Use the Sport Shop data set below and α=0.2
 to calculate the simple exponential smoothing forecast for the number of sports equipment that will be sold in 2022. Assume the forecast for year 2015 to be the actual value of year 2015. Round your answer to two decimal places, if necessary.
 
Year	Number of Sports Equipment
2015	860
2016	981
2017	677
2018	539
2019	713
2020	765
2021	565


To calculate the simple exponential smoothing forecast for 2022 using the given data set and smoothing constant \( \alpha = 0.2 \), we will follow these steps:

### Step-by-Step Process:

1. **Start with the forecast for 2015**: 
   The problem states that the forecast for 2015 is the actual value, so:
   \[
   F_{2015} = A_{2015} = 860
   \]

2. **Apply the simple exponential smoothing formula**:
   The formula for simple exponential smoothing is:
   \[
   F_{t+1} = \alpha \cdot A_t + (1 - \alpha) \cdot F_t
   \]
   Where:
   - \( F_{t+1} \) is the forecast for the next period (year).
   - \( \alpha \) is the smoothing constant (in this case, \( \alpha = 0.2 \)).
   - \( A_t \) is the actual value for the current period.
   - \( F_t \) is the forecast for the current period.

### Calculating Forecasts for Each Year:

- **2016**:
   \[
   F_{2016} = 0.2 \cdot A_{2015} + 0.8 \cdot F_{2015}
   \]
   \[
   F_{2016} = 0.2 \cdot 860 + 0.8 \cdot 860 = 860
   \]

- **2017**:
   \[
   F_{2017} = 0.2 \cdot A_{2016} + 0.8 \cdot F_{2016}
   \]
   \[
   F_{2017} = 0.2 \cdot 981 + 0.8 \cdot 860 = 886.2
   \]

- **2018**:
   \[
   F_{2018} = 0.2 \cdot A_{2017} + 0.8 \cdot F_{2017}
   \]
   \[
   F_{2018} = 0.2 \cdot 677 + 0.8 \cdot 886.2 = 844.96
   \]

- **2019**:
   \[
   F_{2019} = 0.2 \cdot A_{2018} + 0.8 \cdot F_{2018}
   \]
   \[
   F_{2019} = 0.2 \cdot 539 + 0.8 \cdot 844.96 = 783.77
   \]

- **2020**:
   \[
   F_{2020} = 0.2 \cdot A_{2019} + 0.8 \cdot F_{2019}
   \]
   \[
   F_{2020} = 0.2 \cdot 713 + 0.8 \cdot 783.77 = 769.42
   \]

- **2021**:
   \[
   F_{2021} = 0.2 \cdot A_{2020} + 0.8 \cdot F_{2020}
   \]
   \[
   F_{2021} = 0.2 \cdot 765 + 0.8 \cdot 769.42 = 768.54
   \]

- **2022** (Forecast):
   \[
   F_{2022} = 0.2 \cdot A_{2021} + 0.8 \cdot F_{2021}
   \]
   \[
   F_{2022} = 0.2 \cdot 565 + 0.8 \cdot 768.54 = 726.83
   \]

### Final Forecast for 2022:
The forecast for the number of sports equipment to be sold in 2022 is **726.83**.

Would you like further details or have any questions?

### Related Questions:
1. What are the assumptions behind using exponential smoothing for forecasting?
2. How does changing the smoothing constant \( \alpha \) affect the forecast?
3. Can simple exponential smoothing handle data with trends or seasonality?
4. What is the difference between simple and double exponential smoothing?
5. How can one assess the accuracy of a forecast made using exponential smoothing?

### Tip:
In exponential smoothing, a higher \( \alpha \) gives more weight to recent data, making the forecast more responsive to recent changes.

Use the Sport Shop data set below and α=0.2 to calculate the simple exponential smoothing forecast for the number of sports equipment that will be sold in 2022. Assume the forecast for year 2015 to be the actual value of year 2015. Round your answer to two decimal places, if necessary.

Learn how to calculate the simple exponential smoothing forecast for the number of sports equipment sales in 2022 using α=0.2. Starting with the 2015 sales data and smoothing through to 2021, this method provides a forecast for 2022. Key concepts include time series forecasting and exponential smoothing.

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