Y12FM Time Series

The pattern in the time series in the graph shown is best described as:

• Trend only

• trend with random variation

• seasonal

• seasonal with trend

• random

For the time series given in the table, the 3-moving mean for time period 2 is:

• 38

• 39

• 40

• 41

• 42

For the data in the table, the 2-moving mean with centring at time period 6 is:

• 13

• 5,5

• 6.25

• 8.5

• 9.25

Suppose that the seasonal indices for the number of travelers on a tram route are as given in the table.

The value of a is:

• 0.9

• 1.0

• 1.1

• 1.2

• 1.3

The number of visitors recorded at a garden centre each quarter of one year are as follows:

Assuming that there is a seasonal component to the number of visitors to the garden centre, the seasonal index for winter is closest to:

• 8068

• 2017

• 1.47

• 0.12

• 0.49

The seasonal indices for the number of air-conditioners sold at a particular shop are given in the following table:

If the number of air-conditioners sold in the third quarter, Q₃, is 422, then the deseasonalised figure (to the nearest whole number) is:

• 295

• 253

• 422

• 597

• 703

A hotel has noted that their seasonal index for room bookings in the autumn quarter is 1.2. In terms of their quarterly bookings this means that:

• in autumn they have 20% more bookings than in winter

• in autumn they have 20% less bookings than in an average quarter

• each autumn they have 20% more bookings than in the previous autumn

• in autumn they have 20% more bookings than in an average quarter

• in autumn they have 120% more bookings than in an average quarter

Deseasonalised prices (cents/litre) for a petrol outlet for one week are given in the following table.

The equation of the least squares regression line (with day recorded as 1, 2, 3, 4, 5, 6, 7) which would enable us to predict the deseasonalised price is closest to:

• price = 3.11 + 86.9 × day

• price = -21.2 + 0.254 × day

• price = 86.9 + 3.11 × day

• price = 0.25 – 21.2 × day

• price = 92.3 + 1.04 × day

A least squares regression trend line was fitted to a deseasonalised set of quarterly sales data, in which the first data point was summer 2004, the second autumn 2004, the third winter 2004, the fourth spring 2004, and so on. The line was found to have the following rule:

quarterly sales = 930 + 42 x time period

The seasonal indices for the sales in this company are shown in the table:

From the slope of the trend line it can be said that:

• on average sales are increasing by 42 per quarter

• on average sales are increasing by 930 per quarter

• on average sales are increasing by 930 per year

• on average sales are decreasing by 42 per quarter

• on average sales are increasing by 42 per year

The number of lunches sold at the tuck shop one week are as follows.

Assuming that there is a seasonal component to the number of lunches sold, the seasonal index for Monday (calculated on a five-day week) is closest to:

• 335

• 67

• 0.55

• 1.55

• 1.82