.01857 0166677 .006395 0028204 -.0469675 .0546541 . 1032733 -. 0828519 8.303336 .4732335 . 0256192 .0566569 .005238 .016009 .0539954 .0028546 .038338 .0328958 .2283648 .1007342 2.40965 0.045 0.000 0.000 0.001 9.300 0.906 0.325 0.223 0.099 0.652 0.412 0.001 -1.897006 . 0447282 -.3513885 -.0289417 -. 0150318 - 1005213 -. 0028319 -. 1228807 -.0104828 -.3489118 ..2823156 3.531989 -.0229066 .1461852 - 1270157 .0081983 .0483671 . 1133114 .0084728 .0289456 .119791 .5554584 .1166118 13.07468 0.99 -1.23 1.66 0.45 -0.82 3.45 1) Interpret the constant and its p-value. 2) Interpret the coefficient on gas price and carry out a t-test to determine the significance of the coefficient. 3) Interpret the coefficient on temp-coldest and its p-value. 4) Interpret the coefficient on Inland and its p-value. (3x4 marks)= 12 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) Describe when is it better to use nonlinear models than linear models, and what types of relationships are best modelled with this. Apart from quadratic models, what type of nonlinear models do you know? Describe with a few sentences. 3 marks 8) Please describe if MLR 4 is likely to hold or not? 2 marks 9) Please describe if MLR 5 is likely to hold or not? 3 marks QUESTION 2 We want model energy use as follows: Lntpes pc = Bo + BiLnypcpenn + B2Lnypcpenn2+ B3LnGasprice + B4LnAnnualprecip+ B5TempColdest + B6 TempWarmest + Byffrents + BgLnPop + B.LnLand + D_incomegroups +u The variables are defined as follows: Lntpes pc = log of total primary energy consumption per capita (ktoe) Lnypcpenn =log of GDP per capita (USD) Lnypcpenn2 = square of log of GDP per capita (USD) Ln gasprice = log of pump price for gasoline (USD/liter) LnAnnualprecip= log of annual precipitation (mm) Temp coldest = 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) Ln Pop = log of population (in millions) Ln Land = log of land area (in km2) I Incomegroup = refers to income groups "1","2" and 3, low, mid and high income countries. *"'Log" always refers to natural logs or "In" here. Linear regression Number of obs F(11, 119) Prob > F R-squared Root MSE 131 143.13 0.0000 0.8941 .36402 Robust Std. Err. intpes_pc Coef. t P>It! [95% Conf. Intervall -2.03 3.73 -4.22 -3.55 1.04 0.12 Inypcpenn Inypcpenn2 in_gasprice temp_coldest temp_warmest In_annualprecip ffrents Inpop inland _Iincomegro_2 _Iincomegro_3 cons -.9599562 .0954567 -.2392021 -.01857 0166677 .006395 0028204 -.0469675 .0546541 . 1032733 -. 0828519 8.303336 .4732335 . 0256192 .0566569 .005238 .016009 .0539954 .0028546 .038338 .0328958 .2283648 .1007342 2.40965 0.045 0.000 0.000 0.001 9.300 0.906 0.325 0.223 0.099 0.652 0.412 0.001 -1.897006 . 0447282 -.3513885 -.0289417 -. 0150318 - 1005213 -. 0028319 -. 1228807 -.0104828 -.3489118 ..2823156 3.531989 -.0229066 .1461852 - 1270157 .0081983 .0483671 . 1133114 .0084728 .0289456 .119791 .5554584 .1166118 13.07468 0.99 -1.23 1.66 0.45 -0.82 3.45 1) Interpret the constant and its p-value. 2) Interpret the coefficient on gas price and carry out a t-test to determine the significance of the coefficient. 3) Interpret the coefficient on temp-coldest and its p-value. 4) Interpret the coefficient on Inland and its p-value. (3x4 marks)= 12 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) Describe when is it better to use nonlinear models than linear models, and what types of relationships are best modelled with this. Apart from quadratic models, what type of nonlinear models do you know? Describe with a few sentences. 3 marks 8) Please describe if MLR 4 is likely to hold or not? 2 marks 9) Please describe if MLR 5 is likely to hold or not? 3 marks
