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

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?

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 l0=207.0152l_0 = 207.0152
  • Initial slope b0=6.5490b_0 = 6.5490
  • Smoothing constants α=0.2\alpha = 0.2 and γ=0.2\gamma = 0.2
  • The forecast for period 1 is 213.56213.56
  • The smoothed level for period 1 is 210.2513210.2513

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

bt=(ltlt1)b_t = (l_t - l_{t-1})

Using this, we'll compute b1b_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 (α\alpha and γ\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 α\alpha and γ\gamma impact the forecast accuracy?

Tip:

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

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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