Question
In: Operations Management
The quarterly sales data (number of book sold) for Christian book over the past three years...
The quarterly sales data (number of book sold) for Christian book over the past three years in California follow: (You can use Excel to compute the equation)
|
Quarter |
Year 1 |
Year 2 |
Year 3 |
|
1 |
1650 |
1700 |
1750 |
|
2 |
950 |
800 |
1200 |
|
3 |
2600 |
2950 |
3100 |
|
4 |
2700 |
2450 |
2850 |
- Construct a line graph showing the pattern of Christian book sales. Please make sure ‘time/quarter’ is represented by the horizontal line and ‘quarterly sale’ is represented by the vertical line. What type of pattern exists in the data?
- Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data: Quarter1=1 if the sales data point is in Quarter 1, otherwise Quarter 1=0; Quarter 2=1 if the sales data point is in Quarter 2, otherwise, Quarter 2=0; Quarter 3=1 if the sales data point is in Quarter 3, otherwise Quarter 3=0. 3.
- Compute the quarterly forecasts for next year.
- 4. Let t=1 to refer to the observation in quarter 1 of year 1; t=2 to refer to the observation in quarter 2 of year 1;,,,, and t=12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and t, develop an estimated regression equation to account for seasonable effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.
Solutions
Expert Solution
Part a) Following is the required chart:
Following pattern is observed by the above chart: Quarter 2 is having the least sales in all the years follwed by quarter 1 then quarter 3 and then quarter 4.
Part b) Following is the formulated data as per requirement and the ANOVA table:
Required Equation from above
regression model is :
Sales = 2666.67 - 966.67*Q1 - 1683.34*Q2 + 216.67*Q3
Next year forecasts are as follows:
Quarter 1 = 1700 units
Quarter 2 = 983 units
Quarter 3 = 2883 units
Quarter 4 = 2667 units
Part c) Following is the formulated data as per requirement and the ANOVA table:
Required Equation from above regression model is :
Sales = 2416.67 + 31.25*t - 872.92*Q1 - 1620.84*Q2 + 247.92*Q3
Next year forecasts are as follows:
Quarter 1 = 1950 units
Quarter 2 = 1233 units
Quarter 3 = 3133 units
Quarter 4 = 2917 units
keosha answered 10 months agoRelated Solutions
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book over the past three years in California follow:
Year 1
Year
2
Year 3
1690
1800
1850
940
900
1100
2625
2900
2930
2500
2360
2615
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1
1
1690
2
940
3
2625
4
2500
2
1
1800
2
900
3
2900
4
2360
3
1
1850
2
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3
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2615
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The quarterly sales data (number of copies sold) for a college textbook over the past three...
The quarterly sales data (number of copies sold) for a college
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Click on the datafile logo to reference the data.
quarter year 1 year 2 year 3
1 1690 1800 1850
2 940 900 1100
3 2625 2900 2930
4 2500 2360 2615
e. Deseasonalize the time series (to 3
decimals).
Year
Quarter
Deseasonalized Value
1
1
2
3
4
2
1
2
3
4
3
1
2
3
4
f....
The quarterly sales (number of books sold) over the past 3 years are as shown below....
The quarterly sales (number of books sold) over the past 3 years
are as shown below.
Year
Quarter
Period
Sales
1
1
1
1700
1
2
2
1000
1
3
3
2700
1
4
4
2500
2
1
5
1800
2
2
6
900
2
3
7
2900
2
4
8
2400
3
1
9
1800
3
2
10
1100
3
3
11
2900
3
4
12
2600
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Actual
1
300
5
416
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540
6
760
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885
7
1191
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580
8
760
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Actual
1.00
300.00
2.00
540.00
3.00
885.00
4.00
580.00
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416.00
6.00
760.00
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1191.00
8.00
760.00
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