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10 Pages

Chap15_part2

Course: ENGR, STAT 320, 262, , Spring 2008
School: Purdue
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Word Count: 1334

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to Solutions End-of-Section and Chapter Review Problems 675 15.31 (a) Intercept YLag1 YLag2 YLag3 Coefficients Standard Error 2.704449262 5.37548539 0.89294783 0.424505135 -0.708212436 0.602310389 0.802269914 0.491797033 t Stat 0.503107918 2.103503014 -1.175826366 1.631302876 P-value 0.649503147 0.126143957 0.324481541 0.20132482 Since the p-value = 0.20 > 0.05, do not reject H0 that A3 = 0. Third-order...

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to Solutions End-of-Section and Chapter Review Problems 675 15.31 (a) Intercept YLag1 YLag2 YLag3 Coefficients Standard Error 2.704449262 5.37548539 0.89294783 0.424505135 -0.708212436 0.602310389 0.802269914 0.491797033 t Stat 0.503107918 2.103503014 -1.175826366 1.631302876 P-value 0.649503147 0.126143957 0.324481541 0.20132482 Since the p-value = 0.20 > 0.05, do not reject H0 that A3 = 0. Third-order term can be deleted. (b) Intercept YLag1 YLag2 Coefficients Standard Error 3.709551493 4.756100407 0.949708028 0.440786085 0.00080161 0.42035574 t Stat 0.779956514 2.154578061 0.00190698 P-value 0.470706957 0.083758887 0.998552197 Since the p-value = 0.998 > 0.05, do not reject H0 that A2 = 0. Second-order term can be deleted. (c) Intercept YLag1 Coefficients Standard Error 4.824803547 3.189597232 0.930752135 0.05809798 t Stat 1.51266859 16.02038728 P-value 0.17412552 8.96802E-07 Since the p-value is virtually 0, reject H0 that A1 = 0. First-order autoregressive model is the appropriate model. (d) ^ Yi 4.8248 0.9308Yi 1 Year Forecasts 2002 60.2705123 2003 60.92171152 2004 61.52781659 n i 1 ^ (Yi Yi ) 2 p 1 ^ Yi Yi n 15.32 (a) SYX n n i 1 45 12 1 1 2.121 . The standard error of the estimate is 2.121 billion constant 1995 dollars. (b) MAD 18 1.5 . The mean absolute deviation is 1.5 billion constant 12 1995 dollars. n i 1 ^ (Yi Yi ) 2 p 1 ^ Yi Yi n 15.33 (a) SYX n n i 1 305 12 1 1 5.523 . The standard error of the estimate is 5.523 billion constant 1995 dollars. (b) MAD 38 12 3.167 . The mean absolute deviation is 3.167 billion constant 1995 dollars. 676 Chapter 15: Time Series Forecasting and Index Numbers 15.34 (a) Residuals Plot 600 500 400 300 200 100 0 -100 -200 -300 -400 Residuals 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 Year (b) Excel output: Regression Statistics Multiple R 0.988517544 R Square 0.977166935 Adjusted R Square 0.976253613 Standard Error 238.738489 Observations 27 SYX (c) (d) 238.7385 MAD = 5242.6761/27 = 194.1732 The residuals in the linear trend model show strings of consecutive positive and negative values. An autoregressive model will probably do better. 15.35 (a) Residual Plots 150000 100000 50000 Linear 0 Residuals 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 Quadratic Exponential AR1 -50000 -100000 -150000 -200000 Year 2001 Solutions to End-of-Section and Chapter Review Problems 677 15.35 cont. (b),(c) Syx MAD Linear Quadratic Exponential AR1 71717.77 26532.99 80216.94 14815.12 57907.30 22068.16 67748.08 11641.89 (d) The residuals in the three trend models show strings of consecutive positive and negative values. The autoregressive model performs well for the historical data and has a fairly random pattern of residuals. The autoregressive model has the smallest values in MAD. Based on the principle of parsimony, the autoregressive model would probably be the best model for forecasting. 15.36 (a) Residual Plots 2.0000 1.5000 1.0000 Residuals 0.5000 0.0000 1975 1978 1981 1984 1987 1990 1993 1996 1999 -0.5000 -1.0000 -1.5000 -2.0000 Year (b), (c) SYX MAD SSE k Linear Quadratic Exponential AR(1) 0.8747 0.8333 0.8329 0.4913 0.7172 19.8935 1 0.6007 17.3588 2 0.6314 18.0389 1 0.3585 6.0355 1 (d) The residuals in the three trend models show strings of consecutive positive and negative values. The autoregressive model performs well for the historical data and has a fairly random pattern of residuals. The autoregressive model has the smallest values in MAD. Based on the principle of parsimony, the autoregressive model would probably be the best model for forecasting. 2002 Linear Quadratic Exponential AR(1) 678 Chapter 15: Time Series Forecasting and Index Numbers 15.37 (a) Residual Plots 4000.0000 3000.0000 2000.0000 1000.0000 0.0000 -1000.0000 -2000.0000 -3000.0000 -4000.0000 -5000.0000 Linear Quadratic Exponential AR(1) Residuals 1979 1982 1985 1988 1991 1994 1997 Year (b)-(c) Linear SYX MAD SSE k Quadratic Exponential AR(2) 1432.72 1079.75 1199.11 756.82 1161.38 613.53 634.39 516.84 45159166.5604 24482890.4880 31633027.0218 10882886.2455 1 2 1 2 (d) The residuals in the three trend models show strings of consecutive positive and negative values, especially in the right tail. The autoregressive model performs well for the historical data and has a fairly random pattern of residuals. The autoregressive model has the smallest values in MAD. Based on the principle of parsimony, the autoregressive model would probably be the best model for forecasting. 15.38 (a) Residual Plots 60.0000 50.0000 40.0000 30.0000 20.0000 10.0000 0.0000 Linear Quadratic Exponential AR(1) Residuals 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 -10.0000 -20.0000 -30.0000 -40.0000 Year 2000 2000 Solutions to End-of-Section and Chapter Review Problems 679 15.38 (b), (c) cont. SSE SYX MAD k Linear Quadratic Exponential AR(1) 10522.16 3059.93 4908.52 2141.86 18.13 9.94 12.39 8.31 15.11 6.93 5.34 4.28 1 2 1 1 (d) The residuals in the three trend models show strings of consecutive positive and negative values. The autoregressive model performs well for the historical data and has a fairly random pattern of residuals. The autoregressive model also has the smallest values in MAD and SSE. Based on the principle of parsimony, the autoregressive model would probably be the best model for forecasting. 15.39 (a) Residual Plots 1.0000 0.8000 0.6000 Residuals 0.4000 0.2000 0.0000 1992 1993 1994 1995 1996 1997 1998 1999 2000 -0.2000 -0.4000 -0.6000 -0.8000 Year (b),(c) Linear SYX MAD 0.3773 0.2702 Quadratic 0.3850 0.2644 Exponential AR(1) 0.4071 0.4765 0.2902 0.3308 (d) The residuals in all the three trend models show strings of consecutive positive and negative values. The AR(1) model has a fairly random pattern of residuals. The quadratic trend model has the smallest MAD while the linear trend model has the smallest standard error of estimates. Based on the principle of parsimony, the linear trend model would be the best model for forecasting. 2001 Linear Quadratic Exponential AR(1) 680 Chapter 15: Time Series Forecasting and Index Numbers 15.40 (a) (b) (c) log b0 2 . b0 102 100 . This is the fitted value for January 1998 prior to adjustment by the January multiplier. log b1 0.01 . b1 100.01 1.0233 . The estimated monthly growth compound rate is (b1 1)100% = 2.33%. log b2 0.1 . b2 100.1 1.2589 . The January values in the time series are estimated to require a 25.89% increase above the value determined based on the monthly compound growth rate. 15.41 If the weeks follow a common cycle with a month, 3 dummy variables would be required to handle 4 different weekly periods. If the weeks follow a common cycle within a year, 51 dummy variables would be required to handle 52 different weekly periods. (a) (b) (c) 15.42 log b0 3.0 . b0 103.0 1,000 . This is the fitted value for January 1998 prior to adjustment by the quarterly multiplier. log b1 0.1 . b1 100.1 1.2589 . The estimated quarterly compound growth rate is (b1 1)100% = 25.89%. log b3 0.2 . b3 100.2 1.5849 . The second quarter values in the time series are estimated to require a 58.49% increase above the value determined based on the quarterly compound growth rate. 15.43 (a) (b) (c) (d) 15.44 (a) ^ log Y12 ^ log Y13 ^ log Y24 ^ log Y25 104.1 12,589.25 ^ 3.0 0.10(12) 0.25 3.95 . Y13 103.95 8,912.51 ^ 3.0 0.10(23) 5.3 . Y24 105.3 199,526.23 ^ 3.0 0.10(24) 0.25 5.15 . Y25 105.15 141,253.75 ^ 3.0 0.10(11) 4.1 . Y12 S&P Stock Index 1600 Composite Price Index 1400 1200 1000 800 600 400 200 0 0 3 6 9 12 15 18 21 24 27 30 33 Coded Quarter 36 Solutions to End-of-Section and Chapter Review Problems 681 15.44 (b) cont. Regression Analysis Regression Statistics Multiple R 0.754510848 R Square 0.56928662 Adjusted R 0.515447447 Square Standard 0.115022731 Error Observations 37 ANOVA df Regression Residual Total 4 32 36 SS 0.559577113 0.423367319 0.982944432 MS F Significance F 0.139894278 10.57383671 1.41809E-05 0.013230229 Intercept Coded Quarter Q1 Q2 Q3 Coefficients Standard Error 2.747081206 0.0510607 0.011498593 0.001774839 -0.012289508 0.012518416 -0.015485484 t Stat P-value Lower 95% Upper 95% 53.80030457 5.87634E-33 2.643074052 2.85108836 6.478667418 2.73506E-07 0.007883367 0.01511382 0.052879092 -0.232407704 0.81770138 -0.120000602 0.095421586 0.054338302 0.230379236 0.819263577 -0.098164989 0.123201822 0.054251275 -0.28544 0.777146563 -0.125991622 0.095020654 (c) (e) ^ log10 Y 2.7471 0.01150X 0.01229Q1 0.01252Q2 0.01549Q3 ^ ^ Y37 = 1408.4488 Y38 = 1531.2552 (d) ^ ^ ^ 1474.1520 Y 1568.6511 2003: Y = 1531.2552 Y 38 39 40 ^ 2004: Y41 (f) (g) 1565.7969 ^ Y42 ^ ^ 1702.3229 Y43 1638.8403 Y44 1743.8966 log10 b1 0.01150 . b1 100.01150 1.0268 . The estimated quarterly compound growth rate is (b1 1) 100% = 2.68%. log10 b3 0.01252 . b3 100.01252 1.0292 . The second quarter values in the time series are estimated to be on average 2.92% above the fourth quarter values. 682 Chapter 15: Time Series Forecasting and Index Numbers 15.45 (a) Scatter Plot 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 0 10 20 Coded Quarter 30 40 (b) Regression Analysis Regression Statistics Multiple R 0.992736 R Square 0.985525 Adjusted R 0.983716 Square Standard Error 0.005320 Observations 37 ANOVA df Regression Residual Total 4 32 36 Coefficients Intercept Coded Quarter Q1 Q2 Q3 3.8443873 0.0038237 -0.0004290 0.0002913 -0.0008176 SS 0.0616551 0.0009056 0.0625606 Standard Error 0.0023615 0.0000821 0.0024456 0.0025131 0.0025091 MS F Significance F 0.0154138 544.6783730 0.0000000 0.0000283 REal GDP (in billions of 1996 dollars) t Stat 1627.9448577 46.5821395 -0.1754169 0.1159318 -0.3258490 P-value 0.0000000 0.0000000 0.8618574 0.9084311 0.7466599 (c) (d) (e) (f) 3.8444 0.003823X 0.000429Q1 0.0002913Q2 ^ 9585.3960 2002, 1st quarter: Y 37 ^ log10 Y 0.0008176Q3 2002: ^ Y38 9686.2141 ^ Y39 100.003824 9746.9515 ^ Y40 9851.6741 log10 b1 0.003824 . b1 1.0088 . The estimated quarterly compound growth rate is (b1 1) 100% = 0.88%. log10 b2 0.000429 . b2 10 0.000429 0.9990 . The first quarter values in the time series are estimated to be on average 0.10% below the fourth quarter values. Solutions to End-of-Section and Chapter Review Problems 683 15.46 (a) Unemployment 7 6 5 4 3 2 1 0 0 20 40 60 80 100 Coded Month (b) Regression Statistics Multiple R 0.136155 R Square 0.018538 Adjusted R -0.140618 Square Standard Error 0.061811 Observations 87 ANOVA df Regression Residual Total 12 74 86 Coefficients Intercept Coded Month M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 0.676991 0.000199 0.004042 0.004270 0.002576 -0.007265 -0.009982 -0.009627 -0.010060 -0.009588 -0.011485 -0.008657 -0.004355 SS 0.005340 0.282727 0.288067 Standard Error 0.026474 0.000265 0.032018 0.032008 0.032000 0.033107 0.033092 0.033078 0.033066 0.033057 0.033049 0.033044 0.033041 MS 0.000445 0.003821 F Significance F 0.116479 0.999880 t Stat 25.572218 0.750647 0.126252 0.133391 0.080514 -0.219425 -0.301640 -0.291035 -0.304246 -0.290057 -0.347510 -0.261987 -0.131817 P-value 0.000000 0.455246 0.899875 0.894246 0.936045 0.826923 0.763773 0.771839 0.761795 0.772584 0.729194 0.794059 0.895487 Lower 95% 0.624241 -0.000329 -0.059755 -0.059508 -0.061185 -0.073233 -0.075918 -0.075536 -0.075946 -0.075455 -0.077337 -0.074498 -0.070190 Upper 95% 0.729741 0.000727 0.067839 0.068047 0.066338 0.058703 0.055955 0.056282 0.055825 0.056278 0.054367 0.057184 0.061479 ^ log Y 0.6770 0.000199 X 0.004042 M 1 0.004270 M 2 0.002576 M 3 0.007265 M 4 0.009982 M 5 0.009627 M 6 0.01006M 7 0.009588 M 8 0.01149M 9 0.008657 M 10 0.004355 M 11 684 Chapter 15: Time Series Forecasting and Index Numbers 15.46 cont. (c) (d) (e) ^ Y83 ^ Y84 ^ Y88 ^ Y92 ^ Y96 4.8859 % 4.9374 % ^ ^ 4.9858 %, Y86 4.9907 %, Y87 4.9736 %, ^ ^ 4.8363 %, Y 4.8424 %, Y 4.8398 %, 90 91 ^ Forecasts for 2003: Y85 ^ 4.8644 %, Y89 ^ 4.8473 %, Y93 4.9646 % ^ 4.8284 %, Y94 ^ 4.8622 %, Y95 4.9128 %, (f) (g) log b1 0.000199 . b1 100.000199 1.0005 . The estimated monthly compound growth rate is (b1 1) 100% = 0.05%. log b8 0.010060 . b8 10 0.01006 0.9771. The July values in the time series are estimated to be on average 2.29% below the December values. 15.47 (a) Credit Card Charges 70.0 Millions of Dollars 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0 5 10 15 Coded Month 20 25 30 (b) (c) The amount of charges in January and February are among the lowest in a year. The amount of charges in September is usually lower than that in August and October. The largest amount of charges in a year appears in December. In general, there is an upward trend, and, hence, the dollar amounts charged on the bank's credit cards is increasing.
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Review for the mid-term testRemember words please: how to read; how to write; meaning; how to useFrom Lesson 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (should know how to make a sentence) should know how to make a sentence should know how to m
Drexel - MATH - 121
VCU - BIOL - 301
Bio 310 People to focus on/history Mendel- wanted to use mice picked peas- diploid, 2x chromosomes (1 from each parent) easy, countable phenotypes Law of Segregation- 2 of each chromosome in a body cell, dominance/recessiveness, only 1 chromosome per
University of the Sciences in Philadelphia - BS - 212
(2nd half of class) Refer to Figure 19.12- Basic Anatomy of the Eye Cornea- front of eye Pupil- window of eye that changes shape by muscles Lens-helps adapt to near and far vision Figure 19.15 Cones detect three colors: red, green, and blue Rods dete