The director of the Riley County, Kansas, library system would like to forecast evening patron usage for next week. Below are the data for the past 4 weeks: Week 1 Week 2 Week 3 Week 4 Mon 210 215 220 225 Tue Wed Thu Fri Sat 215 160 180 213 165 185 178 250 180 250 176 260 220 175 190 260 225 176 190 178 a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places). Mon Tue Wed Thu Fri Sat Day of the week Seasonal index b) Let x = 1 for Monday of Week 1. If the trend equation for this problem is: y=201.74 +0.18x, the forecast for each day of week 5 is (round your responses to the nearest whole number): Mon Tue Wed Thu Day of week 5 Forecast Fri Sat
The director of the Riley County, Kansas, library system would like to forecast evening patron usage for next week. Below are the data for the past 4 weeks: Week 1 Week 2 Week 3 Week 4 Mon 210 215 220 225 Tue Wed Thu Fri Sat 215 160 180 213 165 185 178 250 180 250 176 260 220 175 190 260 225 176 190 178 a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places). Mon Tue Wed Thu Fri Sat Day of the week Seasonal index b) Let x = 1 for Monday of Week 1. If the trend equation for this problem is: y=201.74 +0.18x, the forecast for each day of week 5 is (round your responses to the nearest whole number): Mon Tue Wed Thu Day of week 5 Forecast Fri Sat
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Part 1
The director of the Riley County, Kansas, library system would like to
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Mon |
Tue |
Wed |
Thu |
Fri |
Sat |
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Week 1 |
210 |
178 |
250 |
215 |
160 |
180 |
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Week 2 |
215 |
180 |
250 |
213 |
165 |
185 |
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Week 3 |
220 |
176 |
260 |
220 |
175 |
190 |
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Week 4 |
225 |
178 |
260 |
225 |
176 |
190 |
Part 2
a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places).
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Part 3
b) Let x
=1 for Monday of Week 1. If the trend equation for this problem is:
y
=201.74
+0.18x,
the forecast for each day of week 5 is (round your responses to the nearest whole number):
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![### Forecasting Evening Patron Usage at Riley County, Kansas Library
The Director of the Riley County, Kansas library system is looking to forecast evening patron usage for the upcoming week. Below are the data for the past 4 weeks:
| | Mon | Tue | Wed | Thu | Fri | Sat |
|----|-----|-----|-----|-----|-----|-----|
| **Week 1** | 210 | 178 | 250 | 215 | 160 | 180 |
| **Week 2** | 215 | 180 | 250 | 213 | 165 | 185 |
| **Week 3** | 220 | 176 | 260 | 220 | 175 | 190 |
| **Week 4** | 225 | 178 | 260 | 225 | 176 | 190 |
**a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places).**
| **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat |
|---------------------|-----|-----|-----|-----|-----|-----|
| **Seasonal index** | | | | | | |
**b) Let \( x = 1 \) for Monday of Week 1. If the trend equation for this problem is:**
\[ \hat{y} = 201.74 + 0.18x \]
The forecast for each day of Week 5 is (round your responses to the nearest whole number):
| **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat |
|---------------------|-----|-----|-----|-----|-----|-----|
| **Forecast** | | | | | | |
### Explanatory Notes:
- **Seasonal Index Calculation**:
- A seasonal index is a value that represents how a certain time period's data values compare to the typical or average data values.
- Typically, a seasonal index is calculated by finding the average value for each day, then dividing each day’s average by the overall average for all days.
- **Trend Equation**:
- The trend equation provided \( \hat{y} = 201.74 + 0.18x \) calculates a predictive value \( \hat{y} \) based on the value of x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F135ae681-a644-4164-9b10-2ae2e87534da%2F9f644c4d-70b4-4050-9878-b734a1b8b26d%2F2xhe8xv_processed.png&w=3840&q=75)
Transcribed Image Text:### Forecasting Evening Patron Usage at Riley County, Kansas Library
The Director of the Riley County, Kansas library system is looking to forecast evening patron usage for the upcoming week. Below are the data for the past 4 weeks:
| | Mon | Tue | Wed | Thu | Fri | Sat |
|----|-----|-----|-----|-----|-----|-----|
| **Week 1** | 210 | 178 | 250 | 215 | 160 | 180 |
| **Week 2** | 215 | 180 | 250 | 213 | 165 | 185 |
| **Week 3** | 220 | 176 | 260 | 220 | 175 | 190 |
| **Week 4** | 225 | 178 | 260 | 225 | 176 | 190 |
**a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places).**
| **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat |
|---------------------|-----|-----|-----|-----|-----|-----|
| **Seasonal index** | | | | | | |
**b) Let \( x = 1 \) for Monday of Week 1. If the trend equation for this problem is:**
\[ \hat{y} = 201.74 + 0.18x \]
The forecast for each day of Week 5 is (round your responses to the nearest whole number):
| **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat |
|---------------------|-----|-----|-----|-----|-----|-----|
| **Forecast** | | | | | | |
### Explanatory Notes:
- **Seasonal Index Calculation**:
- A seasonal index is a value that represents how a certain time period's data values compare to the typical or average data values.
- Typically, a seasonal index is calculated by finding the average value for each day, then dividing each day’s average by the overall average for all days.
- **Trend Equation**:
- The trend equation provided \( \hat{y} = 201.74 + 0.18x \) calculates a predictive value \( \hat{y} \) based on the value of x.
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