5)The above model belongs to the class of nonlinear equations.Calculate the turning point of the nonlinear relationship.

6)Is this a U-shaped or inverted U-shaped relationship?

7)Analyse the relationship between energy use per capita and GDP pc based on these insights. How does energy use per capita change with GDPpc? Prepare graph!

8)Please define MLR 2 and describe if MLR 2 is likely to hold or not?

9)Please define MLR 4 and describe if MLR 4 is likely to hold or not?

Linear regression Number of obs = 131 F(11, 119) II 143. 13 Prob > F II D. 0606 R-squared 5. 8941 ROOL MSE = . 35402 Robust Intpos_pc Coof. Std. Err. [95% Conf. Interval] Inypepenn -. 9599562 . 4732335 -2. 03 9 . 045 -1. 897095 -. 9229065 Inypcpenn2 . 0954567 . 0256192 3. 73 9447282 . 1461852 In_gasprice -. 2392021 .0566569 -4. 22 3 . 609 -. 3513885 -. 1270157 temp_coldest -. 01857 . 005238 -3.55 3. 601 -. $289417 -. 0981983 temp_warrest 0166677 - 016809 1. 04 3. 300 -. $150318 . 0483671 In_annualprecip . 306395 . 6539954 0. 12 0.906 -. 1005213 . 1133114 ffrents . 0026254 . 5028546 0.99 0 . 325 -. 6028319 .0084728 Inpop -. 0469675 . 038335 -1. 23 0. 223 -. 1228657 . 6289456 Inland . 0546541 . 0328958 1. 66 0. 099 -. 5194628 . 119791 Iincomegra_2 1032733 .2283648 3 . 45 0 . 652 -. 3489118 . 5554584 Iincomegro_3 -. 0828519 . 1007342 -0.82 9. 412 -.2823156 . 1166118 cons 8.303336 2. 40965 3. 45 0. 001 3.531989 13 . 97468 Log referrers to natural logarithm!We model energy use per capita of 131 countries in a given year as follows: Lntpes_pc = Bo + BLnypcpenn + B2Lnypcpenn2 + BLnGasprice + B4LnAnnualprecip + TempColdest + TempWarmest + Byffrents + BLnPop + BoLnLand + 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) LnPop = log of population (in millions) LnLand = 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