Based on the OCR data extraction and your input, we know that we need to calculate the smoothed level, smoothed slope, forecasts, errors, and square forecast error for each month in the dataset. Let's start with the given dataBased on the OCR data extraction and your input, we know that we need to calculate the smoothed level, smoothed slope, forecasts, errors, and square forecast error for each month in the dataset. Let's start with the given

Given Information:

• Initial level $l_0 = 207.0152$
• Initial slope $b_0 = 6.5490$
• Smoothing constants $\alpha = 0.2$ and $\gamma = 0.2$
• The forecast for period 1 is $213.56$
• The smoothed level for period 1 is $210.2513$

Let's calculate the slope for period 1 before being smoothed with the previous period slope using the formula:

$b_t = (l_t - l_{t-1})$

Using this, we'll compute $b_1$ and compare the answer choices to find the correct slope for period 1.The slope for period 1 before being smoothed with the previous period slope is approximately 3.2361.

This matches one of the answer choices provided. Would you like me to proceed with further details or calculations?

Related Questions:

1. How do we calculate the smoothed slope for subsequent periods?
2. What is the role of the smoothing constants ($\alpha$ and $\gamma$) in this forecasting model?
3. How do we compute forecast errors and square forecast errors?
4. What is the significance of the initial level and slope in exponential smoothing?
5. How would different values of $\alpha$ and $\gamma$ impact the forecast accuracy?

Tip:

Always ensure that your smoothing constants ($\alpha$ and $\gamma$) are selected carefully to balance responsiveness to changes in data with the stability of forecasts.