The data below is the sale of Television for the past 4 weeks (January). The tel
ID: 3142347 • Letter: T
Question
The data below is the sale of Television for the past 4 weeks (January). The television was produced the day before the sale that is Sunday, Tuesday, and Thursday while sales are conducted every Monday, Wednesday, and Friday for each week.
DAY
Past Data
4 weeks
3 weeks
2 weeks
1 week
Monday
Tuesday
100000
110000
110000
115000
Wednesday
0
0
0
0
Thursday
98000
99000
100000
95000
Friday
0
0
0
Saturday
0
0
0
Sunday
115000
112000
120000
119000
Total
313000
321000
330000
333500
Calculate a forecast on the fifth week (current week) with the following note:
A. Using 4 weeks simple moving average
B. Using a weighted moving average with 0.60, 0.40, 0.30, 0.10 for the previous 4 weeks of data
C. A television manufacturer also plans to make Radio for sale. Sales are expected to reach 20,000 units in the past week as they are only allowed and only 18,000 are sold. What the company should do to forecast sales this week by using exponential smoothing with Lambda = 0.015
D. Predict the number of first week production for the next month with linear forecasting and calculate the standard error estimate, confidence interval, prediction interval with t = 7 and 95% confidence level.
DAY
Past Data
4 weeks
3 weeks
2 weeks
1 week
Monday
0 0 0 0Tuesday
100000
110000
110000
115000
Wednesday
0
0
0
0
Thursday
98000
99000
100000
95000
Friday
00
0
0
Saturday
0
00
0
Sunday
115000
112000
120000
119000
Total
313000
321000
330000
333500
Explanation / Answer
Part (a)
For 4 month moving average, average of 4 actual values before the forecast period is calculated
Ft = ( At-1 + At-2+ At-3 + At-4 ) / 4
where Ft = Forecast at time period t, At = Actual at time period t
Forecast (t) = ( 313000+321000+330000+333500)/4 = 324375
Part (b)
Weighted moving averages are generally used to assign more weightage to the recent values to make sure the latest trend is captured. The catch here is to make sure either the sum of weights is -
Ft = (W1 At-1 +W2 At-2+ W3 At-3 +W4 At-4 ) / (W1 + W2 + W3 + W4)
Ft = ( 313000*0.6 + 321000*0.4 + 330000* 0.3+ 333500*0.1) / (0.6+0.4+0.3+0.1)
Ft = 320393
Part (c)
Ft+1 = Ft + a (Ft - Yt)
a is the smoothing constant, Ft - Last period forecasted value, Yt - Last period actual value
Ft+1 = 20,000 + 0.015 (20,000 - 18,000)
= 20,030
The company should manufacture 20,030 radio sets
Part (d)
For linear forecast, we consider the time series of the first 4 weeks and create a linear regression model on it with independent variable being 1,2,3,4,5 for 5 weeks and dependent variable as sales of 4 weeks.
Method 1: excel has a simple function for it - forecast(X5, Y1: Y4, X1: X4 )
Method 2:Linear regions
Next week forecast - 306750
Standard Error - 1894.07
confidence interval formula - [B0 - t((1-a)/2, n-k-1) SE B0 + t((1-a)/2, n-k-1) SE]
where 0 = Forecast, k = Number of Predictors, n = Sample Size, SE0 = Standard Error, = Percentage of Confidence Interval t = t-Value
95% confidence interval - [298597 to 314903]
X Y 1 333500 2 330000 3 321000 4 313000 5 =FORECAST(F21,G17:G20,F17:F20)Related Questions
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