Suppose you estimated the following price forecasting equation for an annual crop: Dependent Variable: PRICE Method: Least Squares Variable Coefficient Std. Error t-Statistic Prob. PRICE(-1) INCOME POP CNY PS -11.30310 0.257996 -0.000164 0.066704 -0.017009 0.475428 4.432247 -2.550197 0.131677 1.959308 8.63E-05 -1.899769 0.023783 2.804759 0.005124 -3.319135 0.204047 2.329994 0.0196 0.0649 0.0728 0.0113 0.0036 0.0310 where: C is a constant or the intercept PRICE is the price per bushel in the current year PRICE(-1) is the price per bushel in the previous year INCOME is consumer disposable income POP is the population of the U.S. CNY is the average national yield of the crop in bushels per acre PS is the government set price support for the crop Suppose that you wanted to use this equation and the following values for the independent variables to forecast PRICE for 2021-25: PRICE PRICE(-1) CNY INCOME POP PS 2021 2022 2023 2024 2025 1.940000 2.540000 2.360000 2.280000 2.400000 1.500000 1.940000 2.540000 2.360000 2.280000 119.8000 84.60000 116.3000 118.5000 108.6000 13545 14477 15313 16236 16693 243.9340 246.3290 248.7770 251.5230 249.6967 1.820000 1.770000 1.650000 1.570000 1.620000 (a) Forecast PRICE for 2021-25 (I recommend using Excel or some other spreadsheet package). Graph your predicted PRICE vs. the actual PRICE for this time period. Calculate the root mean square error. The formula for root mean square error is (b) sqrt(sum((price; - predictedprice:)2)/5) (c) (d) Compute the elasticities of this price equation with respect to CNY, INCOME, POP, and PS based on 2021 actual price. Suppose that climate change reduced the crop yield (CNY) by 10% lower than the projected yields in the table above from 2021-25. Plot the crop price with and without climate change by plotting the original predicted price in (a) and the new predicted price in (d). Suppose the government increased the price support level to $2.00 for 2021-25. Graph the original predicted price in (a) against the new predicted price with PS=2. Suppose the population projections were low, and the new ones are 1% higher. Plot the original predicted price in (a) against the new population projections in (f). (e) (f) Suppose you estimated the following price forecasting equation for an annual crop: Dependent Variable: PRICE Method: Least Squares Variable Coefficient Std. Error t-Statistic Prob. PRICE(-1) INCOME POP CNY PS -11.30310 0.257996 -0.000164 0.066704 -0.017009 0.475428 4.432247 -2.550197 0.131677 1.959308 8.63E-05 -1.899769 0.023783 2.804759 0.005124 -3.319135 0.204047 2.329994 0.0196 0.0649 0.0728 0.0113 0.0036 0.0310 where: C is a constant or the intercept PRICE is the price per bushel in the current year PRICE(-1) is the price per bushel in the previous year INCOME is consumer disposable income POP is the population of the U.S. CNY is the average national yield of the crop in bushels per acre PS is the government set price support for the crop Suppose that you wanted to use this equation and the following values for the independent variables to forecast PRICE for 2021-25: PRICE PRICE(-1) CNY INCOME POP PS 2021 2022 2023 2024 2025 1.940000 2.540000 2.360000 2.280000 2.400000 1.500000 1.940000 2.540000 2.360000 2.280000 119.8000 84.60000 116.3000 118.5000 108.6000 13545 14477 15313 16236 16693 243.9340 246.3290 248.7770 251.5230 249.6967 1.820000 1.770000 1.650000 1.570000 1.620000 (a) Forecast PRICE for 2021-25 (I recommend using Excel or some other spreadsheet package). Graph your predicted PRICE vs. the actual PRICE for this time period. Calculate the root mean square error. The formula for root mean square error is (b) sqrt(sum((price; - predictedprice:)2)/5) (c) (d) Compute the elasticities of this price equation with respect to CNY, INCOME, POP, and PS based on 2021 actual price. Suppose that climate change reduced the crop yield (CNY) by 10% lower than the projected yields in the table above from 2021-25. Plot the crop price with and without climate change by plotting the original predicted price in (a) and the new predicted price in (d). Suppose the government increased the price support level to $2.00 for 2021-25. Graph the original predicted price in (a) against the new predicted price with PS=2. Suppose the population projections were low, and the new ones are 1% higher. Plot the original predicted price in (a) against the new population projections in (f). (e) (f)