| Date post: | 15-Jan-2016 |
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ForecastingSuppose your fraternity/sorority house consumed the following number of cases of beer for the last 6 weekends:8, 5, 7, 3, 6, 9How many cases do you think your fraternity/sorority will consume this weekend?
Chart1
8
5
7
3
6
9
Cases
Week
Cases
Sheet1
WeekCases
18
25
37
43
56
69
Sheet1
Cases
Week
Cases
Sheet2
Sheet3
ForecastingWe could use a Moving Average forecasting methodUsing a three period moving average, we would get the following forecast:3 + 6 + 9 = 63
Chart2
81
52
73
34
65
96
76
Cases
Forecast
Week
Cases
Sheet1
WeekCasesForecast
18
25
37
43
56
69
76
Sheet1
Cases
Week
Cases
Sheet2
Cases
Forecast
Week
Cases
Sheet3
ForecastingWhat if we used a two period moving average?6 + 9 = 7.52
Chart3
81
52
73
34
65
96
77.5
Cases
Forecast
Week
Cases
Sheet1
WeekCasesForecast
18
25
37
43
56
69
77.5
Sheet1
Cases
Week
Cases
Sheet2
Cases
Forecast
Week
Cases
Sheet3
ForecastingThe number of periods used in the moving average forecast affects the responsiveness of the forecasting method:1 Period2 Period3 Period
Chart5
8111
5222
7333
3444
6555
9666
767.59
Week
Cases
Sheet1
WeekCasesForecast
18
25
37
43
56
69
767.59
Sheet1
Cases
Forecast
Week
Cases
Sheet2
Week
Cases
Sheet3
ForecastingWe can look at the Moving Average method as using a weighted average:
Rather than equal weights, it might make sense to use weights which favor more recent consumption values3 + 6 + 9 =3
ForecastingWith the Weighted Moving Average, we have to select weights that are individually greater than zero and less than 1, and as a group sum to 1:
Valid Weights: .5, .3, .2 .6, .3, .11, 1, 12 3 6
Invalid weights: .5, .2, .1.6, -0.1, 0.5.5, .4, .3, .2
ForecastingA Weighted Moving Average forecast with weights of:1, 1, 12 3 6 is as performed as follows:
How do you make the Weighted Moving Average forecast more responsive?
Forecasting TerminologyInitializationExPostForecastForecastHistorical DataNoHistorical DataHistorical Data
Chart1
19082.75066419371
2147111.47115099292
3183169.8669320723
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5191208.76377888165
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17245223.541732671117
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19202221.857849281819
20208194.401629534820
21215180.2589328921
22173170.693910887622
23105103.812887786523
248981.469764849524
94.7492780503912525
125.42859928041372626
197.45844544061932727
226.99103019381992828
229.80071278032782929
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274.23488402372913131
255.2713913052503232
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113.5223968461113535
85.15599026941273636
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Sheet1
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1161131.7920265007131
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1521.1185.1220352954185
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1561.5302.2351326731302
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1621.1185.1248633178185
1641232.3724479753232
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Sheet1
90.7615319794
147.7104638429
183.77379544
186.4566791401
191.619470807
244.1359793906
226.2756169494
165.0785341154
129.0426136862
151.3294744185
91.3906334845
64.4586797536
87.9891853498
90.2303067681
176.1574717651
226.5823331933
245.2072175132
237.5601433337
202.3677454424
208.5265895658
215.7743340053
173.2858545125
105.5090316042
89.4587285753
91.4739574448
137.4363932343
193.0056654336
199.3021938102
278.4503773468
344.9680620801
291.7202356907
250.8801844954
171.1012848679
152.9696861515
111.1344003996
127.807329562
Sheet2
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Sheet2
Sheet3
Forecasting TerminologyApplying this terminology to our problem using the Moving Average forecast:InitializationExPost ForecastForecastModel Evaluation
We are now looking at a future from here, and the future we were looking at in February now includes some of our past, and we can incorporate the past into our forecast. 1993, the first half, which is now the past and was the future when we issued our first forecast, is now overLaura DAndrea Tyson, Head of the Presidents Council of Economic Advisors, quoted in November of 1993 in the Chicago Tribune, explaining why the Administration reduced its projections of economic growth to 2 percent from the 3.1percent it predicted in February. Forecasting Terminology
Exponential SmoothingExponential Smoothing is designed to give the benefits of the Weighted Moving Average forecast with out the cumbersome problem of specifying weights. In Exponential Smoothing, there is only one parameter:aa= smoothing constant (between 0 and 1)F(t+1) = aA(t) + (1- a) F(t)F(initial) = F(2)=[A(1) +A(2)] / 2
Exponential SmoothingUsing a = 0.4, we get InitializationExPost ForecastForecast
Practice Problem
Practice Problem
Expanding theExponential Smoothing FormulaF(t+1) =aA(t) + (1 a) F(t) = aA(t) + (1 a) [aA(t-1) + (1 a) F(t-1)] =aA(t) + (1 a) aA(t-1) + (1 a)2 F(t-1) =aA(t) + (1 a) aA(t-1) + (1 a)2 [aA(t-2) + (1 a) F(t-2) ]aA(t) + (1 a) aA(t-1) + (1 a)2 aA(t-2) + (1 a)3 F(t-2)and so on . . .
Thus, the exponential smoothing formula considersall previous actual data
Expanding theExponential Smoothing Formula
Sheet1
PeriodWeight
10.053140.035290.007810.000510.00000
20.059050.050420.015630.001700.00001
30.065610.072030.031250.005670.00009
40.07290.10290.06250.01890.0009
50.0810.1470.1250.0630.009
60.090.210.250.210.09
70.10.30.50.70.9
10.05314410.03529470.00781250.00051030.0000009
20.0590490.0504210.0156250.0017010.000009
30.065610.072030.031250.005670.00009
40.07290.10290.06250.01890.0009
50.0810.1470.1250.0630.009
60.090.210.250.210.09
70.10.30.50.70.9
Sheet1
a = 0.1
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Period
Weight
Sheet2
Sheet3
Expanding theExponential Smoothing Formula
Chart1
0.05314410.03529470.00781250.00051030.0000009
0.0590490.0504210.0156250.0017010.000009
0.065610.072030.031250.005670.00009
0.07290.10290.06250.01890.0009
0.0810.1470.1250.0630.009
0.090.210.250.210.09
0.10.30.50.70.9
a = 0.1
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Period
Weight
Sheet1
0.05314410.03529470.00781250.00051030.0000009
0.0590490.0504210.0156250.0017010.000009
0.065610.072030.031250.005670.00009
0.07290.10290.06250.01890.0009
0.0810.1470.1250.0630.009
0.090.210.250.210.09
0.10.30.50.70.9
10.05314410.03529470.00781250.00051030.0000009
20.0590490.0504210.0156250.0017010.000009
30.065610.072030.031250.005670.00009
40.07290.10290.06250.01890.0009
50.0810.1470.1250.0630.009
60.090.210.250.210.09
70.10.30.50.70.9
Sheet1
a = 0.1
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Period
Weight
Sheet2
Sheet3
Outliers (eloping point)Outlier
Chart6
81111
52222
66.0535.453
36.03545.8354
45.124553.85055
154.787154.787153.955153.95515
777.851005711.686545
887.851005811.686545
997.851005911.686545
10107.8510051011.686545
Sheet1
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1121.4178.7694739944178
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1161139.4996839643139
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1200.694.53463417294
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1281.1143.0639367232143
1301.2234.8200472567234
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1381.1184.0164033819184
1401203.4939611159203
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1440.6136.745200514136
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Sheet1
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143.385119704
153.606780586
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320.6988398709
302.9965136985
215.239514257
166.6794577126
161.8793187329
180.6315137226
132.0601431965
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
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202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
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152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
Ex 2
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Data with Trends
Chart7
3
6
5
8
7
9
Sheet1
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1220.469.282053173269
1240.6116.5561668611116
1260.7115.8150039628115
1281.1165.2720479003165
1301.2189.7544373557189
1321.5202.9243072132202
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1401200.771801618200
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Sheet1
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128.7869181264
154.8992631566
120.7869201515
234.7743473543
257.7375840418
282.00694595
320.6988398709
302.9965136985
215.239514257
166.6794577126
161.8793187329
180.6315137226
132.0601431965
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
Ex 2
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
3
6
5
8
7
9
Data with Trends
Chart8
3
64.54.54.54.5
54.955.255.555.85
84.9655.1255.1655.085
75.87556.56257.14957.7085
96.212856.781257.044857.07085
7.0489957.8906258.4134558.807085
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Sheet1
1001000.6124.0333305641124
21020.771.460425520371
1041.1138.7048909634138
1061.2159.5779317808159
1081.5225.7596967192225
1101.7249.3275339851249
1121.4175.7985783944175
1141.1187.0590892235187
1161167.3339003969167
1180.793.318923757493
1200.6147.6513521076147
1220.461.127344925761
1240.6116.9252474631116
1260.7115.965247108115
1281.1216.6181490355216
1301.2230.6302122159230
1321.5248.9770964969248
1341.7255.5637228151255
1361.4254.8153433116254
1381.1219.3124354877219
1401203.8732704174203
1420.7135.8485232008135
1440.6143.051724614143
1460.487.263014367287
1480.690.128016789590
1500.7153.65944366891533
1521.1229.7726549245229
1541.2209.2900189549209
1561.5311.9444708704311
1581.7315.8837534542315
1601.4278.6662840801278
1621.1218.3963910742218
1641194.5613025184194
1660.7183.2788167741183
1680.6151.5293008111151
1700.488.809156772488
Sheet1
61.8630473349
143.385119704
153.606780586
158.2741989788
168.951605027
224.6605091235
225.5269274434
133.1677357893
179.4379097751
90.6588265439
132.189529342
105.4755435859
102.7294620072
126.033152564
193.1590535093
218.5107794322
272.8565324368
241.0914253753
249.1427630621
164.47734008
194.7040302928
123.3289657264
132.7389166806
128.7869181264
154.8992631566
120.7869201515
234.7743473543
257.7375840418
282.00694595
320.6988398709
302.9965136985
215.239514257
166.6794577126
161.8793187329
180.6315137226
132.0601431965
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
Ex 2
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
0.30.50.70.9
A(t)
3
64.54.54.54.5
54.955.255.555.85
84.9655.1255.1655.085
75.87556.56257.14957.7085
96.212856.781257.044857.07085
7.0489957.8906258.4134558.807085
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Simple Linear Regression ModelY = mx + bSimple linear regression can be used to forecast data with trendsY is the regressed forecast value or dependent variable in the model, b is the intercept value of the regression line, and m is the slope of the regression line. 0 1 2 3 4 5 x (Time)Ybm
Simple Linear Regression ModelIn linear regression, thesquared errors are minimizedError
Chart1
2
6
4
9
6
11
Sheet1
1001000.6132.6749088284132
21020.7131.2734754568131
1041.1116.5195546373116
1061.2166.5398066159166
1081.5201.9263445938201
1101.7191.3747287385191
1121.4213.2842938969213
1141.1127.5945047569127
1161136.288127802136
1180.7130.2309171628130
1200.6142.9380649362142
1220.4105.2349111106105
1240.6121.3445043062121
1260.797.91488939397
1281.1156.149059729156
1301.2200.8536416016200
1321.5236.8697105069236
1341.7259.9695997461259
1361.4266.1356770208266
1381.1190.5108158387190
1401162.3567871526162
1420.7115.1839076108115
1440.6105.6581582656105
1460.492.132519306892
1480.6144.4701570196144
1500.7130.15112589851303
1521.1184.0545712312184
1541.2223.862964401223
1561.5254.1694670517254
1581.7342.8524733416342
1601.4276.1093641499276
1621.1212.6708142574212
1641237.1312409447237
1660.7161.7989620673161
1680.6176.8041269467176
1700.4126.6528965701126
Sheet1
61.8630473349
143.385119704
153.606780586
158.2741989788
168.951605027
224.6605091235
225.5269274434
133.1677357893
179.4379097751
90.6588265439
132.189529342
105.4755435859
102.7294620072
126.033152564
193.1590535093
218.5107794322
272.8565324368
241.0914253753
249.1427630621
164.47734008
194.7040302928
123.3289657264
132.7389166806
128.7869181264
154.8992631566
120.7869201515
234.7743473543
257.7375840418
282.00694595
320.6988398709
302.9965136985
215.239514257
166.6794577126
161.8793187329
180.6315137226
132.0601431965
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Ex 2
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
0.30.50.70.9
A(t)
2
64444
44.655.45.8
94.424.54.424.18
65.7946.757.6268.518
115.85586.3756.48786.2518
7.399068.68759.6463410.52518
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Formulas for Calculatingm and b
Simple Linear Regression ProblemApplying the model to the following data:
Calculate m and b
Evaluate Results
Chart2
22.7619047619
64.1904761905
45.619047619
97.0476190476
68.4761904762
119.9047619048
A(t)
F(t)
Sheet1
1001000.6120.4733094003120
21020.7115.3057037631115
1041.1138.6091230597138
1061.2186.2426843664186
1081.5181.6056809172181
1101.7261.44696222261
1121.4200.5163443531200
1141.1155.8878013922155
1161165.1681929478165
1180.7131.2405984887131
1200.697.588781485697
1220.472.489189644572
1240.692.987430968192
1260.7137.1726930982137
1281.1194.9569885735194
1301.2181.9077390103181
1321.5258.2493645779258
1341.7246.1710878909246
1361.4251.9678185468251
1381.1175.9121254389175
1401143.1694380149143
1420.7120.2482286191120
1440.6165.9979946211165
1460.464.51147027164
1480.6158.5237696638158
1500.7161.97745567641613
1521.1213.114493519213
1541.2209.0788096626209
1561.5302.1889578196302
1581.7313.2888428406313
1601.4234.3827672529234
1621.1240.8943028097240
1641182.6417244126182
1660.7185.0408716462185
1680.6161.9976348407161
1700.486.424418126786
Sheet1
61.8630473349
143.385119704
153.606780586
158.2741989788
168.951605027
224.6605091235
225.5269274434
133.1677357893
179.4379097751
90.6588265439
132.189529342
105.4755435859
102.7294620072
126.033152564
193.1590535093
218.5107794322
272.8565324368
241.0914253753
249.1427630621
164.47734008
194.7040302928
123.3289657264
132.7389166806
128.7869181264
154.8992631566
120.7869201515
234.7743473543
257.7375840418
282.00694595
320.6988398709
302.9965136985
215.239514257
166.6794577126
161.8793187329
180.6315137226
132.0601431965
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Ex 2
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
0.30.50.70.9
tA(t)
12
264444
344.655.45.8
494.424.54.424.18
565.7946.757.6268.518
6115.85586.3756.48786.2518
7.399068.68759.6463410.52518
tA(t)
(x)(y)xy
1212
26412
34912
491636
562530
6113666
Sum91158
Average3.56.3333333333
1.4285714286
1.3333333333
tA(t)F(t)
122.76
264.19
345.62
497.05
568.48
6119.90
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
A(t)
F(t)
Practice ProblemQuestion: Given the data below, what is the simple linear regression model that can be used to predict sales?
Calculate m and b
Sheet1
Week (x)Sales (Y)
1150
2157
3162
4166
5177
(x)(Y)(X)(Y)
11501150
21574314
31629486
416616664
517725885
Sum552499
Average3162.4
Sheet2
Sheet3
Evaluate ResultsF(t) = 143.5 + 6.3 (t)
Chart1
150149.8
157156.1
162162.4
166168.7
177175
Sales (Y)
Regression
Sheet1
Week (x)Sales (Y)Regression
1150149.8
2157156.1
3162162.4
4166168.7
5177175
(x)(Y)(X)(Y)
11501150
21574314
31629486
416616664
517725885
Sum552499
Average3162.4
Sheet1
Sales (Y)
Regression
Sheet2
Sheet3
Simple Linear Regressionin ExcelIf the Analysis ToolPak is loaded, extensive regression analysis can be performed using the regression function
Simple Linear Regressionin ExcelTo get the slope and intercept easily, use the slope and intercept functions:
= slope(y-range, x-range)= intercept(y-range, x-range)
Limitations in Linear RegressionAs with the moving average model, all data pointscount equally with simple linear regression
Chart3
3210.2583333333
3822.8119047619
5035.3654761905
6147.919047619
5260.4726190476
6373.0261904762
7285.5797619048
5398.1333333333
99110.6869047619
92123.2404761905
121135.794047619
153148.3476190476
183160.9011904762
179173.4547619048
224186.0083333333
Sheet1
1001000.677.033238313577
21020.7103.8906894267103
1041.1174.9357934702174
1061.2188.1163487821188
1081.5204.9704584737204
1101.7218.5067209772218
1121.4206.8557728123206
1141.1183.751840199183
1161146.1768486656146
1180.7161.8626221564161
1200.678.658231894478
1220.4107.7930241904107
1240.676.16211573176
1260.7134.019168775134
1281.1220.4549994969220
1301.2171.2410367829171
1321.5253.8468188621253
1341.7234.7702365469234
1361.4215.5786379946215
1381.1227.8072124032227
1401219.0863079452219
1420.7157.1532750811157
1440.6126.8754708888126
1460.497.239732365297
1480.689.842421905389
1500.7144.62718883311443
1521.1185.5634858272185
1541.2210.9033358866210
1561.5278.5239247668278
1581.7334.9580842434334
1601.4264.6225623751264
1621.1255.3552486228255
1641211.4523693482211
1660.7174.6670996611174
1680.6133.4516388334133
1700.4144.5706691597144
Sheet1
61.8630473349
143.385119704
153.606780586
158.2741989788
168.951605027
224.6605091235
225.5269274434
133.1677357893
179.4379097751
90.6588265439
132.189529342
105.4755435859
102.7294620072
126.033152564
193.1590535093
218.5107794322
272.8565324368
241.0914253753
249.1427630621
164.47734008
194.7040302928
123.3289657264
132.7389166806
128.7869181264
154.8992631566
120.7869201515
234.7743473543
257.7375840418
282.00694595
320.6988398709
302.9965136985
215.239514257
166.6794577126
161.8793187329
180.6315137226
132.0601431965
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Ex 2
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
Prac 2
0.30.50.70.9
tA(t)
12
264444
344.655.45.8
494.424.54.424.18
565.7946.757.6268.518
6115.85586.3756.48786.2518
7.399068.68759.6463410.52518
tA(t)
(x)(y)xy
1212
26412
34912
491636
562530
6113666
Sum91158
Average3.56.3333333333
1.4285714286
1.3333333333
tA(t)F(t)
122.76
264.19
345.62
497.05
568.48
6119.90
Prac 2
Regr
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Ex5
A(t)
F(t)
tA(t)F(t)
1150149.8
2157156.1
3162162.4
4166168.7
5177175.0
143.5
6.3
SUMMARY OUTPUT
Regression Statistics
Multiple R0.985
R Square0.970
Adjusted R Square0.960
Standard Error2.025
Observations5
ANOVA
dfSSMSFSignificance F
Regression1396.9396.996.8050.002
Residual312.34.1
Total4409.2
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept143.52.12467.5720.000136.74150.26
X Variable 16.30.6409.8390.0024.268.34
tA(t)
1150
2157
3162
4166
5177
=SLOPE(B26:B30,A26:A30)6.3
=INTERCEPT(B26:B30,A26:A30)143.5
13210.2583333333
23822.8119047619
35035.3654761905
46147.919047619
55260.4726190476
66373.0261904762
77285.5797619048
85398.1333333333
999110.6869047619
1092123.2404761905
11121135.794047619
12153148.3476190476
13183160.9011904762
14179173.4547619048
15224186.0083333333
12.5535714286
-2.2952380952
MBD00032866.xls
Sheet1
Week (x)Sales (Y)
1150
2157
3162
4166
5177
Sheet2
Sheet3
MBD00030AFD.xls
Sheet1
WeekSales
1150
2157
3162
4166
5177
&A
Page &P
Sheet2
&A
Page &P
Sheet3
&A
Page &P
Sheet4
&A
Page &P
Sheet5
&A
Page &P
Sheet6
&A
Page &P
Sheet7
&A
Page &P
Sheet8
&A
Page &P
Sheet9
&A
Page &P
Sheet10
&A
Page &P
Sheet11
&A
Page &P
Sheet12
&A
Page &P
Sheet13
&A
Page &P
Sheet14
&A
Page &P
Sheet15
&A
Page &P
Sheet16
&A
Page &P
Holts Trend ModelTo forecast data with trends, we can use an exponential smoothing model with trend, frequently known as Holts model:
We will use linear regression to initialize the modelL(t) = aA(t) + (1- a) F(t)T(t) = [L(t) - L(t-1) ] + (1- ) T(t-1)F(t+1) = L(t) + T(t)
Holts Trend ModelFirst, well initialize the model:L(4) = 20.5+4(9.9)=60.1T(4) = 9.9
Updating in Holts Trend Model52L(t) = aA(t) + (1- a) F(t)= 0.3b = 0.4L(5) = 0.3 (52) + 0.7 (70)=64.6T(t) = [L(t) - L(t-1) ] + (1- ) T(t-1)T(5) = 0.4 [64.6 60.1] + 0.6 (9.9) = 7.74F(t+1) = L(t) + T(t)F(6) = 64.6 + 7.74 = 72.3464.67.74
Updating in Holts Trend Model63= 0.3b = 0.4L(6) = 0.3 (63) + 0.7 (72.34)=69.54T(6) = 0.4 [69.54 64.60] + 0.6 (7.74) = 6.62F(7) = 69.54 + 6.62 = 76.1669.546.6272
Holts Model ResultsInitializationExPost ForecastForecast
Holts Model ResultsInitializationExPostForecastForecastRegression
Chart5
321110.2583333333
382222.8119047619
503335.3654761905
614447.919047619
5270560.4726190476
6372.34673.0261904762
7276.1572785.5797619048
5381.030376898.1333333333
9975.377954089110.6869047619
9288.055904246410123.2404761905
12195.303760853311135.794047619
153112.160809175812148.3476190476
183138.461445900413160.9011904762
179171.216518099614173.4547619048
224193.879086467193.879086467186.0083333333
1616226.8573939482198.5619047619
1717250.7994273695211.1154761905
1818274.7414607909223.669047619
1919298.6834942122236.2226190476
Sheet1
1001000.667.860626954167
21020.7130.8241350949130
1041.1133.0439740764133
1061.2198.9505587343198
1081.5177.4917539681177
1101.7189.6073906715189
1121.4225.71302627225
1141.1196.3213532536196
1161117.8269242768117
1180.7137.7888453541137
1200.699.769058665199
1220.4110.4092539814110
1240.6146.3704780991146
1260.7111.3454485868111
1281.1180.2596534194180
1301.2228.2900750323228
1321.5272.9522400458272
1341.7268.4350613345268
1361.4190.4777967021190
1381.1228.7755915909228
1401144.0901495596144
1420.7103.9154672409103
1440.6164.5331765082164
1460.4127.0303034156127
1480.6110.2820966565110
1500.7109.25453875561093
1521.1224.1998630222224
1541.2191.0793123917191
1561.5296.6061397738296
1581.7272.0151286562272
1601.4275.4980725144275
1621.1190.8265774287190
1641178.8697308523178
1660.7195.0060858861195
1680.6137.9210440748137
1700.4116.0501204584116
Sheet1
61.8630473349
143.385119704
153.606780586
158.2741989788
168.951605027
224.6605091235
225.5269274434
133.1677357893
179.4379097751
90.6588265439
132.189529342
105.4755435859
102.7294620072
126.033152564
193.1590535093
218.5107794322
272.8565324368
241.0914253753
249.1427630621
164.47734008
194.7040302928
123.3289657264
132.7389166806
128.7869181264
154.8992631566
120.7869201515
234.7743473543
257.7375840418
282.00694595
320.6988398709
302.9965136985
215.239514257
166.6794577126
161.8793187329
180.6315137226
132.0601431965
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
Ex 2
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
Prac 2
0.30.50.70.9
tA(t)
12
264444
344.655.45.8
494.424.54.424.18
565.7946.757.6268.518
6115.85586.3756.48786.2518
7.399068.68759.6463410.52518
tA(t)
(x)(y)xy
1212
26412
34912
491636
562530
6113666
Sum91158
Average3.56.3333333333
1.4285714286
1.3333333333
tA(t)F(t)
122.76
264.19
345.62
497.05
568.48
6119.90
Prac 2
Regr
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Ex5
A(t)
F(t)
tA(t)F(t)
1150149.8
2157156.1
3162162.4
4166168.7
5177175.0
143.5
6.3
SUMMARY OUTPUT
Regression Statistics
Multiple R0.985
R Square0.970
Adjusted R Square0.960
Standard Error2.025
Observations5
ANOVA
dfSSMSFSignificance F
Regression1396.9396.996.8050.002
Residual312.34.1
Total4409.2
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept143.52.12467.5720.000136.74150.26
X Variable 16.30.6409.8390.0024.268.34
tA(t)
1150
2157
3162
4166
5177
=SLOPE(B26:B30,A26:A30)6.3
=INTERCEPT(B26:B30,A26:A30)143.5
tA(t)tA(t)
13210.2583333333132
23822.8119047619238
35035.3654761905350
46147.919047619461
55260.4726190476552
66373.0261904762663
77285.5797619048772
85398.1333333333853
999110.6869047619999
1092123.24047619051092
11121135.79404761911121
12153148.347619047612153
13183160.901190476213183
14179173.454761904814179
15224186.008333333315224
12.5535714286
-2.2952380952
xyx2xy
132132
238476tA(t)L(t)T(t)F(t)
3509150132
46116244238
Sum30502350
Average2.545.2546160.19.9
570
tA(t)L(t)T(t)F(t)
132
238
350
46160.19.9
55264.607.7470
672.34
0.30.4
tA(t)L(t)T(t)F(t)
13210.2583333333132
23822.8119047619238
35035.3654761905350
46147.91904761946160.19.9
55270.060.472619047655264.607.7470
66372.373.026190476266369.546.6272.34
77276.285.579761904877274.916.1276.16
85381.098.133333333385372.622.7681.03
99975.4110.686904761999982.465.5975.38
109288.1123.2404761905109289.246.0688.06
1112195.3135.79404761911121103.019.1595.30
12153112.2148.347619047612153124.4114.05112.16
13183138.5160.901190476213183151.8219.39138.46
14179171.2173.454761904814179173.5520.33171.22
15224193.9193.9186.008333333315224202.9223.94193.88
16226.9198.561904761916226.86
17250.8211.115476190517250.80
18274.7223.66904761918274.74
19298.7236.222619047619298.68
MBD0007E27E.unknown
MBD00032866.xls
Sheet1
Week (x)Sales (Y)
1150
2157
3162
4166
5177
Sheet2
Sheet3
MBD00030AFD.xls
Sheet1
WeekSales
1150
2157
3162
4166
5177
&A
Page &P
Sheet2
&A
Page &P
Sheet3
&A
Page &P
Sheet4
&A
Page &P
Sheet5
&A
Page &P
Sheet6
&A
Page &P
Sheet7
&A
Page &P
Sheet8
&A
Page &P
Sheet9
&A
Page &P
Sheet10
&A
Page &P
Sheet11
&A
Page &P
Sheet12
&A
Page &P
Sheet13
&A
Page &P
Sheet14
&A
Page &P
Sheet15
&A
Page &P
Sheet16
&A
Page &P
Practice Problem
Practice Problem
Practice Problem
Chart6
00
2
6
5
8
109.75
1311.52
1513.6544
1415.86956815.869568
917.29213696
1019.08861952
1120.88510208
1222.68158464
Sheet1
1001000.6108.9936572296108
21020.799.045766347299
1041.1166.4228803144166
1061.2136.0028251317136
1081.5238.4568623369238
1101.7215.8950924982215
1121.4217.3808680772217
1141.1151.8371417101151
1161164.3688475598164
1180.7104.1721543056104
1200.6133.0371036591133
1220.4128.1527565559128
1240.6125.5981964246125
1260.7165.4522400066165
1281.1183.1797281131183
1301.2220.0279338587220
1321.5268.9388971363268
1341.7234.0846291668234
1361.4198.1896764683198
1381.1207.8461392572207
1401150.6304371128150
1420.7100.4902132849100
1440.6134.6613557277134
1460.466.689016759566
1480.6121.5041905539121
1500.7162.6325609521623
1521.1185.2861568486185
1541.2199.8481027202199
1561.5240.7747759792240
1581.7279.2936866636279
1601.4240.0210640446240
1621.1223.6462209393223
1641222.3778115012222
1660.7133.3377618546133
1680.6130.4730361097130
1700.469.296968996369
Sheet1
60.7435519558
147.5158250093
182.8800279037
202.4258324269
194.908108574
192.2129206673
227.4625494001
190.5378277537
155.4056615334
90.1397767708
125.6275866204
109.2489472605
76.4894909701
131.9989575545
181.4756297593
214.0632997963
245.9180756537
288.1745119811
194.8103878458
188.4269769171
214.5376232917
156.1811428626
108.2419580298
117.7486716445
106.5196192837
175.0463648031
189.0239000692
256.1124780196
285.7432184662
297.6413462565
249.6979394572
229.1177583156
207.1381314879
140.3034380374
133.3819469487
84.7303676304
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
Ex 2
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
Prac 2
0.30.50.70.9
tA(t)
12
264444
344.655.45.8
494.424.54.424.18
565.7946.757.6268.518
6115.85586.3756.48786.2518
7.399068.68759.6463410.52518
tA(t)
(x)(y)xy
1212
26412
34912
491636
562530
6113666
Sum91158
Average3.56.3333333333
1.4285714286
1.3333333333
tA(t)F(t)
122.76
264.19
345.62
497.05
568.48
6119.90
Prac 2
Regr
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Ex5
A(t)
F(t)
Prac 3
tA(t)F(t)
1150149.8
2157156.1
3162162.4
4166168.7
5177175.0
143.5
6.3
SUMMARY OUTPUT
Regression Statistics
Multiple R0.985
R Square0.970
Adjusted R Square0.960
Standard Error2.025
Observations5
ANOVA
dfSSMSFSignificance F
Regression1396.9396.996.8050.002
Residual312.34.1
Total4409.2
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept143.52.12467.5720.000136.74150.26
X Variable 16.30.6409.8390.0024.268.34
tA(t)
1150
2157
3162
4166
5177
=SLOPE(B26:B30,A26:A30)6.3
=INTERCEPT(B26:B30,A26:A30)143.5
tA(t)tA(t)
13210.2583333333132
23822.8119047619238
35035.3654761905350
46147.919047619461
55260.4726190476552
66373.0261904762663
77285.5797619048772
85398.1333333333853
999110.6869047619999
1092123.24047619051092
11121135.79404761911121
12153148.347619047612153
13183160.901190476213183
14179173.454761904814179
15224186.008333333315224
12.5535714286
-2.2952380952
xyx2xy
132132
238476tA(t)L(t)T(t)F(t)
3509150132
46116244238
Sum30502350
Average2.545.2546160.19.9
570
tA(t)L(t)T(t)F(t)
132
238
350
46160.19.9
55264.607.7470
672.34
0.30.4
tA(t)L(t)T(t)F(t)
13210.2583333333132
23822.8119047619238
35035.3654761905350
46147.91904761946160.19.9
55270.060.472619047655264.607.7470
66372.373.026190476266369.546.6272.34
77276.285.579761904877274.916.1276.16
85381.098.133333333385372.622.7681.03
99975.4110.686904761999982.465.5975.38
109288.1123.2404761905109289.246.0688.06
1112195.3135.79404761911121103.019.1595.30
12153112.2148.347619047612153124.4114.05112.16
13183138.5160.901190476213183151.8219.39138.46
14179171.2173.454761904814179173.5520.33171.22
15224193.9193.9186.008333333315224202.9223.94193.88
16226.9198.561904761916226.86
17250.8211.115476190517250.80
18274.7223.66904761918274.74
19298.7236.222619047619298.68
tA(t)L(t)T(t)F(t)
12
26
35
48
510
613
715
814
9
10
11
12
0.20.4
tA(t)L(t)T(t)F(t)xyxy
121212
2626412
3535915
488.051.7481632
5109.801.729.75Sum3061
61311.821.8411.52Average2.55.25
71513.921.9513.65
81415.501.8015.87
917.29
1019.09
1120.89
1222.68
tA(t)F(t)
12
26
35
48
5109.75
61311.52
71513.65
81415.8715.87
917.29
1019.09
1120.89
1222.68
11
MBD0007E27E.unknown
MBD000F9E87.unknown
MBD00032866.xls
Sheet1
Week (x)Sales (Y)
1150
2157
3162
4166
5177
Sheet2
Sheet3
MBD00030AFD.xls
Sheet1
WeekSales
1150
2157
3162
4166
5177
&A
Page &P
Sheet2
&A
Page &P
Sheet3
&A
Page &P
Sheet4
&A
Page &P
Sheet5
&A
Page &P
Sheet6
&A
Page &P
Sheet7
&A
Page &P
Sheet8
&A
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Sheet9
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Seasonal Model (No Trend)
Chart7
16
27
39
22
18
26
43
23
14
29
41
22
Sheet1
1001000.688.69945841988
21020.775.838586725275
1041.1120.8401397524120
1061.2143.2249549319143
1081.5212.2856897195212
1101.7254.2074462965254
1121.4232.1529829976232
1141.1127.8477486041127
1161168.1220566975168
1180.7138.2349448081138
1200.6140.2276089231140
1220.491.377307425291
1240.695.858316324495
1260.7121.9562767808121
1281.1174.5748418042174
1301.2228.7037256703228
1321.5249.4756413133249
1341.7275.2173132256275
1361.4195.591182678195
1381.1201.3974005189201
1401189.0125704511189
1420.7178.0757218758178
1440.6131.2743489981131
1460.483.35495503883
1480.6157.7767615319157
1500.7125.80560736931253
1521.1189.2400985525189
1541.2249.0149891138249
1561.5271.0599247277271
1581.7280.6399683706280
1601.4286.7845976934286
1621.1186.238306241186
1641206.3390029652206
1660.7135.33951048135
1680.6115.476651272115
1700.4107.1925040778107
Sheet1
60.7435519558
147.5158250093
182.8800279037
202.4258324269
194.908108574
192.2129206673
227.4625494001
190.5378277537
155.4056615334
90.1397767708
125.6275866204
109.2489472605
76.4894909701
131.9989575545
181.4756297593
214.0632997963
245.9180756537
288.1745119811
194.8103878458
188.4269769171
214.5376232917
156.1811428626
108.2419580298
117.7486716445
106.5196192837
175.0463648031
189.0239000692
256.1124780196
285.7432184662
297.6413462565
249.6979394572
229.1177583156
207.1381314879
140.3034380374
133.3819469487
84.7303676304
Ex 1
L(T)T(T)S(T)F(T)
0.30.40.3
19088.50.5418367347166.101694915382.75066419379019082.7506641937
2147118.50.7255102041202.6160337553111.47115099291472147111.4711509929
3183179.51.0989795918166.5181058496169.8669320721833183169.866932072
41862061.2612244898147.4757281553196.10848735271864186196.1084873527
51912181.3346938776143.1039755352208.76377888161915191208.7637788816
6244240.51.4724489796165.7103257103231.66909928842446244231.6690992884
72262141.3102040816172.492211838207.35105060772267226207.3510506077
8165186.51.1418367347144.5040214477181.75902227911658165181.7590222791
91291721.0530612245122.5168.59926292761299129168.5992629276
101511620.9918367347152.2427983539159.712128713815110151159.7121287138
1191980.6151.666666666797.169587459191119197.1695874591
126476.50.4683673469136.644880174376.283923267464126476.2839232674
13870.5418367347160.564971751488.749971122870.5418367347138788.749971122
14900.7255102041124.0506329114119.5041212867900.72551020411490119.5041212867
151761.0989795918160.1485608171182.03501787581761.098979591815176182.0350178758
162261.2612244898179.1909385113210.0729757962261.261224489816226210.072975796
172451.3346938776183.5626911315223.54173267112451.334693877617245223.5417326711
182371.4724489796160.9563409563247.97230060212371.472448979618237247.9723006021
192021.3102040816154.1744548287221.85784928182021.310204081619202221.8578492818
202081.1418367347182.1626452189194.40162953482081.141836734720208194.4016295348
212151.0530612245204.1666666667180.258932892151.053061224521215180.25893289
221730.9918367347174.4238683128170.69391088761730.991836734722173170.6939108876
231050.6175103.81288778651050.623105103.8128877865
24890.4683673469190.021786492481.469764849589173.94416024510.9226806010.4683673469248981.4697648495
91163.333333333391172.79096938330.09233201590.53728008232594.749278050391
1370.922680601137177.66810000892.00625145980.739187359126125.4285992804137
193151.7998258205193178.45728279691.51942399111.093733106427197.4584454406193
199199173.3186462079-1.1438002411.227309406428226.9910301938199
278278183.0086307093.18971365581.390001926629229.8007127803278
344344200.42615914278.8808395671.545617132930274.1675621616344
291291213.145740218310.41633617041.326721767431274.2348840237291
250250222.17709958479.86234544881.136854258232255.271391305250
171171211.14272780251.50365855640.980106470133244.3517421169171
152152194.8277790932-5.62378434990.928338579934210.9104974907152
111111187.9427963204-6.12826371910.597181571535113.522396846111
127127208.61657804974.59255446030.51048884143685.1559902694127
13799.8601957368
238117.0205082925
339164.3910120089
440248.2629733722
541284.2195150133
642328.2794026869
743372.1296732521
844325.5204908972
945284.156230937
1046249.4783813289
1147240.5647181564
1248157.4930425924
Ex 1
Ex 2
Practice
tA(t)F(t)tA(t)F(t)
1818
25256.5
37375.9
436.67436.34
565565.004
695.33695.4024
7676.84144
8686.84144
9696.84144
106106.84144
Ex 3
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
24
39
411
510
6
7
8
tA(t)MA (n=3)Weighted MA(0.6, 0.3, 0.1)
18
246
395.2
41177.46.72
51089.78.432
61010.29.0592
71010.29.0592
81010.29.0592
Ex 4
ExpExp
tA(t)
1818
256.506.5025
366.055.45366.055.45
436.045.84436.0355.835
545.123.85545.12453.8505
6154.793.966154.787154.787153.955153.95515
77.8511.6977.85100511.686545
87.8511.6987.85100511.686545
97.8511.6997.85100511.686545
107.8511.69107.85100511.686545
Ex 4
Prac 2
0.30.50.70.9
tA(t)
12
264444
344.655.45.8
494.424.54.424.18
565.7946.757.6268.518
6115.85586.3756.48786.2518
7.399068.68759.6463410.52518
tA(t)
(x)(y)xy
1212
26412
34912
491636
562530
6113666
Sum91158
Average3.56.3333333333
1.4285714286
1.3333333333
tA(t)F(t)
122.76
264.19
345.62
497.05
568.48
6119.90
Prac 2
Regr
A(t)
a = 0.3
a = 0.5
a = 0.7
a = 0.9
Ex5
A(t)
F(t)
Prac 3
tA(t)F(t)
1150149.8
2157156.1
3162162.4
4166168.7
5177175.0
143.5
6.3
Ex6
SUMMARY OUTPUT
Regression Statistics
Multiple R0.985
R Square0.970
Adjusted R Square0.960
Standard Error2.025
Observations5
ANOVA
dfSSMSFSignificance F
Regression1396.9396.996.8050.002
Residual312.34.1
Total4409.2
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept143.52.12467.5720.000136.74150.26
X Variable 16.30.6409.8390.0024.268.34
tA(t)
1150
2157
3162
4166
5177
=SLOPE(B26:B30,A26:A30)6.3
=INTERCEPT(B26:B30,A26:A30)143.5
tA(t)tA(t)
13210.2583333333132
23822.8119047619238
35035.3654761905350
46147.919047619461
55260.4726190476552
66373.0261904762663
77285.5797619048772
85398.1333333333853
999110.6869047619999
1092123.24047619051092
11121135.79404761911121
12153148.347619047612153
13183160.901190476213183
14179173.454761904814179
15224186.008333333315224
12.5535714286
-2.2952380952
xyx2xy
132132
238476tA(t)L(t)T(t)F(t)
3509150132
46116244238
Sum30502350
Average2.545.2546160.19.9
570
tA(t)L(t)T(t)F(t)
132
238
350
46160.19.9
55264.607.7470
672.34
0.30.4
tA(t)L(t)T(t)F(t)
13210.2583333333132
23822.8119047619238
35035.3654761905350
46147.91904761946160.19.9
55270.060.472619047655264.607.7470
66372.373.026190476266369.546.6272.34
77276.285.579761904877274.916.1276.16
85381.098.133333333385372.622.7681.03
99975.4110.686904761999982.465.5975.38
109288.1123.2404761905109289.246.0688.06
1112195.3135.79404761911121103.019.1595.30
12153112.2148.347619047612153124.4114.05112.16
13183138.5160.901190476213183151.8219.39138.46
14179171.2173.454761904814179173.5520.33171.22
15224193.9193.9186.008333333315224202.9223.94193.88
16226.9198.561904761916226.86
17250.8211.115476190517250.80
18274.7223.66904761918274.74
19298.7236.222619047619298.68
tA(t)L(t)T(t)F(t)
12
26
35
48
510
613
715
814
9
10
11
12
0.20.4
tA(t)L(t)T(t)F(t)xyxy
121212
2626412
3535915
488.051.7481632
5109.801.729.75Sum3061
61311.821.8411.52Average2.55.25
71513.921.9513.65
81415.501.8015.87
917.29
1019.09
1120.89
1222.68
tA(t)F(t)
12
26
35
48
5109.75
61311.52
71513.65
81415.8715.87
917.29
1019.09
1120.89
1222.68
11
Spring 200316
Summer 200327
Fall 200339
Winter 200322
Spring 200418
Summer 200426
Fall 200443
Winter 200423
Spring 200514
Summer 200529
Fall 200541
Winter 200522
MBD0007E27E.unknown
MBD000F9E87.unknown
MBD00032866.xls
Sheet1
Week (x)Sales (Y)
1150
2157
3162
4166
5177
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MBD00030AFD.xls
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Seasonal ModelExponential FormulasL(t) = aA(t) / S(t-p) + (1- a) L(t-1)S(t) = g [A(t) / L(t)] + (1- g) S(t-p)p is the number of periods in a seasonQuarterly data: p = 4Monthly data: p = 12F(t+1) = L(t) * S(t+1-p)
Seasonal Model InitializationS(5) = 0.60S(6) = 1.00S(7) = 1.55S(8) = 0.85
L(8) = 26.5
Seasonal Model Forecastin
