QUESTION 3 (36 MARKS)

The following data represents the sales (R100 000) of a beer producer for each quarter from 1990 to 1993:

Quarterly sales

Year

I

II

III

IV

1990

24

19

25

38

1991

27

22

24

40

1992

31

23

23

41

1993

35

24

21

48

Use the data provided above to determine the following:

3.1) Represent the time series graphically. [4 marks]

3.2) Determine the least squares trend line equation for this data set, and represent it graphically.

[8 marks]

3.3) Use the trend line equation obtained to estimate sales for the first term or 1989 and the second term of 1994 [2+2 marks]

3.4) Calculate centered four-quarterly moving averages and represent them graphically.

[8 marks]

3.5) Calculate the typical seasonal index and represent these indices graphically on the same axes constructed in Question 3.4. [12 marks]