Some time ago Robert launched a new product some years ago at first, sales were good but now the figures are causing concern. Robert wants a more accurate sales forecast to produce detailed cash forecasts.

Since there is some seasonality present in the raw data, the series for sales shown below represents the underlying trend based on an averaging process:

On average, quarters, 1 and 3 are 5% and 6% respectively above trend whilst quarters 2 and 4 are respectively 2% and 9% below trend. Some preliminary calculations on the above ten observations have been carried out and the results are summarised below:

Results from ten periods’ observations:

Linear regression y = a + bx Slope = 82.67 Intercept = 10,472.33 Coefficient of determination = 0.535

It is required to make forecasts of sales for quarters 3 and 4 in 2019 and for quarters 1 and 2 in 2020 but there is some discussion on whether the ten-period data shown above are suitable for forecasting or whether only the last five periods would provide a better basis for forecasting. Linear analysis of the last five periods only gives the following intermediate results:

Results of last five periods’ observations:

y = 555.10

x2 = 330

y2 = 61,627.40

xy = 4,442.15

Note: the y values have been scaled down by 100 times for ease of calculation.

Required:

a. Forecast the sales of the four quarters required using the ten-period observations results.

(6 Marks)

b. Prepare similar forecasts based on the last five periods’ observations.

(8 Marks)

c. Explain which forecasting basis produces the better forecast. (6 Marks)