Question

Quarterly sales for swarthmore cycles are follows:

1997-I 100
1997-II 110
1997-III 115
1997-IV 125
1998-I 130
1998-II 135
1998-III 145
1998-IV 150

a) Plot the sales data and graphically fit a straight line to the points.

b) In using the data for trend prediction, would the constant rate of change or the constant percentage change model be more appropriate. Explain

c) Using the data to estimate the co-efficient of the equation St = So(1+g)².

d) using a calculator or computation method described on pages 115-116 of chapter 4, use the data to estimate the co-efficient of the equation St = So+bt , where St is sales in the t quarter.

significant at the 95 percent pum be Forecast the demand for beef in the third quarter of 1999. 15-4 Quarterly sales for Swarthmore Cycles are as follows: Period Sales Period Sales 1997:1 100 1998:1 130 1997:11 110 1998:11 135 1997:111 115 1998:111145 1997:IV 125 1998:IV 150 a. Plot the sales data and graphically fit a straight line to the points.

Answer 1

Sales 160 140 120 100 80 Sales 60 40 20 0 1997- 1997-11 1997-l11 1997-V 1998- 1998-l1 1998-111 1998-M

b) Since sales vary from quarter to quarter, there is likely to be high cyclical component in every quarter. So if we try to predict sales using quarter to quarter growth rate, then it may not be so good.

But if the growth rate is computed over a year, then the cyclical component gets subsumed in the entire year and the computed growth rate is not vulnerable to cyclical component of the sales. Hence using constant rate of growth seems good.

c) 150=100(1+g)²

=> g = 22.475%

d) using STATA, I regressed Quarterly sales on time where time t=1,2,....8 and t=1 represents 1997:I and so forth. The results are as follows:

Sales = 94.64 + 7.02 t

So, S₀ = 94.64 and b=7.02