question archive Consider the following time series Period 1 2 3 4 5 6 7 8  Demand 16 17 15 9 12 13 8 5 a) Using a trend projection, forecast the demand for Period 9

Consider the following time series Period 1 2 3 4 5 6 7 8  Demand 16 17 15 9 12 13 8 5 a) Using a trend projection, forecast the demand for Period 9

Subject:StatisticsPrice:2.87 Bought7

Consider the following time series

Period 1 2 3 4 5 6 7 8 

Demand 16 17 15 9 12 13 8 5

a) Using a trend projection, forecast the demand for Period 9.

b) Calculate the MAD for this forecast.

a) The forecasted demand for Period 9 is

Round to one decimal place as needed.)

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Answer

 

Period(t)

Demand(D)

t*D

t-square

 

1

16

16

1

 

2

17

34

4

 

3

15

45

9

 

4

9

36

16

 

5

12

60

25

 

6

13

78

36

 

7

8

56

49

 

8

5

40

64

Total

36

95

365

204

A.a) For trend projection, we have below formulae

Dt=b0+b1*t

b1={n*∑t*D-∑t*∑D}/{n*∑t^2-(∑t)^2}

b0=(Y-bar)-(b1*t-bar)

Y-bar=∑D/n

t-bar=∑t/n

First calculate b1

b1=(8*365-36*95)/(8*204-36*36)

upon solving, we get

b1=-500/336=-1.49

b1=-1.49

now, to calculate b0

Y-bar=∑D/n

Y-bar =95/8=11.875

t-bar=∑t/n

t-bar =36/8=4.5

b0=(Y-bar)-(b1*t-bar)

b0=11.875-(-1.49)*4.5

b0=18.58

now to forecast demand for period 9

Dt=b0+b1*t

D9=18.58+(-1.49)*9

D9=5.19

Hence forecast for period 9 demand is 5.19

A.b) calculate MAD

MAD formula is given as

MAD=∑Dt-Ft/n

From the given table, we need to calculate forecasted demand and deviation for each period

Period(t)

Actual Demand(D)

Forecasted Demand(F=b0+b1*t)

Deviation(D-F)

Absolute Deviation|D-F|

1

16

17.09

-1.09

1.09

2

17

15.6

1.4

1.4

3

15

14.11

0.89

0.89

4

9

12.62

-3.62

3.62

5

12

11.13

0.87

0.87

6

13

9.64

3.36

3.36

7

8

8.15

-0.15

0.15

8

5

6.66

-1.66

1.66

∑|Dt-Ft|=13.04

MAD=∑Dt-Ft/n

MAD=13.04/8

MAD=1.63