Question

a) The managing director of Hani Co had collected sales data for a period of three consecutive years in order to look at the trend of the sales. The data are shown in Table 1 bètow. Table 1 Sales data for three consecutive years Year Sales (RM 000) 1Quarter 2nd Quarter 3 Quarter 4th Quarter 60.5 68.7 60.0 2013 74.9 72.8 63.5 i. (10 Marks) Find the trend equation by using the least square method. (5 Marks) i. Forecast the sales for the 3"d quarter of 2015.

Answer 1

Answer:)

(i.)Let us define the following variables:

• t = the time since Q1, 2012 We will call it the quarter label.
  For example, Q4, 2013 will have t = 7, and that of Q1, 2012 will be t = 0.
• y(t) = the sales in that particular quarter label t

Now, we assume a linear trend equation of the form y(t) = mt + c. From the least squares method, we have :

m=

$c = \bar{y} - m\cdot \bar{t}$

Now,

-=--1 ti =5.5 12 12 Lily, 67.5333 y= 12 Σ-l (t, -5.5)(Vi-67.5333) 2.19021 b = 67.533-219021 *5.5 ~ 55.4872

Hence the (linear) trend equation is given by :

y(t)- (2.19021)t + 55.4872

(ii.) We see that Q3, 2015 has a t-value of t = 14. Thus, the predicted value of the sales is

y (14) 86.15014