Assignment3 ECON-309

Month/Year t Yt MA(12) CMA S,I=Y/CMA S DSY=Y/S T Jan/2016 1 1200 1.2857 933.3167 888.2382 Feb 2 1140 1.2041 946.7575 905.1638 Mar 3 1100 1.1520 954.8420 922.0894 Apr 4 1050 1.0901 963.2154 939.0150 May 5 900 0.9464 950.9486 955.9406 Jun 6 880 0.9114 965.5938 972.8662 Jul 7 840 1000.000 1010.000 0.8317 0.8158 1029.6600 989.7918 Aug 8 860 1020.000 1028.750 0.8360 0.8205 1048.1493 1006.7174 Sep 9 880 1037.500 1046.250 0.8411 0.8296 1060.7842 1023.6430 Oct 10 950 1055.000 1063.333 0.8934 0.8954 1060.9314 1040.5686 Nov 11 1050 1071.667 1080.000 0.9722 0.9779 1073.6772 1057.4943 Dec 12 1150 1088.333 1096.250 1.0490 1.0589 1086.0526 1074.4199 Jan/2017 13 1440 1104.167 1106.667 1.3012 1.2857 1119.9801 1091.3455 Feb 14 1350 1109.167 1111.667 1.2144 1.2041 1121.1602 1108.2711 Mar 15 1310 1114.167 1117.083 1.1727 1.1520 1137.1300 1125.1967 Apr 16 1250 1120.000 1125.833 1.1103 1.0901 1146.6850 1142.1223 May 17 1100 1131.667 1139.167 0.9656 0.9464 1162.2706 1159.0479 Jun 18 1070 1146.667 1155.417 0.9261 0.9114 1174.0743 1175.9735 Jul 19 900 1164.167 1170.000 0.7692 0.8158 1103.2071 1192.8991 Aug 20 920 1175.833 1182.083 0.7783 0.8205 1121.2760 1209.8247 Sep 21 950 1188.333 1194.167 0.7955 0.8296 1145.1647 1226.7503 Oct 22 1090 1200.000 1206.250 0.9036 0.8954 1217.2792 1243.6759 Nov 23 1230 1212.500 1219.167 1.0089 0.9779 1257.7362 1260.6015 Dec 24 1360 1225.833 1232.500 1.1034 1.0589 1284.3752 1277.5271 Jan/2018 25 1580 1239.167 1249.583 1.2644 1.2857 1228.8670 1294.4527 Feb 26 1500 1260.000 1270.625 1.1805 1.2041 1245.7335 1311.3783 Mar 27 1450 1281.250 1291.875 1.1224 1.1520 1258.6553 1328.3039 Apr 28 1400 1302.500 1310.417 1.0684 1.0901 1284.2872 1345.2295 May 29 1260 1318.333 1325.000 0.9509 0.9464 1331.3281 1362.1551 Jun 30 1230 1331.667 1337.917 0.9193 0.9114 1349.6368 1379.0807 Jul 31 1150 1344.167 1358.542 0.8465 0.8158 1409.6535 1396.0063 Aug 32 1175 1372.917 1386.875 0.8472 0.8205 1432.0645 1412.9319 Sep 33 1205 1400.833 1414.167 0.8521 0.8296 1452.5510 1429.8576 Oct 34 1280 1427.500 1439.375 0.8893 0.8954 1429.4655 1446.7832 Nov 35 1390 1451.250 1458.958 0.9527 0.9779 1421.3441 1463.7088 Dec 36 1510 1466.667 1474.375 1.0242 1.0589 1426.0342 1480.6344 Jan/2019 37 1925 1482.083 1490.417 1.2916 1.2857 1497.1956 1497.5600 Feb 38 1835 1498.750 1507.292 1.2174 1.2041 1523.9473 1514.4856 Mar 39 1770 1515.833 1524.583 1.1610 1.1520 1536.4275 1531.4112 Apr 40 1685 1533.333 1543.542 1.0916 1.0901 1545.7314 1548.3368 May 41 1445 1553.750 1566.042 0.9227 0.9464 1526.8009 1565.2624 Jun 42 1415 1578.333 1592.292 0.8887 0.9114 1552.6310 1582.1880 Jul 43 1350 1606.250 0.8158 1654.8107 1599.1136 Aug 44 1380 0.8205 1681.9140 1616.0392 Sep 45 1415 0.8296 1705.6927 1632.9648 Oct 46 1525 0.8954 1703.0742 1649.8904

Nov 47 1685 0.9779 1722.9963 1666.8160 Dec 48 1845 1.0589 1742.4061 1683.7416 Jan/2020 49 1.2857 1700.6672 Feb 50 1.2041 1717.5928 Mar 51 1.1520 1734.5184 Apr 52 1.0901 1751.4440 May 53 0.9464 1768.3696 Jun 54 0.9114 1785.2953 Jul 55 0.8158 1802.2209 Aug 56 0.8205 1819.1465 Sep 57 0.8296 1836.0721 Oct 58 0.8954 1852.9977 Nov 59 0.9779 1869.9233 Dec 60 1.0589 1886.8489 The error plot shows mean error very near around the horizontal zero line and random fluctuati around zero, and the trend in error is negligible and downward as decreasing errors as time pas 0 20 40 60 80 100 Regression Residuals 0 5 10 15 20 25 30 35 40 45 -100.0000 -80.0000 -60.0000 -40.0000 -20.0000 0.0000 20.0000 40.0000 60.0000 80.0000 et

et SEASONAL INDEX 1142.0408 57.9592 Year/Month Jan Feb Mar Apr May 1089.9167 50.0833 2016 1062.2683 37.7317 2017 1.3012 1.2144 1.1727 1.1103 0.9656 1023.6192 26.3808 2018 1.2644 1.1805 1.1224 1.0684 0.9509 904.7245 -4.7245 2019 1.2916 1.2174 1.1610 1.0916 0.9227 886.6278 -6.6278 Average 1.2857 1.2041 1.1520 1.0901 0.9464 807.4754 32.5246 826.0054 33.9946 SUMMARY OUTPUT 849.1887 30.8113 931.7663 18.2337 Regression Statistics 1034.1739 15.8261 Multiple R 0.984235 1137.6824 12.3176 R Square 0.968718 1403.1834 36.8166 Adjusted R Square 0.968038 1334.4801 15.5199 Standard Error 43.04203 1296.2526 13.7474 Observations 48 1245.0261 4.9739 1096.9500 3.0500 ANOVA 1071.7308 -1.7308 df SS MS F ignificance 973.1710 -73.1710 Regression 1 2639018 2639018 1424.481 2.929E-36 992.6537 -72.6537 Residual 46 85220.36 1852.616 1017.6814 -67.6814 Total 47 2724238 1113.6366 -23.6366 1232.8021 -2.8021 Coefficients andard Erro t Stat P-value Lower 95% 1352.7487 7.2513 Intercept 871.3126 12.62188 69.03191 4.182E-48 845.9061 1664.3259 -84.3259 t 16.9256 0.448452 37.7423 2.929E-36 16.02292 1579.0436 -79.0436 1530.2368 -80.2368 1466.4331 -66.4331 1289.1754 -29.1754 1256.8339 -26.8339 1138.8666 11.1334 1159.3019 15.6981 1186.1740 18.8260 1295.5069 -15.5069 1431.4304 -41.4304 1567.8150 -57.8150 1925.4685 -0.4685 1823.6070 11.3930 1764.2211 5.7789 1687.8401 -2.8401 1481.4009 -36.4009 1441.9370 -26.9370 1304.5621 45.4379 1325.9501 54.0499 1354.6667 60.3333 1477.3772 47.6228 Y =S*T The chart shows monthly data of sales (Yt) for four yea clearly shows a seasonal pattern with the peak in Janu Moreover, there is also a clear upward trend from yea 0 5 10 15 20 25 30 0 500 1000 1500 2000 2500 Yt

1630.0586 54.9414 1782.8814 62.1186 2186.6110 2068.1704 1998.2053 1909.2471 MSE 1673.6263 1695.9333 1627.0401 RMSE 1470.2577 41.1817 1492.5984 1523.1594 1659.2474 1828.6869 1997.9477 The plot of CMA reflects the trendline wh tions sses. The plot of seasonally adjusted data shows that it follows the linear tren fluctuations. 0 5 10 15 20 25 30 0 500 1000 1500 2000 2500 CMA vs Yt Yt Linear (Yt) 1000.0000 1500.0000 2000.0000 2500.0000 Yt vs DSY 50 55 0 10 20 30 40 0 500 1000 1500 2000 2500 Y vs Yhat (Ratio to MA Prediction o Yt Linear (Yt)

Jun Jul Aug Sep Oct Nov Dec 0.8317 0.8360 0.8411 0.8934 0.9722 1.0490 0.9261 0.7692 0.7783 0.7955 0.9036 1.0089 1.1034 0.9193 0.8465 0.8472 0.8521 0.8893 0.9527 1.0242 0.8887 0.9114 0.8158 0.8205 0.8296 0.8954 0.9779 1.0589 F Upper 95% Lower 95.0% Upper 95.0% 896.7191 845.9061 896.7191 17.82829 16.02292 17.82829 ars in millions from 2016 to 2019. The data uuary's and the trough in July's every year. ar to year. 35 40 45 50 55

hich we expected. ndline very closely. It is largely devoid of the sesonal 35 40 45 50 55 CMA 0 50 60 70 of Monthly Sales) Yhat

SUMMARY OUTPUT Regression Statistics Multiple R 0.984235 R Square 0.968718 Adjusted R 0.968038 Standard E 43.04203 Observatio 48 ANOVA df SS MS F ignificance F Regression 1 2639018 2639018 1424.481 2.929E-36 Residual 46 85220.36 1852.616 Total 47 2724238 Coefficients tandard Erro t Stat P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% Intercept 871.3126 12.62188 69.03191 4.182E-48 845.9061 896.7191 845.9061 896.7191 t 16.9256 0.448452 37.7423 2.929E-36 16.02292 17.82829 16.02292 17.82829 RESIDUAL OUTPUT Observation dicted DSY= Residuals 1 888.2382 45.07854 2 905.1638 41.59367 3 922.0894 32.75255 4 939.015 24.20041 5 955.9406 -4.991985 6 972.8662 -7.27242 7 989.7918 39.86815 8 1006.717 41.43187 9 1023.643 37.14112 10 1040.569 20.36279 11 1057.494 16.18297 12 1074.42 11.6327 13 1091.345 28.63463 14 1108.271 12.8891 15 1125.197 11.9333 16 1142.122 4.562761 17 1159.048 3.222678 18 1175.973 -1.899195 19 1192.899 -89.69197 20 1209.825 -88.54869 21 1226.75 -81.58558 22 1243.676 -26.39667 23 1260.602 -2.865328 0 10 -100 -80 -60 -40 -20 0 20 40 60 80 100

24 1277.527 6.848087 25 1294.453 -65.58567 26 1311.378 -65.6448 27 1328.304 -69.64861 28 1345.23 -60.94229 29 1362.155 -30.82704 30 1379.081 -29.44394 31 1396.006 13.6472 32 1412.932 19.13251 33 1429.858 22.69349 34 1446.783 -17.31764 35 1463.709 -42.36463 36 1480.634 -54.60014 37 1497.56 -0.364364 38 1514.486 9.461764 39 1531.411 5.016338 40 1548.337 -2.60536 41 1565.262 -38.46152 42 1582.188 -29.55704 43 1599.114 55.69708 44 1616.039 65.8748 45 1632.965 72.72791 46 1649.89 53.18374 47 1666.816 56.18029 48 1683.742 58.66444

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