Assume you have a project to develop a model to forecast natural gas consumption for the residential sector in the Washington, DC, metropolitan area. The level of natural gas consumption is influenced by a variety of factors. You decided that the most important factors include local weather, the state of the national and the local economies, the purchasing power of the dollar (because at least some of the natural gas is imported), and the prices for other commodities. The following variables have been identified and recorded on a quarterly basis (the data cover the period 1997Q1 through 2008Q3, with all data measured quarterly): GASCONS: consumption of natural gas in DC metro area (million cubic feet) AVETEMP: average temperature for the period in the DC metro area GDP: annualized percentage change in GDP UNEMP: percentage unemployment in the DC metro area GAS_PRICE: price of natural gas ($/100 cubic feet) DOLLAR: value index for the U.S. dollar relative to a basket of international currencies OIL_PRICE: price of crude oil ($/barrel) RESERVES: reserves of natural gas (million cubic feet) Develop a multiple regression model and interpret the coefficients of AveTemp and GasPrice. discuss/ check the model’s adequacy with regard to the regression assumptions. Test your model for overall significance at 95% significance. Test the coefficients with including your hypothesis. Evaluate your model, if you need to drop any variables from the model, re-estimate your model. Give your reasoning why you do/ don’t drop any variable from the initial model. Test your models forecasting performance with estimating the multiple regression between 1997 to 2006 Q=4. Then forecast 2007 and 2008 (upto Q=3 of 2008). Develop 95% prediction intervals for your forecast. Then plot the time series of actual gas consumption vs forecasted gas consumption with your prediction intervals. Give your comments on your model’s forecasting performance. Year Quarter Year.Qtr GASCONS AVETEMP GDP UNEMP PRICE_GAS DOLLAR PRICE_OIL_Qtrly Aver. RESERVES 1997 1 1997.1 2470.7 39.4 0.77 8.20 6.66 94.2 22.37 1208473 1997 2 1997.2 940.7 59.7 1.52 8.30 7.17 95.9 18.67 1382389 1997 3 1997.3 394.7 71.5 1.25 8.30 8.77 98.6 18.20 2342252 1997 4 1997.4 1462.7 45.6 0.81 8.37 6.93 97.7 18.67 2586394 1998 1 1998.1 2275.7 41.9 1.11 8.30 6.26 100.7 14.44 1440386 1998 2 1998.2 757.3 63.8 0.67 8.13 7.50 100.5 12.78 1757737 1998 3 1998.3 346.7 74.0 1.15 8.27 8.68 99.2 12.38 2684551 1998 4 1998.4 1036.7 48.4 1.52 7.67 6.64 94.7 11.75 3025307 1999 1 1999.1 2517.7 38.1 0.84 7.37 5.91 98.3 10.95 1741442 1999 2 1999.2 785.7 62.6 0.84 6.67 7.00 102.1 15.32 1826407 1999 3 1999.3 336.7 73.5 1.18 6.30 8.44 99.4 18.84 2637400 1999 4 1999.4 1075.7 47.9 1.78 6.20 6.69 101.0 22.13 2887340 2000 1 2000.1 2549.7 39.4 0.27 5.73 6.18 105.5 25.93 1405750 2000 2 2000.2 832.7 63.1 1.56 5.60 7.70 108.6 25.36 1450975 2000 3 2000.3 370.3 69.8 -0.13 5.60 9.43 111.8 27.97 2231995 2000 4 2000.4 1393.0 42.9 0.52 5.73 8.10 113.8 28.16 2297796 2001 1 2001.1 2442.3 36.6 -0.13 6.10 9.12 113.4 24.19 973138 2001 2 2001.2 731.7 62.9 0.30 6.20 9.82 118.1 23.24 1438263 2001 3 2001.3 300.3 70.9 -0.35 6.40 9.63 114.7 22.69 2593609 2001 4 2001.4 841.3 49.7 0.40 6.57 7.04 116.1 17.38 3100528 2002 1 2002.1 2014.3 41.1 0.67 6.70 6.47 119.3 17.33 1899840 2002 2 2002.2 576.0 63.6 0.55 6.73 7.60 111.0 22.07 1978280 2002 3 2002.3 325.0 74.6 0.59 6.77 9.10 107.1 23.68 2784551 2002 4 2002.4 1835.0 44.7 0.05 6.80 7.16 105.0 23.74 2806587 2003 1 2003.1 2577.0 34.2 0.30 6.83 7.69 99.6 28.27 1034291 2003 2 2003.2 653.0 60.4 0.86 6.90 9.54 95.1 24.36 1318689 2003 3 2003.3 257.0 72.8 1.82 7.30 10.89 95.9 25.16 2468970 2003 4 2003.4 1565.0 46.9 0.67 7.23 8.60 90.0 25.35 2910262 2004 1 2004.1 2467.3 35.7 0.81 7.43 8.42 87.4 28.65 1321737 2004 2 2004.2 556.7 64.6 0.86 7.63 9.89 89.4 30.87 1633050 2004 3 2004.3 298.0 72.2 0.89 7.63 11.35 88.8 34.44 2731244 2004 4 2004.4 1436.7 46.8 0.62 7.40 9.51 82.5 37.22 3080952 2005 1 2005.1 2271.7 36.4 0.81 7.27 9.01 83.4 37.15 1614259 2005 2 2005.2 544.0 61.7 0.64 6.70 10.47 87.1 40.81 1857095 2005 3 2005.3 280.0 75.1 0.94 6.37 12.64 88.8 48.26 2681376 2005 4 2005.4 1522.0 46.4 0.32 6.13 12.51 90.9 46.41 3006208 2006 1 2006.1 1798.3 40.1 1.18 6.13 11.23 89.6 47.37 1983008 2006 2 2006.2 440.7 63.0 0.67 5.87 11.22 85.4 52.15 2290622 2006 3 2006.3 304.0 73.0 0.20 5.80 12.42 85.4 53.06 3023871 2006 4 2006.4 1261.3 48.7 0.37 5.80 9.87 84.0 44.66 3309616 2007 1 2007.1 2178.0 36.9 0.02 5.70 9.65 83.7 43.38 1879155 2007 2 2007.2 643.7 62.5 1.18 5.70 11.25 81.9 48.04 2162255 2007 3 2007.3 264.7 73.5 1.18 5.70 12.54 79.8 55.90 3077496 2007 4 2007.4 1370.3 48.4 -0.05 5.70 9.92 76.4 65.85 3295557 2008 1 2008.1 2056.0 38.4 0.22 6.07 9.38 73.6 70.42 1589334 2008 2 2008.2 530.7 62.6 0.69 6.50 11.89 72.6 87.47 1814450 2008 3 2008.3 267.7 71.9 -0.13 7.10 13.97 76.7 85.48 2848615
Assume you have a project to develop a model to forecast natural gas consumption for the residential sector in the Washington, DC, metropolitan area. The level of natural gas consumption is influenced by a variety of factors. You decided that the most important factors include local weather, the state of the national and the local economies, the purchasing power of the dollar (because at least some of the natural gas is imported), and the prices for other commodities. The following variables have been identified and recorded on a quarterly basis (the data cover the period 1997Q1 through 2008Q3, with all data measured quarterly): GASCONS: consumption of natural gas in DC metro area (million cubic feet) AVETEMP: average temperature for the period in the DC metro area GDP: annualized percentage change in GDP UNEMP: percentage unemployment in the DC metro area GAS_PRICE: price of natural gas ($/100 cubic feet) DOLLAR: value index for the U.S. dollar relative to a basket of international currencies OIL_PRICE: price of crude oil ($/barrel) RESERVES: reserves of natural gas (million cubic feet) Develop a multiple regression model and interpret the coefficients of AveTemp and GasPrice. discuss/ check the model’s adequacy with regard to the regression assumptions. Test your model for overall significance at 95% significance. Test the coefficients with including your hypothesis. Evaluate your model, if you need to drop any variables from the model, re-estimate your model. Give your reasoning why you do/ don’t drop any variable from the initial model. Test your models forecasting performance with estimating the multiple regression between 1997 to 2006 Q=4. Then forecast 2007 and 2008 (upto Q=3 of 2008). Develop 95% prediction intervals for your forecast. Then plot the time series of actual gas consumption vs forecasted gas consumption with your prediction intervals. Give your comments on your model’s forecasting performance. Year Quarter Year.Qtr GASCONS AVETEMP GDP UNEMP PRICE_GAS DOLLAR PRICE_OIL_Qtrly Aver. RESERVES 1997 1 1997.1 2470.7 39.4 0.77 8.20 6.66 94.2 22.37 1208473 1997 2 1997.2 940.7 59.7 1.52 8.30 7.17 95.9 18.67 1382389 1997 3 1997.3 394.7 71.5 1.25 8.30 8.77 98.6 18.20 2342252 1997 4 1997.4 1462.7 45.6 0.81 8.37 6.93 97.7 18.67 2586394 1998 1 1998.1 2275.7 41.9 1.11 8.30 6.26 100.7 14.44 1440386 1998 2 1998.2 757.3 63.8 0.67 8.13 7.50 100.5 12.78 1757737 1998 3 1998.3 346.7 74.0 1.15 8.27 8.68 99.2 12.38 2684551 1998 4 1998.4 1036.7 48.4 1.52 7.67 6.64 94.7 11.75 3025307 1999 1 1999.1 2517.7 38.1 0.84 7.37 5.91 98.3 10.95 1741442 1999 2 1999.2 785.7 62.6 0.84 6.67 7.00 102.1 15.32 1826407 1999 3 1999.3 336.7 73.5 1.18 6.30 8.44 99.4 18.84 2637400 1999 4 1999.4 1075.7 47.9 1.78 6.20 6.69 101.0 22.13 2887340 2000 1 2000.1 2549.7 39.4 0.27 5.73 6.18 105.5 25.93 1405750 2000 2 2000.2 832.7 63.1 1.56 5.60 7.70 108.6 25.36 1450975 2000 3 2000.3 370.3 69.8 -0.13 5.60 9.43 111.8 27.97 2231995 2000 4 2000.4 1393.0 42.9 0.52 5.73 8.10 113.8 28.16 2297796 2001 1 2001.1 2442.3 36.6 -0.13 6.10 9.12 113.4 24.19 973138 2001 2 2001.2 731.7 62.9 0.30 6.20 9.82 118.1 23.24 1438263 2001 3 2001.3 300.3 70.9 -0.35 6.40 9.63 114.7 22.69 2593609 2001 4 2001.4 841.3 49.7 0.40 6.57 7.04 116.1 17.38 3100528 2002 1 2002.1 2014.3 41.1 0.67 6.70 6.47 119.3 17.33 1899840 2002 2 2002.2 576.0 63.6 0.55 6.73 7.60 111.0 22.07 1978280 2002 3 2002.3 325.0 74.6 0.59 6.77 9.10 107.1 23.68 2784551 2002 4 2002.4 1835.0 44.7 0.05 6.80 7.16 105.0 23.74 2806587 2003 1 2003.1 2577.0 34.2 0.30 6.83 7.69 99.6 28.27 1034291 2003 2 2003.2 653.0 60.4 0.86 6.90 9.54 95.1 24.36 1318689 2003 3 2003.3 257.0 72.8 1.82 7.30 10.89 95.9 25.16 2468970 2003 4 2003.4 1565.0 46.9 0.67 7.23 8.60 90.0 25.35 2910262 2004 1 2004.1 2467.3 35.7 0.81 7.43 8.42 87.4 28.65 1321737 2004 2 2004.2 556.7 64.6 0.86 7.63 9.89 89.4 30.87 1633050 2004 3 2004.3 298.0 72.2 0.89 7.63 11.35 88.8 34.44 2731244 2004 4 2004.4 1436.7 46.8 0.62 7.40 9.51 82.5 37.22 3080952 2005 1 2005.1 2271.7 36.4 0.81 7.27 9.01 83.4 37.15 1614259 2005 2 2005.2 544.0 61.7 0.64 6.70 10.47 87.1 40.81 1857095 2005 3 2005.3 280.0 75.1 0.94 6.37 12.64 88.8 48.26 2681376 2005 4 2005.4 1522.0 46.4 0.32 6.13 12.51 90.9 46.41 3006208 2006 1 2006.1 1798.3 40.1 1.18 6.13 11.23 89.6 47.37 1983008 2006 2 2006.2 440.7 63.0 0.67 5.87 11.22 85.4 52.15 2290622 2006 3 2006.3 304.0 73.0 0.20 5.80 12.42 85.4 53.06 3023871 2006 4 2006.4 1261.3 48.7 0.37 5.80 9.87 84.0 44.66 3309616 2007 1 2007.1 2178.0 36.9 0.02 5.70 9.65 83.7 43.38 1879155 2007 2 2007.2 643.7 62.5 1.18 5.70 11.25 81.9 48.04 2162255 2007 3 2007.3 264.7 73.5 1.18 5.70 12.54 79.8 55.90 3077496 2007 4 2007.4 1370.3 48.4 -0.05 5.70 9.92 76.4 65.85 3295557 2008 1 2008.1 2056.0 38.4 0.22 6.07 9.38 73.6 70.42 1589334 2008 2 2008.2 530.7 62.6 0.69 6.50 11.89 72.6 87.47 1814450 2008 3 2008.3 267.7 71.9 -0.13 7.10 13.97 76.7 85.48 2848615
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Question
- Assume you have a project to develop a model to forecast natural gas consumption for the residential sector in the Washington, DC, metropolitan area. The level of natural gas consumption is influenced by a variety of factors. You decided that the most important factors include local weather, the state of the national and the local economies, the purchasing power of the dollar (because at least some of the natural gas is imported), and the prices for other commodities. The following variables have been identified and recorded on a quarterly basis (the data cover the period 1997Q1 through 2008Q3, with all data measured quarterly):
GASCONS: consumption of natural gas in DC metro area (million cubic feet)
AVETEMP: average temperature for the period in the DC metro area
GDP: annualized percentage change in GDP
UNEMP: percentage unemployment in the DC metro area
GAS_PRICE: price of natural gas ($/100 cubic feet)
DOLLAR: value index for the U.S. dollar relative to a basket of international currencies
OIL_PRICE: price of crude oil ($/barrel)
RESERVES: reserves of natural gas (million cubic feet)
- Develop a multiple regression model and interpret the coefficients of AveTemp and GasPrice.
- discuss/ check the model’s adequacy with regard to the regression assumptions.
- Test your model for overall significance at 95% significance. Test the coefficients with including your hypothesis.
- Evaluate your model, if you need to drop any variables from the model, re-estimate your model. Give your reasoning why you do/ don’t drop any variable from the initial model.
- Test your models forecasting performance with estimating the multiple regression between 1997 to 2006 Q=4. Then forecast 2007 and 2008 (upto Q=3 of 2008). Develop 95% prediction intervals for your forecast. Then plot the time series of actual gas consumption vs forecasted gas consumption with your prediction intervals. Give your comments on your model’s forecasting performance.
| Year | Quarter | Year.Qtr | GASCONS | AVETEMP | GDP | UNEMP | PRICE_GAS | DOLLAR | PRICE_OIL_Qtrly Aver. | RESERVES |
| 1997 | 1 | 1997.1 | 2470.7 | 39.4 | 0.77 | 8.20 | 6.66 | 94.2 | 22.37 | 1208473 |
| 1997 | 2 | 1997.2 | 940.7 | 59.7 | 1.52 | 8.30 | 7.17 | 95.9 | 18.67 | 1382389 |
| 1997 | 3 | 1997.3 | 394.7 | 71.5 | 1.25 | 8.30 | 8.77 | 98.6 | 18.20 | 2342252 |
| 1997 | 4 | 1997.4 | 1462.7 | 45.6 | 0.81 | 8.37 | 6.93 | 97.7 | 18.67 | 2586394 |
| 1998 | 1 | 1998.1 | 2275.7 | 41.9 | 1.11 | 8.30 | 6.26 | 100.7 | 14.44 | 1440386 |
| 1998 | 2 | 1998.2 | 757.3 | 63.8 | 0.67 | 8.13 | 7.50 | 100.5 | 12.78 | 1757737 |
| 1998 | 3 | 1998.3 | 346.7 | 74.0 | 1.15 | 8.27 | 8.68 | 99.2 | 12.38 | 2684551 |
| 1998 | 4 | 1998.4 | 1036.7 | 48.4 | 1.52 | 7.67 | 6.64 | 94.7 | 11.75 | 3025307 |
| 1999 | 1 | 1999.1 | 2517.7 | 38.1 | 0.84 | 7.37 | 5.91 | 98.3 | 10.95 | 1741442 |
| 1999 | 2 | 1999.2 | 785.7 | 62.6 | 0.84 | 6.67 | 7.00 | 102.1 | 15.32 | 1826407 |
| 1999 | 3 | 1999.3 | 336.7 | 73.5 | 1.18 | 6.30 | 8.44 | 99.4 | 18.84 | 2637400 |
| 1999 | 4 | 1999.4 | 1075.7 | 47.9 | 1.78 | 6.20 | 6.69 | 101.0 | 22.13 | 2887340 |
| 2000 | 1 | 2000.1 | 2549.7 | 39.4 | 0.27 | 5.73 | 6.18 | 105.5 | 25.93 | 1405750 |
| 2000 | 2 | 2000.2 | 832.7 | 63.1 | 1.56 | 5.60 | 7.70 | 108.6 | 25.36 | 1450975 |
| 2000 | 3 | 2000.3 | 370.3 | 69.8 | -0.13 | 5.60 | 9.43 | 111.8 | 27.97 | 2231995 |
| 2000 | 4 | 2000.4 | 1393.0 | 42.9 | 0.52 | 5.73 | 8.10 | 113.8 | 28.16 | 2297796 |
| 2001 | 1 | 2001.1 | 2442.3 | 36.6 | -0.13 | 6.10 | 9.12 | 113.4 | 24.19 | 973138 |
| 2001 | 2 | 2001.2 | 731.7 | 62.9 | 0.30 | 6.20 | 9.82 | 118.1 | 23.24 | 1438263 |
| 2001 | 3 | 2001.3 | 300.3 | 70.9 | -0.35 | 6.40 | 9.63 | 114.7 | 22.69 | 2593609 |
| 2001 | 4 | 2001.4 | 841.3 | 49.7 | 0.40 | 6.57 | 7.04 | 116.1 | 17.38 | 3100528 |
| 2002 | 1 | 2002.1 | 2014.3 | 41.1 | 0.67 | 6.70 | 6.47 | 119.3 | 17.33 | 1899840 |
| 2002 | 2 | 2002.2 | 576.0 | 63.6 | 0.55 | 6.73 | 7.60 | 111.0 | 22.07 | 1978280 |
| 2002 | 3 | 2002.3 | 325.0 | 74.6 | 0.59 | 6.77 | 9.10 | 107.1 | 23.68 | 2784551 |
| 2002 | 4 | 2002.4 | 1835.0 | 44.7 | 0.05 | 6.80 | 7.16 | 105.0 | 23.74 | 2806587 |
| 2003 | 1 | 2003.1 | 2577.0 | 34.2 | 0.30 | 6.83 | 7.69 | 99.6 | 28.27 | 1034291 |
| 2003 | 2 | 2003.2 | 653.0 | 60.4 | 0.86 | 6.90 | 9.54 | 95.1 | 24.36 | 1318689 |
| 2003 | 3 | 2003.3 | 257.0 | 72.8 | 1.82 | 7.30 | 10.89 | 95.9 | 25.16 | 2468970 |
| 2003 | 4 | 2003.4 | 1565.0 | 46.9 | 0.67 | 7.23 | 8.60 | 90.0 | 25.35 | 2910262 |
| 2004 | 1 | 2004.1 | 2467.3 | 35.7 | 0.81 | 7.43 | 8.42 | 87.4 | 28.65 | 1321737 |
| 2004 | 2 | 2004.2 | 556.7 | 64.6 | 0.86 | 7.63 | 9.89 | 89.4 | 30.87 | 1633050 |
| 2004 | 3 | 2004.3 | 298.0 | 72.2 | 0.89 | 7.63 | 11.35 | 88.8 | 34.44 | 2731244 |
| 2004 | 4 | 2004.4 | 1436.7 | 46.8 | 0.62 | 7.40 | 9.51 | 82.5 | 37.22 | 3080952 |
| 2005 | 1 | 2005.1 | 2271.7 | 36.4 | 0.81 | 7.27 | 9.01 | 83.4 | 37.15 | 1614259 |
| 2005 | 2 | 2005.2 | 544.0 | 61.7 | 0.64 | 6.70 | 10.47 | 87.1 | 40.81 | 1857095 |
| 2005 | 3 | 2005.3 | 280.0 | 75.1 | 0.94 | 6.37 | 12.64 | 88.8 | 48.26 | 2681376 |
| 2005 | 4 | 2005.4 | 1522.0 | 46.4 | 0.32 | 6.13 | 12.51 | 90.9 | 46.41 | 3006208 |
| 2006 | 1 | 2006.1 | 1798.3 | 40.1 | 1.18 | 6.13 | 11.23 | 89.6 | 47.37 | 1983008 |
| 2006 | 2 | 2006.2 | 440.7 | 63.0 | 0.67 | 5.87 | 11.22 | 85.4 | 52.15 | 2290622 |
| 2006 | 3 | 2006.3 | 304.0 | 73.0 | 0.20 | 5.80 | 12.42 | 85.4 | 53.06 | 3023871 |
| 2006 | 4 | 2006.4 | 1261.3 | 48.7 | 0.37 | 5.80 | 9.87 | 84.0 | 44.66 | 3309616 |
| 2007 | 1 | 2007.1 | 2178.0 | 36.9 | 0.02 | 5.70 | 9.65 | 83.7 | 43.38 | 1879155 |
| 2007 | 2 | 2007.2 | 643.7 | 62.5 | 1.18 | 5.70 | 11.25 | 81.9 | 48.04 | 2162255 |
| 2007 | 3 | 2007.3 | 264.7 | 73.5 | 1.18 | 5.70 | 12.54 | 79.8 | 55.90 | 3077496 |
| 2007 | 4 | 2007.4 | 1370.3 | 48.4 | -0.05 | 5.70 | 9.92 | 76.4 | 65.85 | 3295557 |
| 2008 | 1 | 2008.1 | 2056.0 | 38.4 | 0.22 | 6.07 | 9.38 | 73.6 | 70.42 | 1589334 |
| 2008 | 2 | 2008.2 | 530.7 | 62.6 | 0.69 | 6.50 | 11.89 | 72.6 | 87.47 | 1814450 |
| 2008 | 3 | 2008.3 | 267.7 | 71.9 | -0.13 | 7.10 | 13.97 | 76.7 | 85.48 | 2848615 |
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