Math Problem Statement
The initial level and growth rate (slope). Run a regression on the first twelve months and report the initial level (l0) and growth rate (b0). The INTERCEPT and SLOPE function in Excel to get the coefficients 207.0152 , 6.5490 Assuming an initial value of alpha = 0.2 and gamma = 0.2, calculate the smoothed level, smoothed slope, forecasts, errors and square forecast error for each month in the dataset. The forecast for period 1 is 213.56 The smoothed level for period 1 is 210.2513 What is the slope in period 1 before being smoothed with the previous period slope? Group of answer choices 3.2576 3.9918 3.6049 3.2361
Solution
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
- Initial slope
- Smoothing constants and
- The forecast for period 1 is
- The smoothed level for period 1 is
Let's calculate the slope for period 1 before being smoothed with the previous period slope using the formula:
Using this, we'll compute 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:
- How do we calculate the smoothed slope for subsequent periods?
- What is the role of the smoothing constants ( and ) in this forecasting model?
- How do we compute forecast errors and square forecast errors?
- What is the significance of the initial level and slope in exponential smoothing?
- How would different values of and impact the forecast accuracy?
Tip:
Always ensure that your smoothing constants ( and ) are selected carefully to balance responsiveness to changes in data with the stability of forecasts.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Smoothing Techniques
Time Series Forecasting
Formulas
Linear regression formula: y = mx + b
Smoothing level: l_t = α * y_t + (1 − α) * (l_{t−1} + b_{t−1})
Smoothing slope: b_t = γ * (l_t − l_{t−1}) + (1 − γ) * b_{t−1}
Forecasting formula: F_{t+1} = l_t + b_t
Theorems
Exponential Smoothing Theorem
Simple Linear Regression
Suitable Grade Level
Undergraduate Level
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