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Course: H ADM 301, Fall 2007School: Cornell
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A Q1 B2 C D E Forecast for October 2006 Nave Moving Average (four periods) Weighted moving average (0.7, 0.3) Weighted moving average (0.5, 0.3, 0.2) Exponential smoothing (alpha = 0.65) Forecast 702 636 724.5 702.7 698.8 BIAS 13 34 20 25 19 MAD 134 172 133 140 129 MSE 24,784 40,342 24,800 29,041 24,760 Q2 A B C Q3 A B Q4 Best method If biis is the criteria: Nave method if MAD is the criteria: Exponential...
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A Q1 B2 C D E
Forecast for October 2006 Nave Moving Average (four periods) Weighted moving average (0.7, 0.3) Weighted moving average (0.5, 0.3, 0.2) Exponential smoothing (alpha = 0.65) Forecast 702 636 724.5 702.7 698.8 BIAS 13 34 20 25 19 MAD 134 172 133 140 129 MSE 24,784 40,342 24,800 29,041 24,760
Q2 A B C Q3 A B Q4
Best method If biis is the criteria: Nave method if MAD is the criteria: Exponential smoothing if MSE is the criteria: Exponential smoothing Best weights Best alpha = 0.670 W1 = 1; W2 = 0, W3 = 0 Regression Regression Equation Revenue = -2585.98 + 79.04 (Room Nights)
The model is very good. Adjusted R-Square is 0.928 which means 92.8% of variation is revenue is explained by Ro Prediction for 675 room-nights sold $50,766.02
iation is revenue is explained by Room Nights sold
Data
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August
Room-Nights Sold 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
Revenue $20,492 $19,275 $23,925 $23,983 $30,919 $35,782 $67,037 $52,565 $29,624 $53,288 $41,846 $40,384 $22,481 $16,616 $20,064 $26,910 $32,361 $34,935 $56,702 $46,389 $29,295 $57,443 $39,563 $45,990 $21,804 $15,437 $22,815 $23,865 $31,506 $49,812 $61,189 $45,806
Page 3
Naive
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August September
RoomNights Sold
Nave A-F ABS(A-F) 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702 -50 33 33 102 164 202 -148 -189 271 -178 58 -330 -66 95 8 157 79 186 -76 -238 270 -197 91 -268 -65 87 32 102 121 184 -75 50 33 33 102 164 202 148 189 271 178 58 330 66 95 8 157 79 186 76 238 270 197 91 268 65 87 32 102 121 184 75 A-F)^2 2500 1089 1089 10404 26896 40804 21904 35721 73441 31684 3364 108900 4356 9025 64 24649 6241 34596 5776 56644 72900 38809 8281 71824 4225 7569 1024 10404 14641 33856 5625
307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
BIAS 13
MAD 134
MSE 24,784
Page 4
MA4
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August September
RoomNights Sold Moving Average
4 Time Periods A-F ABS(A-F) A-F)^2
307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
294 324 407 532 612 619 653 592 583 538 409 348 275 324 408 516 602 590 626 565 547 521 411 372 319 358 443 553 636
131 265 384 111 -158 106 -106 13 -308 -329 -105 -36 194 225 326 142 -182 100 -133 19 -231 -270 -73 -2 153 235 334 149
130.8 265.3 384.3 111.0 158.0 105.8 106.3 12.8 307.8 329.0 105.0 36.3 194.0 224.5 325.8 142.3 182.3 100.0 132.5 18.8 230.8 269.8 73.0 2.3 153.3 235.3 333.8 149.0
17095.6 70357.6 147648.1 12321.0 24964.0 11183.1 11289.1 162.6 94710.1 108241.0 11025.0 1314.1 37636.0 50400.3 106113.1 20235.1 33215.1 10000.0 17556.3 351.6 53245.6 72765.1 5329.0 5.1 23485.6 55342.6 111389.1 22201.0
BIAS 34
MAD 172
MSE 40,342
Page 5
WMA2
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August September
RoomNights Sold 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
Wt moving average (0.7, 0.3)
A-F ABS(A-F)
A-F)^2
272 280 313 394 540 730 687 511 644 600 588 374 229 276 310 422 524 678 681 491 609 552 557 396 271 312 360 441 557 722 725
18 43 112 195 251 -87 -233 214 -97 5 -313 -165 75 37 159 126 210 -20 -261 199 -116 32 -241 -145 68 58 112 152 220 -20
18.0 42.9 111.9 194.6 251.2 87.4 233.4 214.3 96.7 4.6 312.6 165.0 75.2 36.5 159.4 126.1 209.7 20.2 260.8 198.6 116.0 31.9 240.7 145.4 67.5 58.1 111.6 151.6 220.3 19.8
324.0 1840.4 12521.6 37869.2 63101.4 7638.8 54475.6 45924.5 9350.9 21.2 97718.8 27225.0 5655.0 1332.3 25408.4 15901.2 43974.1 408.0 68016.6 39442.0 13456.0 1017.6 57936.5 21141.2 4556.3 3375.6 12454.6 22982.6 48532.1 392.0
BIAS 20
MAD 133
MSE 24,800
Page 6
WMA2
WT1 WT2
0.7 0.3
Page 7
WMA3
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August September
RoomNights Sold 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
Wt moving average (0.5, 0.3, 0.2)
A-F ABS(A-F)
A-F)^2
284 300 367 487 657 677 578 627 582 612 428 308 270 289 389 477 625 659 554 538 603 578 432 337 308 337 415 512 661 703
40 125 222 304 -14 -223 147 -80 23 -337 -219 -4 42 180 159 257 33 -239 136 -110 47 -262 -181 1 63 135 178 265 41
39.5 1560.3 125.1 15650.0 221.6 49106.6 304.4 92659.4 14.2 201.6 222.6 49550.8 146.9 21579.6 80.3 6448.1 23.2 538.2 336.6 113299.6 219.4 48136.4 4.0 16.0 42.3 1789.3 180.0 32400.0 159.1 25312.8 256.9 65997.6 32.8 1075.8 238.8 57025.4 135.8 18441.6 109.6 12012.2 46.5 2162.3 261.9 68591.6 180.8 32688.6 0.9 0.8 62.5 3906.3 135.4 18333.2 178.4 31826.6 264.9 70172.0 41.2 1697.4
BIAS 25
MAD 140
MSE 29,041
Page 8
WMA3
WT1 WT2 WT3
0.5 0.3 0.2
Page 9
ES
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August September
RoomNights Sold 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
Exponential smoothing A-F ABS(A-F) 307 307 275 285 310 385 517 695 661 527 656 585 598 388 272 293 305 412 500 652 656 503 624 539 568 404 305 326 355 431 536 693 699 -50 16 38 115 204 274 -52 -207 198 -109 20 -323 -179 32 19 164 136 234 6 -236 187 -131 45 -252 -153 33 44 117 162 241 9 A-F)^2
50.0 2500.0 15.5 240.3 38.4 1476.5 115.4 13328.4 204.4 41782.2 273.5 74825.5 52.3 2731.1 207.3 42969.6 198.4 39381.7 108.5 11781.6 20.0 400.4 323.0 104326.8 179.0 32058.5 32.3 1045.4 19.3 373.1 163.8 26817.6 136.3 18582.1 233.7 54620.7 5.8 33.6 236.0 55682.0 187.4 35122.6 131.4 17267.6 45.0 2025.7 252.2 63628.7 153.3 23496.8 33.3 1112.2 43.7 1907.3 117.3 13755.9 162.0 26260.2 240.7 57944.9 9.3 85.6
BIAS 19
MAD 129
MSE 24,760
Page 10
ES
Alpha
0.65
Page 11
ES_BEST
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August September
RoomNights Sold 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
Exponential smoothing A-F ABS(A-F) 307 307 274 285 310 387 522 702 663 523 658 584 598 382 266 291 305 415 504 658 658 499 627 537 569 399 300 325 355 433 540 699 701 -50 16 38 115 202 269 -59 -209 202 -111 21 -323 -173 38 21 164 133 230 0 -238 191 -134 47 -253 -148 38 45 117 160 237 3 A-F)^2
50.0 2500.0 16.5 271.5 38.4 1478.0 114.7 13157.0 201.9 40765.2 268.7 72209.9 59.2 3504.9 208.6 43498.6 202.1 40836.5 111.2 12370.5 21.2 451.4 323.0 104315.5 172.7 29835.0 37.9 1438.1 20.5 421.5 163.8 26825.4 133.1 17721.6 230.0 52895.5 0.0 0.0 238.0 56644.0 191.4 36616.0 133.8 17893.8 46.8 2189.9 252.5 63774.5 148.5 22037.5 37.9 1439.8 44.5 1983.7 116.7 13623.0 159.6 25462.4 236.7 56040.9 3.2 10.4
BIAS 19
MAD 128
MSE 24,587
Page 12
ES_BEST
Alpha
0.670
Page 13
WMA3_BEST
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August September
RoomNights Sold 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
Wt moving average (0.5, 0.3, 0.2)
A-F ABS(A-F)
A-F)^2
290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
33 102 164 202 -148 -189 271 -178 58 -330 -66 95 8 157 79 186 -76 -238 270 -197 91 -268 -65 87 32 102 121 184 -75
33.0 1089.0 102.0 10404.0 164.0 26896.0 202.0 40804.0 148.0 21904.0 189.0 35721.0 271.0 73441.0 178.0 31684.0 58.0 3364.0 330.0 108900.0 66.0 4356.0 95.0 9025.0 8.0 64.0 157.0 24649.0 79.0 6241.0 186.0 34596.0 76.0 5776.0 238.0 56644.0 270.0 72900.0 197.0 38809.0 91.0 8281.0 268.0 71824.0 65.0 4225.0 87.0 7569.0 32.0 1024.0 102.0 10404.0 121.0 14641.0 184.0 33856.0 75.0 5625.0
BIAS 14
MAD 140
MSE 26,370
Page 14
WMA3_BEST
WT1 WT2 WT3 Sum Wts
1 0 0 1
Page 15
REGRESSION
Month 2005 January February March April May June July August September October November December 2006 January February March April May June July August September October November December 2007 January February March April May June July August
Room-Nights Sold 307 257 290 323 425 589 791 643 454 725 547 605 275 209 304 312 469 548 734 658 420 690 493 584 316 251 338 370 472 593 777 702
Revenue $20,492 $19,275 $23,925 $23,983 $30,919 $35,782 $67,037 $52,565 $29,624 $53,288 $41,846 $40,384 $22,481 $16,616 $20,064 $26,910 $32,361 $34,935 $56,702 $46,389 $29,295 $57,443 $39,563 $45,990 $21,804 $15,437 $22,815 $23,865 $31,506 $49,812 $61,189 $45,806
Page 16
REGRESSION
SUMMARY OUTPUT Regression Statistics Multiple R 0.96 R Square 0.93 Adjusted R Square 0.93 Standard Error 3850.35 Observations 32 ANOVA df Regression Residual Total 1 30 31 SS ### ### ### MS ### ### F Significance F 402.56 0
Intercept Room-Nights Sold
Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0% -2585.98 2022.59 -1.28 0.21 -6716.67 1544.7 -6716.67 79.04 3.94 20.06 0 71 87.09 71
Page 17
REGRESSION
Upper 95.0% 1544.7 87.09
Page 18
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Homework 9 6. Many observations have been made about planetary motion that support the idea that the solar system formed from a rotating cloud of interstellar gas. On clear nights Ptolemy observed dim white patches of light and a rotating cloud of in
Cornell - PHYS - 203
Homework 10 1. Herschel classified nebulae into several categories as follows: I. Bright Nebulae II. Faint Nebulae III. Very faint Nebulae IV. Planetary Nebulae V. Very large Nebulae VI. Very compressed and rich star clusters VII. Compressed clusters