Use the Sport Shop data set below and α=0.3
 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	745
2016	742
2017	713
2018	689
2019	510
2020	755
2021	525

To calculate the simple exponential smoothing (SES) forecast for the number of sports equipment that will be sold in 2022 with a smoothing factor \(\alpha = 0.3\), we need to use the formula:

\[
F_{t+1} = \alpha \cdot A_t + (1 - \alpha) \cdot F_t
\]

Where:
- \( F_{t+1} \) is the forecast for the next period (2022 in our case),
- \( A_t \) is the actual value for the current period,
- \( F_t \) is the forecast for the current period,
- \( \alpha = 0.3 \) is the smoothing factor.

Given that the forecast for 2015 is assumed to be the actual value of 2015 (\(F_{2015} = 745\)), we can proceed year by year to calculate the forecast up to 2022.

Let's go through the calculations step by step.

### 1. Forecast for 2016:
\[
F_{2016} = \alpha \cdot A_{2015} + (1 - \alpha) \cdot F_{2015}
\]
\[
F_{2016} = 0.3 \cdot 745 + 0.7 \cdot 745 = 745
\]

### 2. Forecast for 2017:
\[
F_{2017} = \alpha \cdot A_{2016} + (1 - \alpha) \cdot F_{2016}
\]
\[
F_{2017} = 0.3 \cdot 742 + 0.7 \cdot 745 = 743.10
\]

### 3. Forecast for 2018:
\[
F_{2018} = \alpha \cdot A_{2017} + (1 - \alpha) \cdot F_{2017}
\]
\[
F_{2018} = 0.3 \cdot 713 + 0.7 \cdot 743.10 = 733.17
\]

### 4. Forecast for 2019:
\[
F_{2019} = \alpha \cdot A_{2018} + (1 - \alpha) \cdot F_{2018}
\]
\[
F_{2019} = 0.3 \cdot 689 + 0.7 \cdot 733.17 = 719.42
\]

### 5. Forecast for 2020:
\[
F_{2020} = \alpha \cdot A_{2019} + (1 - \alpha) \cdot F_{2019}
\]
\[
F_{2020} = 0.3 \cdot 510 + 0.7 \cdot 719.42 = 655.59
\]

### 6. Forecast for 2021:
\[
F_{2021} = \alpha \cdot A_{2020} + (1 - \alpha) \cdot F_{2020}
\]
\[
F_{2021} = 0.3 \cdot 755 + 0.7 \cdot 655.59 = 685.41
\]

### 7. Forecast for 2022:
\[
F_{2022} = \alpha \cdot A_{2021} + (1 - \alpha) \cdot F_{2021}
\]
\[
F_{2022} = 0.3 \cdot 525 + 0.7 \cdot 685.41 = 637.79
\]

### Final Result:
The simple exponential smoothing forecast for the number of sports equipment sold in 2022 is **637.79**.

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Do you need further details or have any questions?

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Here are 5 related questions to explore:
1. How does the smoothing factor \(\alpha\) affect the forecast in exponential smoothing?
2. What would the forecast be if \(\alpha = 0.5\) instead?
3. How would a trend or seasonality affect simple exponential smoothing?
4. Can exponential smoothing be used for short-term vs long-term forecasts, and what are the limitations?
5. How does exponential smoothing compare to other forecasting methods like moving averages?

**Tip:** In exponential smoothing, lower \(\alpha\) values give more weight to past forecasts, making the model slower to react to recent changes.

Use the Sport Shop data set below and α=0.3 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 sold in 2022 using the Sport Shop data set and α=0.3. This problem covers time series forecasting concepts and uses the formula F_{t+1} = α ⋅ A_t + (1 - α) ⋅ F_t. The forecast starts from 2015 and proceeds year by year, with a final result of 637.79 for 2022.

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