The following are historical demand data:

 

YEAR	SEASON	ACTUAL
DEMAND
2011	Spring	204
 	Summer	150
 	Fall	372
 	Winter	585
2012	Spring	475
 	Summer	281
 	Fall	693
 	Winter	953
 

Use regression analysis on deseasonalized demand to forecast demand in summer 2013. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

 



To forecast demand for Summer 2013 using regression analysis on deseasonalized demand, we'll follow these steps:

### Steps:

1. **Calculate Seasonal Indices**:
   We first need to calculate the seasonal indices for each season (Spring, Summer, Fall, Winter) over the two years provided (2011 and 2012).

2. **Deseasonalize Demand**:
   Deseasonalized demand is calculated by dividing the actual demand by the seasonal index for each season.

3. **Perform Regression Analysis**:
   We'll use linear regression on the deseasonalized demand values to estimate the trend over time (i.e., to find the relationship between the year and demand).

4. **Forecast the Deseasonalized Demand for Summer 2013**:
   Using the regression model, we’ll project the deseasonalized demand for Summer 2013.

5. **Reseasonalize the Demand**:
   Multiply the deseasonalized forecast for Summer 2013 by the seasonal index for summer to obtain the final forecast.

Let’s start by calculating the seasonal indices. The formula for a seasonal index is:

\[
\text{Seasonal Index} = \frac{\text{Average Demand for the Season}}{\text{Average Demand for the Year}}
\]

### Data for Each Year:
- 2011 Total Demand: \( 204 + 150 + 372 + 585 = 1311 \)
- 2012 Total Demand: \( 475 + 281 + 693 + 953 = 2402 \)

### Average Demand for Each Season (2011 and 2012):
- **Spring**: \( \frac{204 + 475}{2} = 339.5 \)
- **Summer**: \( \frac{150 + 281}{2} = 215.5 \)
- **Fall**: \( \frac{372 + 693}{2} = 532.5 \)
- **Winter**: \( \frac{585 + 953}{2} = 769 \)

### Average Demand for Each Year:
- 2011: \( 1311 / 4 = 327.75 \)
- 2012: \( 2402 / 4 = 600.5 \)

### Seasonal Indices:
- **Spring**: \( \frac{339.5}{(327.75 + 600.5)/2} \)
- **Summer**: \( \frac{215.5}{(327.75 + 600.5)/2} \)
- **Fall**: \( \frac{532.5}{(327.75 + 600.5)/2} \)
- **Winter**: \( \frac{769}{(327.75 + 600.5)/2} \)

I'll compute these values for you.The seasonal indices for each season are:

- **Spring**: 0.7315
- **Summer**: 0.4643
- **Fall**: 1.1473
- **Winter**: 1.6569

Next, we will deseasonalize the demand for each season by dividing the actual demand by the corresponding seasonal index. Then, we will perform regression analysis on the deseasonalized data to forecast the demand for Summer 2013.

### Deseasonalized Demand Calculation:

\[
\text{Deseasonalized Demand} = \frac{\text{Actual Demand}}{\text{Seasonal Index}}
\]

Let's compute the deseasonalized demand for 2011 and 2012.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can guide you through the manual process of deseasonalizing the demand and performing the regression. 

Feel free to ask for further assistance!

Here are 5 related questions you might be interested in:
1. How do you perform linear regression by hand?
2. What are the different methods for forecasting demand?
3. How are seasonal indices calculated in time series analysis?
4. What is the difference between deseasonalizing and de-trending data?
5. How does seasonality affect demand forecasting?

**Tip**: Deseasonalizing data helps in identifying the underlying trends by removing the fluctuations caused by regular seasonal patterns.

Use regression analysis on deseasonalized demand to forecast demand in summer 2013. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Learn how to forecast demand for Summer 2013 using regression analysis on deseasonalized demand. This guide covers seasonal index calculation, deseasonalizing data, and applying linear regression to predict future demand, suitable for students in Grades 11-12.

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