Albatross Plc, the Australian subsidiary of a British packaging company, is preparing its budget for the year to 30 June 2019.

In respect of fuel oil consumption, it is desired to estimate an equation of the form

y = a + bx, where y is the total expense at an activity level x, a is the fixed expense and b is the rate of variable cost.

The following data relates to the year ending 30 June 2018:

Month

Machine Hours (R000)

Fuel oil expense

(R000)

Month

Machine Hours (R000)

Fuel oil expense

(R000)

July

44

660

January

36

520

August

40

640

February

36

520

September

44

640

March

41

550

October

49

610

April

45

570

November

52

520

May

53

600

December

42

550

June

58

700

The annual total and monthly average figures for the year ending 30 June 2018 were as follows:

Machine Hours

(R000)

Fuel oil expense

(R000)

Annual total

540

7080

Monthly Average

45

590

You are required to:

(a) estimate fixed and variable elements of fuel oil expense from the above data by both the following methods:

(i) high and low points (4 marks)

(ii) least-squares regression analysis; (8 marks)

(b) compare briefly the methods used in (a) above in relation to the task of estimating fixed and variable elements of a semi-variable cost; (7 marks)

(c) accepting that the coefficient of determination arising from the data given in the question is approximately 0.25, interpret the significance of this fact. (6 marks