Question

Use the data below to answer this questions.

a.) Generate a scatter of the data

b. ) Report the monthly averages (January for all years, February for all years etc.)

c.) Is there seasonality? Is there a trend?

d.) How can you forecast the value for March 2020? Generate that forecast.

e.) (Not technical) This forecast will for sure be wrong. Why?

Reference period	Employment 3
	Persons
Jan-01	1,879.50
Feb-01	1,901.00
Mar-01	1,925.30
Apr-01	1,914.60
May-01	1,961.50
Jun-01	1,960.60
Jul-01	1,953.40
Aug-01	1,940.20
Sep-01	1,928.00
Oct-01	1,909.20
Nov-01	1,896.40
Dec-01	1,881.40
Jan-02	1,880.20
Feb-02	1,884.00
Mar-02	1,902.60
Apr-02	1,913.40
May-02	1,937.40
Jun-02	1,990.90
Jul-02	1,994.80
Aug-02	2,013.10
Sep-02	2,002.30
Oct-02	1,982.50
Nov-02	1,969.00
Dec-02	1,959.20
Jan-03	1,928.20
Feb-03	1,952.40
Mar-03	1,980.40
Apr-03	1,972.00
May-03	1,987.80
Jun-03	2,018.70
Jul-03	2,027.80
Aug-03	2,030.20
Sep-03	2,012.20
Oct-03	2,032.30
Nov-03	2,008.30
Dec-03	2,026.80
Jan-04	1,982.30
Feb-04	1,967.20
Mar-04	1,981.60
Apr-04	1,977.40
May-04	2,020.50
Jun-04	2,074.90
Jul-04	2,069.50
Aug-04	2,064.10
Sep-04	2,050.80
Oct-04	2,057.30
Nov-04	2,037.30
Dec-04	2,056.50
Jan-05	2,017.60
Feb-05	2,030.60
Mar-05	2,039.10
Apr-05	2,051.70
May-05	2,097.70
Jun-05	2,115.90

Answer 1

Answers:

Answer a)

Months	Persons
Jan-01	1,879.50
Feb-01	1,901.00
Mar-01	1,925.30
Apr-01	1,914.60
May-01	1,961.50
Jun-01	1,960.60
Jul-01	1,953.40
Aug-01	1,940.20
Sep-01	1,928.00
Oct-01	1,909.20
Nov-01	1,896.40
Dec-01	1,881.40
Jan-02	1,880.20
Feb-02	1,884.00
Mar-02	1,902.60
Apr-02	1,913.40
May-02	1,937.40
Jun-02	1,990.90
Jul-02	1,994.80
Aug-02	2,013.10
Sep-02	2,002.30
Oct-02	1,982.50
Nov-02	1,969.00
Dec-02	1,959.20
Jan-03	1,928.20
Feb-03	1,952.40
Mar-03	1,980.40
Apr-03	1,972.00
May-03	1,987.80
Jun-03	2,018.70
Jul-03	2,027.80
Aug-03	2,030.20
Sep-03	2,012.20
Oct-03	2,032.30
Nov-03	2,008.30
Dec-03	2,026.80
Jan-04	1,982.30
Feb-04	1,967.20
Mar-04	1,981.60
Apr-04	1,977.40
May-04	2,020.50
Jun-04	2,074.90
Jul-04	2,069.50
Aug-04	2,064.10
Sep-04	2,050.80
Oct-04	2,057.30
Nov-04	2,037.30
Dec-04	2,056.50
Jan-05	2,017.60
Feb-05	2,030.60
Mar-05	2,039.10
Apr-05	2,051.70
May-05	2,097.70
Jun-05	2,115.90

Scatter of the data is as under:

Answer b)

The monthly averages (January for all years, February for all years etc.):

Month Year-01	Persons	Month Year-02	Persons	Month Year-03	Persons (Monthly Average)
Jan-01	1,879.50	Jan-02	1,880.20	Jan-03	1,879.85
Feb-01	1,901.00	Feb-02	1,884.00	Feb-03	1,892.50
Mar-01	1,925.30	Mar-02	1,902.60	Mar-03	1,913.95
Apr-01	1,914.60	Apr-02	1,913.40	Apr-03	1,914.00
May-01	1,961.50	May-02	1,937.40	May-03	1,949.45
Jun-01	1,960.60	Jun-02	1,990.90	Jun-03	1,975.75
Jul-01	1,953.40	Jul-02	1,994.80	Jul-03	1,974.10
Aug-01	1,940.20	Aug-02	2,013.10	Aug-03	1,976.65
Sep-01	1,928.00	Sep-02	2,002.30	Sep-03	1,965.15
Oct-01	1,909.20	Oct-02	1,982.50	Oct-03	1,945.85
Nov-01	1,896.40	Nov-02	1,969.00	Nov-03	1,932.70
Dec-01	1,881.40	Dec-02	1,959.20	Dec-03	1,920.30

Third year monthly average = (Month Year 01 + Month Year 02) / 2

Answer c)

There is both seasonality and trend:

As can be seen, there is cyclic changes in the monthly numbers so it is seasonal.

Also there is a trend increase from year 1 to year 2 (denoted by the straight line) so there is a trend.

Answer d)

Calculation of forecast the value for March 2020.

Yearly total for Year 2001 and Year 2002 is as under:

Year	Yearly total
Year-01	23051.1
Year-02	23429.4

Linear trend line for this forecast is :

y = 378.3x + 22673

“x” is the number of year (for year 2020, x=20)

Based on the linear trend line formula, the forecast till year 2020 is as under:

Year	Yearly total
Year-01	23051.1
Year-02	23429.4
Year-03	23807.9
Year-04	24186.2
Year-05	24564.5
Year-06	24942.8
Year-07	25321.1
Year-08	25699.4
Year-09	26077.7
Year-10	26456
Year-11	26834.3
Year-12	27212.6
Year-13	27590.9
Year-14	27969.2
Year-15	28347.5
Year-16	28725.8
Year-17	29104.1
Year-18	29482.4
Year-19	29860.7
Year-20	30239

Seasonal factor of the forecast is as under:

Month Year-01	Persons	Seaonal Factor	Month Year-02	Persons	Seaonal Factor
Jan-01	1,879.50	0.978	Jan-02	1,880.20	0.963
Feb-01	1,901.00	0.990	Feb-02	1,884.00	0.965
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