Calculate And Answer Parts A Through D. Include All Calculat
Calculate and answer parts a through d. Include all calculations and spreadsheets in your post. Explain why the moving average method was used instead of another forecasting method. What might be another forecasting method that could prove to be just as useful?
Calculate and answer parts a through d. Include all calculations and spreadsheets in your post. Explain why the moving average method was used instead of another forecasting method. What might be another forecasting method that could prove to be just as useful? The figures below indicate the number of mergers that took place in the savings and loan industry over a 12-year period.
Year Mergers Year Mergers Calculate a 5-year moving average to forecast the number of mergers for 2012. Use the moving average technique to determine the forecast for 2005 to 2011. Calculate measurement error using MSE and MAD. Calculate a 5-year weighted moving average to forecast the number of mergers for 2012. Use weights of 0.10, 0.15, 0.20, 0.25, and 0.30, with the most recent year weighted being the largest. Use regression analysis to forecast the number of mergers in 2012.
Paper For Above instruction
Introduction
Forecasting the trend of mergers in the savings and loan industry is vital for strategic planning and investment decision-making. Due to the historical data spanning twelve years, various quantitative techniques such as moving averages and regression analysis can be employed to project future activity. This paper performs multiple forecasting calculations, including a 5-year simple moving average, a weighted moving average, and regression analysis to predict the number of mergers in 2012. Additionally, it discusses the rationale behind choosing these methods and considers alternative approaches.
Data Overview
The data consists of the annual number of mergers in the savings and loan industry over twelve years. Although specific figures are not provided in the prompt, for illustrative purposes, suppose the following merger counts:
| Year | Mergers |
|---|---|
| 2001 | 45 |
| 2002 | 50 |
| 2003 | 55 |
| 2004 | 47 |
| 2005 | 52 |
| 2006 | 58 |
| 2007 | 54 |
| 2008 | 57 |
| 2009 | 60 |
| 2010 | 62 |
| 2011 | 65 |
| 2012 | NA |
This illustrative data form the basis of our analysis.
Part A: 5-Year Moving Average Forecast for 2012
The 5-year moving average method involves averaging the mergers from the previous five years to forecast the next year's mergers. For the year 2012, the forecast will be based on the average mergers from 2007 to 2011.
Calculations:
- 2007–2011 mergers: 54, 57, 60, 62, 65
- Sum = 54 + 57 + 60 + 62 + 65 = 298
- 5-year moving average = 298 / 5 = 59.6
Forecast for 2012: approximately 60 mergers.
Similarly, forecasts for 2005–2011 are computed using their respective five-year windows:
- 2005: average of 2001–2005 (45, 50, 55, 47, 52) = (45+50+55+47+52)/5 = 249/5 = 49.8
- 2006: average of 2002–2006 (50, 55, 47, 52, 58) = (50+55+47+52+58)/5 = 262/5 = 52.4
- 2007: average of 2003–2007 (55, 47, 52, 58, 54) = (55+47+52+58+54)/5 = 266/5 = 53.2
- 2008: average of 2004–2008 (47, 52, 58, 54, 57) = (47+52+58+54+57)/5 = 268/5 = 53.6
- 2009: average of 2005–2009 (52, 58, 54, 57, 60) = (52+58+54+57+60)/5 = 281/5 = 56.2
- 2010: average of 2006–2010 (58, 54, 57, 60, 62) = (58+54+57+60+62)/5 = 291/5 = 58.2
- 2011: average of 2007–2011 (54, 57, 60, 62, 65) = 298/5 = 59.6
Part B: Calculation of Measurement Error (MAD and MSE)
Measurement errors evaluate forecast accuracy:
- Mean Absolute Deviation (MAD): average of absolute forecast errors
- Mean Squared Error (MSE): average of squared forecast errors
Using the actual and forecasted values:
| Year | Actual Mergers | Forecast | Error = Actual - Forecast | | Error squared |
|--------|----------------|----------|---------------------------|----------------|
| 2005 | 52 | 49.8 | 2.2 | 4.84 |
| 2006 | 58 | 52.4 | 5.6 | 31.36 |
| 2007 | 54 | 53.2 | 0.8 | 0.64 |
| 2008 | 57 | 53.6 | 3.4 | 11.56 |
| 2009 | 60 | 56.2 | 3.8 | 14.44 |
| 2010 | 62 | 58.2 | 3.8 | 14.44 |
| 2011 | 65 | 59.6 | 5.4 | 29.16 |
Calculations:
- MAD = (2.2 + 5.6 + 0.8 + 3.4 + 3.8 + 3.8 + 5.4) / 7 ≈ 3.7
- MSE = (4.84 + 31.36 + 0.64 + 11.56 + 14.44 + 14.44 + 29.16) / 7 ≈ 14.75
These errors suggest the simple moving average forecasts are reasonably accurate but can be improved with weighted methods.
Part C: 5-Year Weighted Moving Average Forecast for 2012
The weighted moving average assigns greater importance to recent years:
- Weights: 0.10, 0.15, 0.20, 0.25, 0.30 (most recent year=2011 with weight=0.30)
Using the data for 2007–2011:
- 2007: 54
- 2008: 57
- 2009: 60
- 2010: 62
- 2011: 65
Calculations:
Forecast for 2012 = (54 × 0.10) + (57 × 0.15) + (60 × 0.20) + (62 × 0.25) + (65 × 0.30)
= 5.4 + 8.55 + 12 + 15.5 + 19.5 = 60.95
Forecast for 2012: approximately 61 mergers.
Part D: Regression Analysis for Forecasting 2012
Regression analysis models the relationship between years (independent variable) and mergers (dependent variable). For simplicity, we assign numerical values to years (e.g., 2001=1, ..., 2011=11).
Using the data points:
- Years: 1 to 11
- Mergers: corresponding values
Applying linear regression:
Y = a + bX
Calculations (using least squares):
- Compute averages:
- X̄ = (1+2+...+11)/11 = 6
- Ȳ = (45+50+55+47+52+58+54+57+60+62+65)/11 ≈ 56.45
- Slope (b):
- Numerator: Σ(Xi - X̄)(Yi - Ȳ) = ∑XiYi - nX̄Ȳ
- Sum of XiYi: 1×45 + 2×50 + 3×55 + 4×47 + 5×52 + 6×58 + 7×54 + 8×57 + 9×60 + 10×62 + 11×65 = 3520
- ΣXi = 66, ΣYi = 621
- b = [ ΣXiYi - nX̄Ȳ ] / [ ΣXi^2 - nX̄^2 ]
- ΣXi^2 = 1^2+2^2+...+11^2= 506
- b = (3520 - 11×6×56.45) / (506 - 11×36) = (3520 - 11×6×56.45) / (506 - 396)
- 11×6×56.45 ≈ 11×338.7 ≈ 3725.7
- b ≈ (3520 - 3725.7) / 110 ≈ -205.7 / 110 ≈ -1.87
- Intercept (a):
- a = Ȳ - bX̄ = 56.45 - (-1.87)×6 ≈ 56.45 + 11.22 ≈ 67.67
Forecast for 2012 (X=12):
- Y = 67.67 - 1.87×12 ≈ 67.67 - 22.44 ≈ 45.23
Forecast for 2012: approximately 45 mergers.
This regression indicates a slight decreasing trend, which might oversimplify the industry dynamics, but provides a quantifiable forecast.
Discussion of Methodologies
The moving average method is favored for its simplicity and effectiveness in smoothing out short-term fluctuations, making it suitable where data exhibit no strong trend or seasonal pattern. However, it does not account for trend or other underlying factors influencing mergers. The weighted moving average improves upon this by emphasizing recent data, allowing the forecast to be more responsive to recent changes.
Regression analysis offers a statistical approach to model trends over time, capturing linear relationships between variables. It is particularly useful when historical data show a clear trend, either increasing or decreasing, as observed in the merger activity data. Regression can also incorporate multiple variables if needed, making it versatile.
Another method that could be useful is exponential smoothing, especially Holt’s linear trend method. Exponential smoothing assigns exponentially decreasing weights to past observations and can adapt to changes in the trend and level more dynamically than simple averages.
Conclusion
Predicting future mergers in the savings and loan industry requires careful selection of forecasting techniques. The 5-year simple and weighted moving averages provide straightforward insights, with the weighted approach showing slightly improved accuracy. Regression analysis introduces a trend component, predicting a decline in mergers, although industry dynamics must be considered to refine forecasts. Combining these methods with qualitative insights can lead to more reliable predictions. The choice of method depends on the data characteristics—whether trends, seasonality, or randomness dominate—and the accuracy needs of decision-makers.
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