Problem 3 The following table shows quarter data on sales of Turner Industries i

Question

Problem 3 The following table shows quarter data on sales of Turner Industries in the last 4 years. 118 135 160 152 126 143 170 162 133 153 178 175 145 173 199 193 a) Use the data to calculate the CMA, seasonal ratios, and the seasonal indices b) Use the seasonal indices to deseasonalize the sales' data. c) Estimate the trend line Y = A, +BT + ? , where T is the time variable (attach the output of the regression). d) Forecast the Ist and 2nd quarters in the year 5 using the estimated trend line. e) Adjust the forecast in d) for seasonality using the seasonal indices.

Explanation / Answer

a)

CMA: with 3 Moving Average

Qtr1 Qtr2 Qtr3 Qtr4
NA 137.6667 149.0000 146.0000
140.3333 146.3333 158.3333 155.0000
149.3333 154.6667 168.6667 166.0000
164.3333 172.3333 188.3333 NA

Seasonal Ratio - the ratio of the original series to the estimated trend

Qtr1 Qtr2 Qtr3 Qtr4
NA 0.9806295 1.0738255 1.0410959
0.8978622 0.9772210 1.0736842 1.0451613
0.8906250 0.9892241 1.0553360 1.0542169
0.8823529 1.0038685 1.0566372 NA

Seasonal Index

Q1 Q2 Q3 Q4

-22.614583 -4.281250 17.968750 8.927083

b) Add seasonal index to original values to deaseasonalize

Qtr1 Qtr2 Qtr3 Qtr4
141.0715 140.0076 141.4591 142.4617
149.0715 148.0076 151.4591 152.4617
156.0715 158.0076 159.4591 165.4617
168.0715 178.0076 180.4591 183.4617

c)

Call:
lm(formula = Sales ~ T)

Coefficients:
(Intercept) TQ2 TQ3 TQ4  
130.50 20.50 46.25 40.00  

Y = 130.5 + 20.50X2 + 46.25 X3 + 40 X4

d)

Forecast for 1st and 2nd quarters in the 5th year are 130.50 and 151.00

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