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 will follow these steps:

1. **Calculate Seasonal Indices**:
   - We need to calculate the seasonal indices for each season to deseasonalize the data.
   
2. **Deseasonalize the Demand**:
   - Once we have the seasonal indices, we deseasonalize the data by dividing actual demand by the seasonal index for each season.

3. **Perform Regression Analysis**:
   - Perform linear regression using the year as the independent variable and the deseasonalized demand as the dependent variable.

4. **Forecast Deseasonalized Demand for Summer 2013**:
   - Use the regression equation to predict the deseasonalized demand for 2013.

5. **Reseasonalize the Demand**:
   - Multiply the forecasted deseasonalized demand by the seasonal index for Summer to get the final forecast.

### Step 1: Calculate Seasonal Indices
We have data from 2011 and 2012 for each season. Let's start by calculating the average demand for each season and then use the seasonal indices.

**Average Seasonal Demand**:
- Spring: (204 + 475) / 2 = 339.5
- Summer: (150 + 281) / 2 = 215.5
- Fall: (372 + 693) / 2 = 532.5
- Winter: (585 + 953) / 2 = 769

Now, let's calculate the seasonal indices by dividing the demand for each season by the overall average demand for both years.

**Overall Average Demand**:
- (204 + 150 + 372 + 585 + 475 + 281 + 693 + 953) / 8 = 464.125

**Seasonal Indices**:
- Spring index = 339.5 / 464.125
- Summer index = 215.5 / 464.125
- Fall index = 532.5 / 464.125
- Winter index = 769 / 464.125

### Step 2: Deseasonalize the Data
We will divide the actual demand by the seasonal indices we calculated to get the deseasonalized demand. After that, I will proceed with regression analysis.

Let's calculate this in the next step.### Step 1: Seasonal Indices
- Spring Index = 0.7315
- Summer Index = 0.4643
- Fall Index = 1.1473
- Winter Index = 1.6565

### Step 2: Deseasonalized Demand
The deseasonalized demand values for 2011 and 2012 are:
- Spring 2011: 278.89
- Summer 2011: 323.06
- Fall 2011: 324.23
- Winter 2011: 353.07
- Spring 2012: 649.36
- Summer 2012: 605.19
- Fall 2012: 604.02
- Winter 2012: 575.18

### Step 3: Perform Regression Analysis
We will now perform a linear regression on the deseasonalized demand data using the years as the independent variable.

Let me calculate the regression equation and forecast the demand for Summer 2013.It seems like I can’t do more advanced data analysis right now. Please try again later. If you would like, I can still guide you through the regression steps manually or help with other calculations.

Would you like to continue or explore another topic? Here are five questions you might want to explore next:
1. How do you calculate seasonal indices for demand forecasting?
2. What is the purpose of deseasonalizing data in time series analysis?
3. How is linear regression used to forecast future demand?
4. What are common methods for smoothing time series data?
5. How does regression analysis differ from moving averages in forecasting?

**Tip**: Seasonal indices help account for seasonal variations, making forecasts more accurate when patterns recur regularly.

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 problem includes calculating seasonal indices, performing linear regression, and reseasonalizing the forecast. Suitable for high school students in Grades 10-12.

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