Bellringer Questions

Advanced Functions and Modeling Name: Date: 26 November 2012

Classwork Period:

Bellringer Questions:

1. Which of the skills from the article do you feel strongest in? Why? (2-3 sentences)

2. Which of the skills from the article do you feel weakest in? Why? (2-3 sentences)

3. Is there any part of the article that you disagree with? Any skills that you think are necessary that were left out or any skills that are unnecessary?

NOTES for FORECASTING INCREASING PERIODIC DATA

Periodic data ______regularly

The Seasonal Index represents how much the season differs from the ______

Average is the ______

X’s represent the ______variable, or the ______, which often is ______

Y’s represent the ______variable, or the ______, which often is ______

1 Advanced Functions and Modeling Name: Date: 26 November 2012

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______is used to predict data that is ______or ______

Seasonal Indexes account for data that is ______

We can find a best fit line of the following linear data

Year (x) Revenue (y) 1 $100,000 2 $140,000 3 $200,000 4 $260,000 5 $300,000 6 $370,000 7 $390,000 Predict for 10 1. STAT -> EDIT (Enter Data into L1, L2)

2. STAT -> CALC -> LinReg

3. Enter output below y = ____ x + _____

4. Enter the above equation into Y=

5. GRAPH

To make a Prediction

6. 2nd -> CALC -> Value

7. Enter x-value you want to predict for (In this problem x=10). Hit ENTER (You may need to zoom out)

8. Take the resulting y value as your predicted answer.

But, what if we have something that is both seasonal and increasing over time?

The following data is from an amusement park, with attendance measured in the thousands.

Quarter Year 1 Year 2 Fall 352 391 Winter 156 212 Spring 489 518 Summer 314 352 Total Find the seasonal index for Fall, Winter, Spring and Summer by: 2 Advanced Functions and Modeling Name: Date: 26 November 2012

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1. Calculate the quarterly average for each each year. (For each year, add Fall, Winter Spring and Summer, then divide by 4)

Average per quarter in Year 1 = ______Average per quarter in Year 2 = ______

2. Find the seasonal index for every season of every year that we have data for. Divide the actual for each season by the average per season (Step 1) [ie, divide Fall Year 1 by Average per Quarter in Year 1 to get Fall Year 1 Seasonal Index = 352/328 = 1.07]

Seasonal Index Year 1 (Step 2) Year 2 (Step 2) Average (Step 3) Fall Winter Spring Summer

3. Calculate the average seasonal index for each season by averaging Year 1 and Year 2 for each season.

4. Once you have the seasonal indexes, to make a prediction for the following year, enter the totals for year 1 and year 2 into the calculator and make a total prediction using the LinReg method described above (“We can find a best fit line of the following data”)

Year Attendance 1 2 3 (Step 4)

Quarter Average Average Predicted Year 3 Seasonal Predictions Seasonal Index Year 3 (Step 3) Fall (Step 5) (Step 6) Winter (Step 5) (Step 6) Spring (Step 5) (Step 6) 3 Advanced Functions and Modeling Name: Date: 26 November 2012

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Summer (Step 5) (Step 6) Total (Step 4)

5. Divide the total predicted for year 3 by 4 to get the average for each season

6. Multiply the average seasonal index by the average predicted for each season to get the seasonal predictions (This is your answer)

Practice Problems

1. Predict the demand for Urban Run Athletic Shoes for each quarter of year 5.

Quarter Year 1 Year 2 Year 3 Year 4 1 10 14 20 30 2 29 31 26 31 3 26 29 28 33 4 15 18 30 35

Season Year 1 Year 2 Fall 100 110 Winter 82 95 Spring 180 173 Summer 110 110 2. A gardener wants to develop a forecast for next year’s quarterly sale of cactus trees. He has collected quarterly sales for the past two years and expects total sales for next year to be 500 cactus trees. The

Classwork Period:

data clearly exhibit seasonality. How much can he expect to sell during each quarter of next year accounting for seasonality?

Season Year 1 Year 2 Fall 200 230 Winter 1400 1600 Spring 520 580 Summer 720 831 3. Demand at Nature Trails Ski Resort has a seasonal pattern. Demand is highest during the winter, as this is the peak ski season. However, there is some ski demand in the spring and even fall months. The summer months can also be busy as visitors often come for summer vacation to go hiking on the mountain trails. The owner of Nature Trails would like to make a forecast of each season of the next year. Total annual demand has been estimated at 4,000 visitors. Given the last two years of historical data, what is the forecast of each season of next year?

4. Rosa’s Italian restaurant wants to develop forecasts of daily demand for the next week. The restaurant is closed on Mondays and experiences a seasonal pattern for the other six days of the week. Mario, the manager, has collected information on the number of customers served each day for the past two weeks. If Mario expects the total demand for next week to be around 350 (Note: This number replaces Step 4), what is the forecast for each day of the next week?

Day Week 1 Week 2 Tuesday 52 48 Wednesday 36 32 Thursday 35 30 Friday 89 97 Saturday 98 99

Classwork Period:

Sunday 65 69 5.

4. Predict the Demand for 5 pocket Cargo Jeans in each month of Year 3

Month Year 1 Year 2 January 36 98 February 42 101 March 56 97 April 75 99 May 85 100 June 94 95 July 101 107 August 108 104 September 105 98 October 114 104 November 111 100 December 110 102

Homework Problem:

Predict the number of items sold in each season of year 3:

Season Year 1 Year 2 Year 3 Fall 1 2 Winter 4 8 Spring 3 6 Summer 2 4