Spreadsheet: 539677d1506331666-forecasting-seasonal-forecast-test-25092017
Sheet: TABEL

 | Cold drink sales at a Starbucks |  |  |  |  |  |  |  |  |  |  | Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 |  | Total
 |  |  |  |  |  |  |  |  |  |  |  | 2015 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 37 | 64 | 80 | 46 | 125 | 48 | 77 | 162 | 156 | 174 | 484 | 532 | 346 | 294 | 641 | 440 | 380 | 455 | 386 | 410 | 248 | 502 | 283 | 277 | 314 | 260 | 379 | 332 | 441 | 393 | 358 | 328 | 297 | 326 | 267 | 178 |  | 10792
Input: |  |  |  |  |  |  | Annual |  |  |  |  | 2016 | 23 | 19 | 16 | 16 | 18 | 21 | 17 | 20 | 55 | 45 | 64 | 90 | 102 | 82 | 88 | 104 | 179 | 99 | 136 | 236 | 99 | 180 | 409 | 324 | 302 | 252 | 258 | 463 | 231 | 426 | 247 | 212 | 213 | 188 | 154 | 168 | 231 | 275 | 263 | 325 | 245 | 206 | 198 | 176 |  | 7475
 | Year | Spring | Summer | Fall | Winter |  | Total |  |  |  |  | 2017 | 26 | 25 | 9 | 25 | 12 | 16 | 18 | 9 | 68 | 69 | 61 | 77 | 126 | 91 | 97 | 101 | 117 | 128 | 174 | 206 | 337 | 499 | 354 | 397 | 457 | 275 | 275 | 232 | 254 | 418 | 305 | 428 | 240 | 212 | 196 | 305 | 303 | 343 | 289 | 260 | 191 | 198 | 174 | 36 |  | 8433
 |  |  |  |  |  |  |  |  |  |  | Forecast | 2018 | 48.78871166211064 | 46.33309681705285 | 35.41252690101675 | 45.48079342165085 | 39.3601178128749 | 44.09000560094412 | 43.28162081662656 | 39.92362854450504 | 101.9842995121579 | 114.5608232379206 | 133.208669775595 | 139.7272859704033 | 233.7548019406678 | 147.714889453205 | 176.7429529689885 | 249.8498133471732 | 310.5185492162945 | 277.9676659366003 | 555.3112596061634 | 687.2375659113235 | 556.6127225598931 | 698.5937944286858 | 1016.745199243654 | 847.9662468389176 | 838.957796862691 | 729.4023673097191 | 688.3039140697396 | 834.4615077945422 | 558.0820432032964 | 1033.142897208993 | 646.0925735450635 | 715.224988693273 | 602.9847800791633 | 522.9565023732706 | 582.1477581401499 | 647.8276575726011 | 790.6792849084186 | 826.1400364102944 | 749.2481632316045 | 757.3772222223834 | 612.60192584123 | 614.6194161772246 | 541.9631625013452 | 333.1929599389882 |  | 20216.57399960842
 | 1999 | 520 | 730 | 820 | 530 |  | 2600
 | 2000 | 590 | 810 | 900 | 600 |  | 2900 |  |  |  |  | Total | 83 | 78 | 59 | 75 | 64 | 71 | 69 | 63 | 160 | 178 | 205 | 213 | 353 | 221 | 262 | 367 | 452 | 401 | 794 | 974 | 782 | 973 | 1404 | 1161 | 1139 | 982 | 919 | 1105 | 733 | 1346 | 835 | 917 | 767 | 660 | 729 | 805 | 975 | 1011 | 910 | 913 | 733 | 730 | 639 | 390 |  | 26700
 | 2001 | 650 | 900 | 1000 | 650 |  | 3200
 |  |  |  |  |  |  |  |  |  |  |  | Weekly Average | 27.66666666666667 | 26 | 19.66666666666667 | 25 | 21.33333333333333 | 23.66666666666667 | 23 | 21 | 53.33333333333334 | 59.33333333333334 | 68.33333333333333 | 71 | 117.6666666666667 | 73.66666666666667 | 87.33333333333333 | 122.3333333333333 | 150.6666666666667 | 133.6666666666667 | 264.6666666666667 | 324.6666666666667 | 260.6666666666667 | 324.3333333333333 | 468 | 387 | 379.6666666666667 | 327.3333333333333 | 306.3333333333333 | 368.3333333333333 | 244.3333333333333 | 448.6666666666667 | 278.3333333333333 | 305.6666666666667 | 255.6666666666667 | 220 | 243 | 268.3333333333333 | 325 | 337 | 303.3333333333333 | 304.3333333333333 | 244.3333333333333 | 243.3333333333333 | 213 | 130 |  | 202.2727272727273
 | Totals | 1760 | 2440 | 2720 | 1780 |  | 8700
 |  |  |  |  |  |  |  |  |  |  |  | Seasonal Indices | 0.1367790262172285 | 0.1285393258426966 | 0.09722846441947566 | 0.1235955056179775 | 0.1054681647940075 | 0.1170037453183521 | 0.1137078651685393 | 0.1038202247191011 | 0.2636704119850187 | 0.2933333333333333 | 0.3378277153558052 | 0.3510112359550562 | 0.5817228464419476 | 0.3641947565543071 | 0.4317602996254681 | 0.6047940074906366 | 0.7448689138576778 | 0.6608239700374531 | 1.308464419475655 | 1.605093632958801 | 1.288689138576779 | 1.603445692883895 | 2.313707865168539 | 1.913258426966292 | 1.877003745318352 | 1.618277153558052 | 1.514456928838951 | 1.820973782771535 | 1.207940074906367 | 2.21812734082397 | 1.376029962546816 | 1.511161048689139 | 1.263970037453183 | 1.087640449438202 | 1.201348314606742 | 1.326591760299625 | 1.606741573033708 | 1.666067415730337 | 1.499625468164794 | 1.504569288389513 | 1.207940074906367 | 1.202996254681648 | 1.053033707865169 | 0.6426966292134831
 | Quarter Average | 586.6666666666666 | 813.3333333333334 | 906.6666666666666 | 593.3333333333334 |  | 725
 |  |  |  |  |  |  |  |  |  |  |  | Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44
 | Seasonal Indices | 0.8091954022988506 | 1.12183908045977 | 1.250574712643678 | 0.8183908045977012 |  |  |  |  |  |  | 2015 | 248.5761226725082 | 264.5104895104895 | 349.6918335901386 | 275.0909090909091 | 322.3721590909091 | 290.5889884763124 | 299.0118577075099 | 327.4891774891775 | 140.3267045454545 | 218.1818181818182 | 236.8070953436807 | 131.0499359795134 | 214.8789595673448 | 131.7976141505553 | 178.3396946564886 | 267.8597968788705 | 209.4328238133548 | 263.3076399909318 | 369.8992443324937 | 331.4448385290274 | 268.4898860730062 | 183.3551340745585 | 277.0444832944833 | 229.9741602067184 | 202.4503152685769 | 281.163210516571 | 254.8768424176477 | 225.1542575071987 | 205.3081979412129 | 226.3170336350128 | 205.6641262928688 | 183.3027659363537 | 248.4236102880171 | 239.0495867768595 | 315.4788627010849 | 250.2653867871259 | 274.4685314685315 | 235.88481251686 | 238.7262737262737 | 218.0025888678682 | 245.8731241473397 | 270.9900373599004 | 253.5531370038412 | 276.958041958042
 |  |  |  |  |  |  |  |  |  |  |  | 2016 | 168.1544359255203 | 147.8146853146853 | 164.5608628659476 | 129.4545454545455 | 170.6676136363637 | 179.4814340588989 | 149.5059288537549 | 192.6406926406927 | 208.59375 | 153.4090909090909 | 189.4456762749446 | 256.4020486555698 | 175.3412310069534 | 225.1542575071987 | 203.8167938931298 | 171.9593757740897 | 240.3107401448109 | 149.8129675810474 | 103.9386306388825 | 147.0319208512227 | 76.82225063938618 | 112.2582453517705 | 176.772533022533 | 169.3446088794926 | 160.8947242397637 | 155.7211627476393 | 170.3580967454743 | 254.2595639654463 | 191.2346521145975 | 192.0538970687559 | 179.5019052803484 | 140.2894815108556 | 168.5166528386868 | 172.8512396694215 | 128.1893004115226 | 126.6403162055336 | 143.7692307692308 | 165.0593471810089 | 175.3771228771229 | 216.0086627501743 | 202.8246310306338 | 171.239103362391 | 188.0281690140845 | 273.8461538461539
Analysis |  |  |  |  |  |  |  |  |  |  |  | 2017 | 190.0876232201533 | 194.493006993007 | 92.56548536209553 | 202.2727272727273 | 113.7784090909091 | 136.7477592829705 | 158.300395256917 | 86.6883116883117 | 257.8977272727273 | 235.2272727272727 | 180.5654101995566 | 219.3661971830986 | 216.5979912438836 | 249.8663101604278 | 224.6616932685635 | 166.9990091652217 | 157.0746178600161 | 193.6975742462027 | 132.9803068468056 | 128.3414224379317 | 261.5060451057893 | 311.2048023918528 | 153.0011655011655 | 207.4994127319709 | 243.4731423098412 | 169.9338085539715 | 181.5832426550599 | 127.4043603455368 | 210.2753317623713 | 188.4472511144131 | 221.6521502449646 | 283.2259343709725 | 189.877918691478 | 194.9173553719008 | 163.1500187055742 | 229.9124788255223 | 188.5804195804196 | 205.8740221203129 | 192.7147852147853 | 172.8069302001394 | 158.1204266402083 | 164.5890410958904 | 165.2368758002561 | 56.01398601398601
 | Now Deseasonalize the Sales Using Seasonal Indices
 |  |  |  |  |  |  |  |  |  |  |  | Year | Season | Cumulative Season (X) | Sales (Y) |  | sum x^2 | sum y^2 | sum x*y
 | Year | Spring | Summer | Fall | Winter |  |  |  |  |  |  | 2015 | 1 | 1 | 248.5854326396495 |  | 1 | 61794.71732064172 | 248.5854326396495
 | 1999 | 642.6136363636364 | 650.717213114754 | 655.6985294117648 | 647.6123595505618 |  |  |  |  |  |  |  | 2 | 2 | 264.5203962703963 |  | 4 | 69971.0400430475 | 529.0407925407926
 | 2000 | 729.1193181818182 | 722.02868852459 | 719.6691176470588 | 733.1460674157303 |  |  |  |  |  |  |  | 3 | 3 | 349.7049306625578 |  | 9 | 122293.5385297044 | 1049.114791987673
 | 2001 | 803.2670454545455 | 802.2540983606557 | 799.6323529411765 | 794.2415730337078 |  |  |  |  |  |  |  | 4 | 4 | 275.1012121212121 |  | 16 | 75680.67691056016 | 1100.404848484849
 |  |  |  |  |  |  |  |  |  |  |  |  | 5 | 5 | 323.4910682702511 |  | 25 | 104646.4712506283 | 1617.455341351256
 |  |  |  |  |  |  |  |  |  |  |  |  | 6 | 6 | 291.7094896331739 |  | 36 | 85094.42634204676 | 1750.256937799043
 | Is there a trend in the data? |  |  | Let us check the trend with linear regression. |  |  |  |  |  |  |  |  | 7 | 7 | 300.1343124384641 |  | 49 | 90080.6055029096 | 2100.940187069249
 |  |  |  |  |  |  |  |  |  |  |  |  | 8 | 8 | 328.6055515630615 |  | 64 | 107981.6085180638 | 2628.844412504492
 |  |  | Cumulative |  |  |  |  |  |  |  |  |  | 9 | 9 | 140.3319602272727 |  | 81 | 19693.05906122885 | 1262.987642045455
 | Year | Season | Season (x) | Sales (y) |  | sum x^2 | sum y^2 | sum x*y |  |  |  |  | 10 | 10 | 218.1899897854954 |  | 100 | 47606.87164259458 | 2181.899897854954
 | 1999 | 1 | 1 | 642.6136363636364 |  | 1 | 412952.2856404959 | 642.6136363636364 |  |  |  |  | 11 | 11 | 236.8159645232816 |  | 121 | 56081.80105309217 | 2604.975609756098
 |  | 2 | 2 | 650.717213114754 |  | 4 | 423432.8914438322 | 1301.434426229508 |  |  |  |  | 12 | 12 | 131.054844216816 |  | 144 | 17175.37219269392 | 1572.658130601792
 |  | 3 | 3 | 655.6985294117648 |  | 9 | 429940.5614727509 | 1967.095588235294 |  |  |  |  | 13 | 13 | 214.8870074684522 |  | 169 | 46176.42597874664 | 2793.531097089879
 |  | 4 | 4 | 647.6123595505618 |  | 16 | 419401.7682426461 | 2590.449438202247 |  |  |  |  | 14 | 14 | 131.8025503907857 |  | 196 | 17371.9122895156 | 1845.235705471
 | 2000 | 1 | 5 | 729.1193181818182 |  | 25 | 531614.9801459195 | 3645.596590909091 |  |  |  |  | 15 | 15 | 178.3463740458015 |  | 225 | 31807.42913528495 | 2675.195610687023
 |  | 2 | 6 | 722.02868852459 |  | 36 | 521325.4270525395 | 4332.17213114754 |  |  |  |  | 16 | 16 | 267.8698290810008 |  | 256 | 71754.24533188457 | 4285.917265296012
 |  | 3 | 7 | 719.6691176470588 |  | 49 | 517923.6388948961 | 5037.683823529412 |  |  |  |  | 17 | 17 | 209.4406677393403 |  | 289 | 43865.39330310075 | 3560.491351568785
 |  | 4 | 8 | 733.1460674157303 |  | 64 | 537503.1561671505 | 5865.168539325842 |  |  |  |  | 18 | 18 | 263.3175017002948 |  | 324 | 69336.10670168474 | 4739.715030605306
 | 2001 | 1 | 9 | 803.2670454545455 |  | 81 | 645237.9463132749 | 7229.40340909091 |  |  |  |  | 19 | 19 | 369.9130982367758 |  | 361 | 136835.7002471305 | 7028.34886649874
 |  | 2 | 10 | 802.2540983606557 |  | 100 | 643611.6383364686 | 8022.540983606557 |  |  |  |  | 20 | 20 | 331.4572521933918 |  | 400 | 109863.9100315937 | 6629.145043867837
 |  | 3 | 11 | 799.6323529411765 |  | 121 | 639411.8998702422 | 8795.95588235294 |  |  |  |  | 21 | 21 | 268.4999418739828 |  | 441 | 72092.21878633213 | 5638.498779353638
 |  | 4 | 12 | 794.2415730337078 |  | 144 | 630819.6763350586 | 9530.898876404493 |  |  |  |  | 22 | 22 | 183.3620013080445 |  | 484 | 33621.62352369131 | 4033.964028776978
 |  |  |  |  |  |  |  |  |  |  |  |  | 23 | 23 | 277.0548594923595 |  | 529 | 76759.39516833104 | 6372.261768324268
 |  | Total | 78 | 8700 |  | 650 | 6353175.869915275 | 58961.01332539748 |  |  |  |  | 24 | 24 | 229.9827734711456 |  | 576 | 52892.07609348026 | 5519.586563307494
 |  |  |  |  |  |  |  |  |  |  |  |  | 25 | 25 | 202.4578976773884 |  | 625 | 40989.20033194789 | 5061.447441934711
 |  |  |  |  |  |  |  |  |  |  |  |  | 26 | 26 | 281.1737409738938 |  | 676 | 79058.6726132543 | 7310.517265321238
 | By linear regression equations: |  |  | b | a |  |  |  |  |  |  |  | 27 | 27 | 254.8863883668019 |  | 729 | 64967.07097467216 | 6881.932485903651 |  |  | b | a
 |  |  |  | 16.86023304473761 | 615.4084852092055 |  |  |  |  |  |  |  | 28 | 28 | 225.1626902509256 |  | 784 | 50698.23708103425 | 6304.555327025915 |  |  | 3.761356883075647 | -143.5497890826821
 |  |  |  | Sales=b(Season)+a |  |  |  |  |  |  |  |  | 29 | 29 | 205.3158873868287 |  | 841 | 42154.61361344094 | 5954.160734218033 |  |  | Sales=b(Season)+a
 |  |  |  |  |  |  |  |  |  |  |  |  | 30 | 30 | 226.3255099284074 |  | 900 | 51223.23644435362 | 6789.765297852221
 | You may need to check r^2 to decide on the goodness of the fit. |  |  |  |  |  |  |  |  |  |  |  | 31 | 31 | 205.6718290691345 |  | 961 | 42300.90127264327 | 6375.826701143169
 |  |  |  |  |  |  |  |  |  |  |  |  | 32 | 32 | 183.3096312084862 |  | 1024 | 33602.4208937912 | 5865.908198671557
 |  |  |  |  |  |  |  |  |  |  |  |  | 33 | 33 | 248.432914543084 |  | 1089 | 61718.91302837129 | 8198.286179921774
 | Let us generate the deseasoned forecasts for 2002 |  |  |  |  |  |  |  |  |  |  |  | 34 | 34 | 239.0585399449036 |  | 1156 | 57148.98552058907 | 8127.990358126723
 |  |  |  |  |  |  |  |  |  |  |  |  | 35 | 35 | 315.4906783888266 |  | 1225 | 99534.368150242 | 11042.17374360893
 | Year | Spring | Summer | Fall | Winter |  |  |  |  |  |  |  | 36 | 36 | 250.2747600225862 |  | 1296 | 62637.45550436309 | 9009.8913608131
 | 2002 | 834.5915147907945 | 851.451747835532 | 868.3119808802696 | 885.1722139250073 |  |  |  |  |  |  |  | 37 | 37 | 274.4788111888112 |  | 1369 | 75338.61779162308 | 10155.71601398602
 |  |  |  |  |  |  |  |  |  |  |  |  | 38 | 38 | 235.8936471540329 |  | 1444 | 55645.81276763138 | 8963.95859185325
 |  |  |  |  |  |  |  |  |  |  |  |  | 39 | 39 | 238.7352147852148 |  | 1521 | 56994.50277854264 | 9310.673376623377
 | Seasonality indices | 0.8091954022988506 | 1.12183908045977 | 1.250574712643678 | 0.8183908045977012 |  |  |  |  |  |  |  | 40 | 40 | 218.010753758837 |  | 1600 | 47528.68875449627 | 8720.43015035348
 |  |  |  |  |  |  |  |  |  |  |  |  | 41 | 41 | 245.8823328785812 |  | 1681 | 60458.1216218134 | 10081.17564802183
 |  |  |  |  |  |  |  |  |  |  |  |  | 42 | 42 | 271.0001867995019 |  | 1764 | 73441.10124536492 | 11382.00784557908
Output: | Let us generate the seasonalized forecasts for 2002 |  |  |  |  |  |  |  |  |  |  |  | 43 | 43 | 253.5626333760137 |  | 1849 | 64294.00904457871 | 10903.19323516859
 |  |  |  |  |  |  |  |  |  |  |  |  | 44 | 44 | 276.9684149184149 |  | 1936 | 76711.50286241923 | 12186.61025641026
 | Year | Spring | Summer | Fall | Winter |  |  |  |  |  |  | 2016 | 1 | 45 | 168.1607338444688 |  | 2025 | 28278.03240711027 | 7567.233023001095
 | 2002 | 675.3476165663441 | 955.1918458476774 | 1085.889005974406 | 724.4168003616153 |  |  |  |  |  |  |  | 2 | 46 | 147.8202214452214 |  | 2116 | 21850.81786811431 | 6799.730186480187
 |  |  |  |  |  |  |  |  |  |  |  |  | 3 | 47 | 164.5670261941448 |  | 2209 | 27082.30611038435 | 7734.650231124807
 |  |  |  |  |  |  |  |  |  |  |  |  | 4 | 48 | 129.4593939393939 |  | 2304 | 16759.73467915519 | 6214.050909090909
 |  |  |  |  |  |  |  |  |  |  |  |  | 5 | 49 | 170.0099044923948 |  | 2401 | 28903.36762551319 | 8330.485320127344
 |  |  |  |  |  |  |  |  |  |  |  |  | 6 | 50 | 178.8583732057416 |  | 2500 | 31990.31766580436 | 8942.918660287081
 |  |  |  |  |  |  |  |  |  |  |  |  | 7 | 51 | 148.9717755169019 |  | 2601 | 22192.58990065821 | 7597.560551361996
 |  |  |  |  |  |  |  |  |  |  |  |  | 8 | 52 | 191.8864534674811 |  | 2704 | 36820.4110243278 | 9978.09558030902
 |  |  |  |  |  |  |  |  |  |  |  |  | 9 | 53 | 208.6015625 |  | 2809 | 43514.61187744141 | 11055.8828125
 |  |  |  |  |  |  |  |  |  |  |  |  | 10 | 54 | 153.4148365679264 |  | 2916 | 23536.11207916358 | 8284.401174668028
 |  |  |  |  |  |  |  |  |  |  |  |  | 11 | 55 | 189.4527716186253 |  | 3025 | 35892.352673979 | 10419.90243902439
 |  |  |  |  |  |  |  |  |  |  |  |  | 12 | 56 | 256.4116517285531 |  | 3136 | 65746.93514216482 | 14359.05249679897
 |  |  |  |  |  |  |  |  |  |  |  |  | 13 | 57 | 175.347798094257 |  | 3249 | 30746.85029650433 | 9994.82449137265
 |  |  |  |  |  |  |  |  |  |  |  |  | 14 | 58 | 225.1626902509256 |  | 3364 | 50698.23708103425 | 13059.43603455368
 |  |  |  |  |  |  |  |  |  |  |  |  | 15 | 59 | 203.824427480916 |  | 3481 | 41544.3972379232 | 12025.64122137405
 |  |  |  |  |  |  |  |  |  |  |  |  | 16 | 60 | 171.9658162001486 |  | 3600 | 29572.2419413833 | 10317.94897200892
 |  |  |  |  |  |  |  |  |  |  |  |  | 17 | 61 | 240.3197405470636 |  | 3721 | 57753.57769660796 | 14659.50417337088
 |  |  |  |  |  |  |  |  |  |  |  |  | 18 | 62 | 149.818578553616 |  | 3844 | 22445.606479826 | 9288.75187032419
 |  |  |  |  |  |  |  |  |  |  |  |  | 19 | 63 | 103.9425234714907 |  | 3969 | 10804.0481856214 | 6548.378978703916
 |  |  |  |  |  |  |  |  |  |  |  |  | 20 | 64 | 147.0374276647377 |  | 4096 | 21620.00513426298 | 9410.395370543214
 |  |  |  |  |  |  |  |  |  |  |  |  | 21 | 65 | 76.82512787723785 |  | 4225 | 5902.100273353948 | 4993.63331202046
 |  |  |  |  |  |  |  |  |  |  |  |  | 22 | 66 | 112.2624497804354 |  | 4356 | 12602.85763070478 | 7409.321685508736
 |  |  |  |  |  |  |  |  |  |  |  |  | 23 | 67 | 176.7791537166537 |  | 4489 | 31250.86918877628 | 11844.2032990158
 |  |  |  |  |  |  |  |  |  |  |  |  | 24 | 68 | 169.3509513742072 |  | 4624 | 28679.74473134909 | 11515.86469344609
 |  |  |  |  |  |  |  |  |  |  |  |  | 25 | 69 | 160.9007502593982 |  | 4761 | 25889.05143403723 | 11102.15176789847
 |  |  |  |  |  |  |  |  |  |  |  |  | 26 | 70 | 155.7269950009258 |  | 4900 | 24250.89697201836 | 10900.8896500648
 |  |  |  |  |  |  |  |  |  |  |  |  | 27 | 71 | 170.364477198536 |  | 5041 | 29024.05509113049 | 12095.87788109605
 |  |  |  |  |  |  |  |  |  |  |  |  | 28 | 72 | 254.2690867955574 |  | 5184 | 64652.7684998467 | 18307.37424928013
 |  |  |  |  |  |  |  |  |  |  |  |  | 29 | 73 | 191.2418144611187 |  | 5329 | 36573.43159838095 | 13960.65245566167
 |  |  |  |  |  |  |  |  |  |  |  |  | 30 | 74 | 192.0610900986086 |  | 5476 | 36887.46232986587 | 14212.52066729704
 |  |  |  |  |  |  |  |  |  |  |  |  | 31 | 75 | 179.5086281981492 |  | 5625 | 32223.34759758135 | 13463.14711486119
 |  |  |  |  |  |  |  |  |  |  |  |  | 32 | 76 | 140.2947357985526 |  | 5776 | 19682.61289278567 | 10662.39992069
 |  |  |  |  |  |  |  |  |  |  |  |  | 33 | 77 | 168.5229643238118 |  | 5929 | 28399.98950448474 | 12976.26825293351
 |  |  |  |  |  |  |  |  |  |  |  |  | 34 | 78 | 172.8577134986226 |  | 6084 | 29879.78911597189 | 13482.90165289256
 |  |  |  |  |  |  |  |  |  |  |  |  | 35 | 79 | 128.1941015089163 |  | 6241 | 16433.72766167835 | 10127.33401920439
 |  |  |  |  |  |  |  |  |  |  |  |  | 36 | 80 | 126.6450592885376 |  | 6400 | 16038.9710421972 | 10131.60474308301
 |  |  |  |  |  |  |  |  |  |  |  |  | 37 | 81 | 143.7746153846154 |  | 6561 | 20671.14002899409 | 11645.74384615385
 |  |  |  |  |  |  |  |  |  |  |  |  | 38 | 82 | 165.0655291790307 |  | 6724 | 27246.62892315343 | 13535.37339268052
 |  |  |  |  |  |  |  |  |  |  |  |  | 39 | 83 | 175.3836913086913 |  | 6889 | 30759.43917706233 | 14556.84637862138
 |  |  |  |  |  |  |  |  |  |  |  |  | 40 | 84 | 216.0167529622623 |  | 7056 | 46663.23756035905 | 18145.40724883003
 |  |  |  |  |  |  |  |  |  |  |  |  | 41 | 85 | 202.8322274587622 |  | 7225 | 41140.91249588307 | 17240.73933399479
 |  |  |  |  |  |  |  |  |  |  |  |  | 42 | 86 | 171.2455168119552 |  | 7396 | 29325.02702819362 | 14727.11444582814
 |  |  |  |  |  |  |  |  |  |  |  |  | 43 | 87 | 188.0352112676056 |  | 7569 | 35357.24067645308 | 16359.06338028169
 |  |  |  |  |  |  |  |  |  |  |  |  | 44 | 88 | 273.8564102564102 |  | 7744 | 74997.33343852728 | 24099.3641025641
 |  |  |  |  |  |  |  |  |  |  |  | 2017 | 1 | 89 | 190.0947426067908 |  | 7921 | 36136.01116674204 | 16918.43209200438
 |  |  |  |  |  |  |  |  |  |  |  |  | 2 | 90 | 194.5002913752914 |  | 8100 | 37830.36334507325 | 17505.02622377623
 |  |  |  |  |  |  |  |  |  |  |  |  | 3 | 91 | 92.56895223420646 |  | 8281 | 8569.010917738799 | 8423.774653312788
 |  |  |  |  |  |  |  |  |  |  |  |  | 4 | 92 | 202.280303030303 |  | 8464 | 40917.32099403122 | 18609.78787878788
 |  |  |  |  |  |  |  |  |  |  |  |  | 5 | 93 | 113.3399363282632 |  | 8649 | 12845.94116689475 | 10540.61407852848
 |  |  |  |  |  |  |  |  |  |  |  |  | 6 | 94 | 136.2730462519936 |  | 8836 | 18570.343134798 | 12809.6663476874
 |  |  |  |  |  |  |  |  |  |  |  |  | 7 | 95 | 157.7348211355432 |  | 9025 | 24880.2737986618 | 14984.8080078766
 |  |  |  |  |  |  |  |  |  |  |  |  | 8 | 96 | 86.34890406036651 |  | 9216 | 7456.133232426379 | 8289.494789795184
 |  |  |  |  |  |  |  |  |  |  |  |  | 9 | 97 | 257.9073863636364 |  | 9409 | 66516.219940922 | 25017.01647727273
 |  |  |  |  |  |  |  |  |  |  |  |  | 10 | 98 | 235.2360827374872 |  | 9604 | 55336.01462167792 | 23053.13610827375
 |  |  |  |  |  |  |  |  |  |  |  |  | 11 | 99 | 180.5721729490022 |  | 9801 | 32606.30964352436 | 17876.64512195122
 |  |  |  |  |  |  |  |  |  |  |  |  | 12 | 100 | 219.3744131455399 |  | 10000 | 48125.13314295003 | 21937.44131455399
 |  |  |  |  |  |  |  |  |  |  |  |  | 13 | 101 | 216.6061035281998 |  | 10201 | 46918.20408566923 | 21877.21645634818
 |  |  |  |  |  |  |  |  |  |  |  |  | 14 | 102 | 249.8756684491979 |  | 10404 | 62437.84968293345 | 25487.31818181818
 |  |  |  |  |  |  |  |  |  |  |  |  | 15 | 103 | 224.6701075641915 |  | 10609 | 50476.6572329054 | 23141.02107911173
 |  |  |  |  |  |  |  |  |  |  |  |  | 16 | 104 | 167.0052638097597 |  | 10816 | 27890.75814016744 | 17368.54743621501
 |  |  |  |  |  |  |  |  |  |  |  |  | 17 | 105 | 157.0805008045052 |  | 11025 | 24674.28373299418 | 16493.45258447305
 |  |  |  |  |  |  |  |  |  |  |  |  | 18 | 106 | 193.7048288369984 |  | 11236 | 37521.56071477087 | 20532.71185672183
 |  |  |  |  |  |  |  |  |  |  |  |  | 19 | 107 | 132.9852873826426 |  | 11449 | 17685.08666024403 | 14229.42574994275
 |  |  |  |  |  |  |  |  |  |  |  |  | 20 | 108 | 128.3462292327795 |  | 11664 | 16472.75455827319 | 13861.39275714019
 |  |  |  |  |  |  |  |  |  |  |  |  | 21 | 109 | 261.5158393396885 |  | 11881 | 68390.53422554175 | 28505.22648802604
 |  |  |  |  |  |  |  |  |  |  |  |  | 22 | 110 | 311.2164580024292 |  | 12100 | 96855.68373157781 | 34233.81038026722
 |  |  |  |  |  |  |  |  |  |  |  |  | 23 | 111 | 153.0068958818959 |  | 12321 | 23411.11018741332 | 16983.76544289044
 |  |  |  |  |  |  |  |  |  |  |  |  | 24 | 112 | 207.5071842455563 |  | 12544 | 43059.23151351927 | 23240.80463550231
 |  |  |  |  |  |  |  |  |  |  |  |  | 25 | 113 | 243.4822611541224 |  | 12769 | 59283.61149672428 | 27513.49551041583
 |  |  |  |  |  |  |  |  |  |  |  |  | 26 | 114 | 169.9401731160896 |  | 12996 | 28879.66243872651 | 19373.17973523422
 |  |  |  |  |  |  |  |  |  |  |  |  | 27 | 115 | 181.5900435255713 |  | 13225 | 32974.94390761888 | 20882.8550054407
 |  |  |  |  |  |  |  |  |  |  |  |  | 28 | 116 | 127.4091320444262 |  | 13456 | 16233.08692831402 | 14779.45931715344
 |  |  |  |  |  |  |  |  |  |  |  |  | 29 | 117 | 210.2832072429617 |  | 13689 | 44219.02724838637 | 24603.13524742651
 |  |  |  |  |  |  |  |  |  |  |  |  | 30 | 118 | 188.454309063893 |  | 13924 | 35515.0266047493 | 22237.60846953937
 |  |  |  |  |  |  |  |  |  |  |  |  | 31 | 119 | 221.6604518236255 |  | 14161 | 49133.3559026538 | 26377.59376701143
 |  |  |  |  |  |  |  |  |  |  |  |  | 32 | 120 | 283.2365420838703 |  | 14400 | 80222.93877162803 | 33988.38505006443
 |  |  |  |  |  |  |  |  |  |  |  |  | 33 | 121 | 189.8850302240133 |  | 14641 | 36056.32470317443 | 22976.0886571056
 |  |  |  |  |  |  |  |  |  |  |  |  | 34 | 122 | 194.9246556473829 |  | 14884 | 37995.62137925081 | 23780.80798898072
 |  |  |  |  |  |  |  |  |  |  |  |  | 35 | 123 | 163.1561291931662 |  | 15129 | 26619.92249329715 | 20068.20389075945
 |  |  |  |  |  |  |  |  |  |  |  |  | 36 | 124 | 229.9210897797855 |  | 15376 | 52863.70752552417 | 28510.2151326934
 |  |  |  |  |  |  |  |  |  |  |  |  | 37 | 125 | 188.5874825174825 |  | 15625 | 35565.23856228177 | 23573.43531468532
 |  |  |  |  |  |  |  |  |  |  |  |  | 38 | 126 | 205.8817327578455 |  | 15876 | 42387.28788337293 | 25941.09832748854
 |  |  |  |  |  |  |  |  |  |  |  |  | 39 | 127 | 192.722002997003 |  | 16129 | 37141.77043917683 | 24475.69438061938
 |  |  |  |  |  |  |  |  |  |  |  |  | 40 | 128 | 172.8134023698098 |  | 16384 | 29864.4720386298 | 22120.11550333566
 |  |  |  |  |  |  |  |  |  |  |  |  | 41 | 129 | 158.1263487535657 |  | 16641 | 25003.94217013428 | 20398.29898920997
 |  |  |  |  |  |  |  |  |  |  |  |  | 42 | 130 | 164.5952054794521 |  | 16900 | 27091.58166682305 | 21397.37671232877
 |  |  |  |  |  |  |  |  |  |  |  |  | 43 | 131 | 165.2430644472898 |  | 17161 | 27305.27034793116 | 21646.84144259496
 |  |  |  |  |  |  |  |  |  |  |  |  | 44 | 132 | 56.01608391608391 |  | 17424 | 3137.801657293755 | 7394.123076923077
 |  |  |  |  |  |  |  |  |  |  |  |  | Total | 8778 | 26701.00000000001 |  | 775390 | 5842285.628990074 | 1656438.465000242
 |  |  |  |  |  |  |  |  |  |  |  | Year | Season | Cumulative Season (X) | Sales (Y) |  | Seasonal Indices | Forecast
 |  |  |  |  |  |  |  |  |  |  |  | 2017 | 1 | 133 | 356.7106763663789 |  | 0.1367739035991161 | 48.78871166211064
 |  |  |  |  |  |  |  |  |  |  |  |  | 2 | 134 | 360.4720332494546 |  | 0.1285345118160368 | 46.33309681705285
 |  |  |  |  |  |  |  |  |  |  |  |  | 3 | 135 | 364.2333901325302 |  | 0.09722482304033557 | 35.41252690101675
 |  |  |  |  |  |  |  |  |  |  |  |  | 4 | 136 | 367.9947470156059 |  | 0.1235908767461893 | 45.48079342165085
 |  |  |  |  |  |  |  |  |  |  |  |  | 5 | 137 | 371.7561038986815 |  | 0.1058761844125688 | 39.3601178128749
 |  |  |  |  |  |  |  |  |  |  |  |  | 6 | 138 | 375.5174607817572 |  | 0.1174113329088798 | 44.09000560094412
 |  |  |  |  |  |  |  |  |  |  |  |  | 7 | 139 | 379.2788176648329 |  | 0.1141155761956481 | 43.28162081662656
 |  |  |  |  |  |  |  |  |  |  |  |  | 8 | 140 | 383.0401745479085 |  | 0.104228306055953 | 39.92362854450504
 |  |  |  |  |  |  |  |  |  |  |  |  | 9 | 141 | 386.8015314309841 |  | 0.2636605370585371 | 101.9842995121579
 |  |  |  |  |  |  |  |  |  |  |  |  | 10 | 142 | 390.5628883140598 |  | 0.2933223474776226 | 114.5608232379206
 |  |  |  |  |  |  |  |  |  |  |  |  | 11 | 143 | 394.3242451971354 |  | 0.3378150631062507 | 133.208669775595
 |  |  |  |  |  |  |  |  |  |  |  |  | 12 | 144 | 398.0856020802111 |  | 0.3509980899591776 | 139.7272859704033
 |  |  |  |  |  |  |  |  |  |  |  |  | 13 | 145 | 401.8469589632867 |  | 0.5817010598853976 | 233.7548019406678
 |  |  |  |  |  |  |  |  |  |  |  |  | 14 | 146 | 405.6083158463624 |  | 0.3641811168121044 | 147.714889453205
 |  |  |  |  |  |  |  |  |  |  |  |  | 15 | 147 | 409.369672729438 |  | 0.4317441294333546 | 176.7429529689885
 |  |  |  |  |  |  |  |  |  |  |  |  | 16 | 148 | 413.1310296125137 |  | 0.6047713568780195 | 249.8498133471732
 |  |  |  |  |  |  |  |  |  |  |  |  | 17 | 149 | 416.8923864955893 |  | 0.7448410171903673 | 310.5185492162945
 |  |  |  |  |  |  |  |  |  |  |  |  | 18 | 150 | 420.653743378665 |  | 0.6607992210029586 | 277.9676659366003
 |  |  |  |  |  |  |  |  |  |  |  |  | 19 | 151 | 424.4151002617406 |  | 1.308415415152991 | 555.3112596061634
 |  |  |  |  |  |  |  |  |  |  |  |  | 20 | 152 | 428.1764571448163 |  | 1.605033519343845 | 687.2375659113235
 |  |  |  |  |  |  |  |  |  |  |  |  | 21 | 153 | 431.9378140278919 |  | 1.2886408748736 | 556.6127225598931
 |  |  |  |  |  |  |  |  |  |  |  |  | 22 | 154 | 435.6991709109675 |  | 1.603385640987229 | 698.5937944286858
 |  |  |  |  |  |  |  |  |  |  |  |  | 23 | 155 | 439.4605277940432 |  | 2.313621212688663 | 1016.745199243654
 |  |  |  |  |  |  |  |  |  |  |  |  | 24 | 156 | 443.2218846771189 |  | 1.91318677203101 | 847.9662468389176
 |  |  |  |  |  |  |  |  |  |  |  |  | 25 | 157 | 446.9832415601945 |  | 1.876933448185461 | 838.957796862691
 |  |  |  |  |  |  |  |  |  |  |  |  | 26 | 158 | 450.7445984432701 |  | 1.618216546196771 | 729.4023673097191
 |  |  |  |  |  |  |  |  |  |  |  |  | 27 | 159 | 454.5059553263458 |  | 1.514400209729972 | 688.3039140697396
 |  |  |  |  |  |  |  |  |  |  |  |  | 28 | 160 | 458.2673122094214 |  | 1.820905584060522 | 834.4615077945422
 |  |  |  |  |  |  |  |  |  |  |  |  | 29 | 161 | 462.0286690924971 |  | 1.207894835399423 | 558.0820432032964
 |  |  |  |  |  |  |  |  |  |  |  |  | 30 | 162 | 465.7900259755727 |  | 2.218044268004944 | 1033.142897208993
 |  |  |  |  |  |  |  |  |  |  |  |  | 31 | 163 | 469.5513828586484 |  | 1.375978427774241 | 646.0925735450635
 |  |  |  |  |  |  |  |  |  |  |  |  | 32 | 164 | 473.312739741724 |  | 1.511104453016741 | 715.224988693273
 |  |  |  |  |  |  |  |  |  |  |  |  | 33 | 165 | 477.0740966247997 |  | 1.263922699524362 | 602.9847800791633
 |  |  |  |  |  |  |  |  |  |  |  |  | 34 | 166 | 480.8354535078753 |  | 1.087599715366466 | 522.9565023732706
 |  |  |  |  |  |  |  |  |  |  |  |  | 35 | 167 | 484.596810390951 |  | 1.20130332197296 | 582.1477581401499
 |  |  |  |  |  |  |  |  |  |  |  |  | 36 | 168 | 488.3581672740266 |  | 1.326542077075765 | 647.8276575726011
 |  |  |  |  |  |  |  |  |  |  |  |  | 37 | 169 | 492.1195241571022 |  | 1.606681397700461 | 790.6792849084186
 |  |  |  |  |  |  |  |  |  |  |  |  | 38 | 170 | 495.8808810401779 |  | 1.666005018538631 | 826.1400364102944
 |  |  |  |  |  |  |  |  |  |  |  |  | 39 | 171 | 499.6422379232536 |  | 1.49956930452043 | 749.2481632316045
 |  |  |  |  |  |  |  |  |  |  |  |  | 40 | 172 | 503.4035948063292 |  | 1.504512939590277 | 757.3772222223834
 |  |  |  |  |  |  |  |  |  |  |  |  | 41 | 173 | 507.1649516894048 |  | 1.207894835399423 | 612.60192584123
 |  |  |  |  |  |  |  |  |  |  |  |  | 42 | 174 | 510.9263085724805 |  | 1.202951200329576 | 614.6194161772246
 |  |  |  |  |  |  |  |  |  |  |  |  | 43 | 175 | 514.6876654555562 |  | 1.052994269877533 | 541.9631625013452
 |  |  |  |  |  |  |  |  |  |  |  |  | 44 | 176 | 518.4490223386318 |  | 0.6426725590801843 | 333.1929599389882