# For the Unit VIII assignment, please refer to Section 5.4 of the text.( I have attached a copy of the text pages)Monica works at a regional weather office on the Atlantic coast. She notes (from the of

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For the Unit VIII assignment, please refer to Section 5.4 of the text.( I have attached a copy of the text pages)

Monica works at a regional weather office on the Atlantic coast. She notes (from the office records) that hurricanes have made landfall on the coast somewhere near their city of Johnstown in the past 11 years. Monica notes that forecasted landfall has been different from actual observed landfall as shown in the table below.

YEAR ACTUAL (MILES FROM JOHNSTOWN) 24-HOUR FORECAST (MILES FROM JOHNSTOWN)

1 4 6

2 5 5

3 30 40

4 2 10

5 12 13

6 7 5

7 11 11

8 21 25

9 12 8

10 12 15

11 6 9

How accurate has the forecast been? Do you think this difference matters to a beach town? Can you develop a forecasting system model that may be more accurate?

Explain your methodology and ideas in a paper of at least four page

s. Be sure to research sources to support your ideas, and integrate the sources using APA-formatted citations and matching reference lists. Additionally, use Times New Roman12pt. double-spaced font.

Text Book

Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2015). Quantitative analysis for management (12th ed.). UpperSaddle River, NJ: Pearson

For the Unit VIII assignment, please refer to Section 5.4 of the text.( I have attached a copy of the text pages)Monica works at a regional weather office on the Atlantic coast. She notes (from the of

MSL 5080, Methods of Analysis for Business Operations 1 Cou rse Learning Outcomes for Unit VIII Upon completion of this unit, students should be able to: 7. Assess the differences between correlation and causation . 7.1 Develop a forecasting model. 7.2 Justify the selection of a forecasting model over other techniques in a gi ven scenario. Reading Assignment Chapter 5: Forecasting Unit Lesson As noted in Unit VI, decision -making under certainty is still work , but work with a certain advantage of knowing . Often, it is just a matter of comparing more than one outcome’s alternative (e.g., comparin g rates on bonds for purchase ). Mostl y, though, as noted in Chapter 5, leaders make decision s without knowing future events. This is why — as discussed throughout the course — determining causation and forecasting are such lucrative activities. Does weather foreca sting look intere sting to you? Quantitative analysis has made it better, as you will see in this u nit and Ch apter 5. Types of Forecasting Models Figure 5.1 on page 150 of the text book shows you how to organize forecasting. Some of these appro aches are now familiar to you . Qualitative Models: The Qualitative Models ar e, by their nature, subjective. Without using mathematics, finding and leveraging judgments based on experience counts toward getting close to the “futur e truth” that you may profit by. Qualitative models ma y be used in combination with the other ca tegories of approaches. For example, these types listed — the Delphi Method, Jury of E xecutive Opinion, Sales Force Composite, and Consumer Market Survey — all treat the recipients of the questions as subject matter ex perts (or at least experienced, such as shoppe rs) and collect their opinions. These responses may be guided by presenting them quantitative anal ysis that were performed first. Perhaps this makes it easier to ask the panels the right questions in hopes of g etting useful answers, but care should be taken not to add bias to the whole analysis effort, or the actual events could be nowhere near the qualitative models’ forecast. Causal Models : These consist of regression analyses or multiple regressions that fo recast with collect ed data, which by definition occurr ed in the past. Because these models have dependent variables , which are influenced by independent variables in their equations, these models are considered to be casual — have determined t hat one change causes another. If you are reading this, you have probably completed Unit VII and alr eady worked with these models. So, you will explore new models! Time -Series Models : These are quantitative models that also use past -occurring data, but add to them the valu es of their occurrence in time. Time matters in time -series models, whether the data shows trends, seasonal changes, cycl es, or just random occurrences. Accordingly, time -series approaches have these poss ible phenomenon as components: a trend component ( = T), seasonal component ( = S), cyclical component ( = C), and random component ( = R), with two time -series model forms generally used: UNIT VIII STUDY GUIDE Causation and Forecasting MSL 5080, Methods of Analysis for Business Operations 2 UNIT x STUDY GUIDE Title The multiplicative model, where Demand = T x S x C X R, or the additive model, where Demand = T + S + C + R Measu res of Forecast Accuracy As with regression analysis for correlation, you can use similar mathematics to assess how accurate forecasts are or how mini mized the error is in them. Forecast error = actual value minus forecast value , as it does in the family budgets. Again , like similar equations, you can find the mean of the errors (mean absolute deviation [MAD ]) if you have collected past data and time intervals, as shown with the Walker Distributors example in Table 5.1 on page 153 of the text book . In this example, this equation was used to find the MAD of Walker’s sales forecast by dividing the sum of the absolute values of forecast errors by the numbers of errors n: MAD = ∑ | Forecast error | n The absolute value was taken for the same reason you would take squares in regression analyses : to prevent errors from cancelling each other out and distorting the data from trends, seasonal movements, or cycles. An effective way t o understand how important the MAD can be to forecasts on behalf of society is to consider the hurricane landfall forecast example on page 154 of the text book , and further peruse the National Hurricane Center information at noaa.gov. Hurricanes are a perma nent part of North American geography and can have enough force to destroy and damage much of the area where it makes landfall and travels before dissipatio n. T he storm’s effect s can also injure or kill many people. Certainly , the ramifications of hurrican e occurrence are of great interest to the countries of the Caribbean Sea (this includes the U nited States ) where the left hook –shaped tracks of hurric anes traditionally are traced. The MADs regarding predicted and actual landfalls become a serious matter w ith so much at stake, and the U.S. government invests in a significant amount of resources in working on the task of forecasting , to include defining the problem (Step 1 of the Quantitative Analysis Approach, as you know) of the accurate forecasts that are needed. A point can be noted here about a “quick” way to forecast , and you do this all the time. The Naïve Model is taking the last measured value and forecasting that this value wi ll be the next one that occurs. The Naïve Model obviously d oes not take i nto account time intervals; instead, the user more or less concedes, “well, it was this just the last time, so I say i t will be this the next time.” The model is obviously well named! Even though there seems to be little science about the approach, there i s quite a bit of reality to the answer. Indeed, whatever just happen ed (e.g., yesterday’s high temperature ) tends to frequently happen again — and for a while — before shifting to a different value (such as the onset of winter temperatures). Moving -Averages Among the time -ser ies models, you use moving -averages if variations are random, and the situation does not involve trend, seasonal, or cyclic variations. The m oving -average model is one of the models that “smooths” the forecast so random variations do not influence the solution more than their values and occurrences make logical. As you can see on pages 156 –7 of the text book , calculating the moving -average f orecast as the sum of numbers in previous periods t-1 divided by the number of periods n is taking ju st a certain number of recent values occurring in the past and calculating where the avera ge may be moving. As you may see in Table 5.2 on page 157 of the text book , values from a year ago may not be interesting; but what happened in the past three months, or four, or six, would be interesting as changes tend to gradually happen. Weighted Moving -Averages If you have a moving -average model and approach, you can also have a weighted moving -average model. This entails assigning weight, or multiplying wi to va lues, before summing them, and then dividing t his by the sum of the weights. These weighted factors account for things with a higher probability occurring more than things with a lower probability. What could be the issue with any averages? Moving -average models are slow to pick up the firs t signs of significant change. It is possible, then, that a business depending too much on forecasts from averages may miss a shift in product popularity, changing trends, or outside changes. MSL 5080, Methods of Analysis for Business Operations 3 UNIT x STUDY GUIDE Title Exponential Smoothing Next in the time -series models is exponential s moothing , which is a type of moving -average approach but using little past data, as can be seen by its equation: New Forecast = Last Period’s Forecast + α(Last Period’s Actual Demand – Last Period’s Forecast) with α a s a weight, or smooth ing constant, between 0 and 1. With exponential smoothing, you adjust the last forecast by the error determin ed from what actually happened. As can be seen in the example described on page 159 of the text book , once a forecast is found to have an error in a certain direction, exponential smoothing wil l move the next forecast in the direction that the actual values seem to be moving. When actual values move in time intervals, you may see that they don’t seem rando m but are following a pattern. As can be seen on page 163 of the text book , exponential smoothing can be accomplished while taking the trend into account by using an additi onal constant β. Another common approach is the trend projection method. This method is just a matter of taking the linear regression equation Ŷ = b0 + b1X to represent the data, using a least squares method for checking the fit and measuring significance (as was practiced in Unit VII), and projecting a continuance of the trend — often by extending th e line of the linear equation. This projection may accurately forecast the trend for a while, but as you know, trends do not last forever . This signals practical lim itations with believing too much in such a forecast. Seasonal Indices As the planet Earth has seasons, the societal change in dynamics aligned with these seasons is inevitable and shows in such phenomenon as sales, travel, agriculture, and other activiti es that include the weather and outdoors. Forecasting with taking into account seasonal cycles or other movements can be expected, as practical leaders acknowledge such expected tendencies. In terms of most seasonal adjustments for forecasting, an average season is assumed to have a value of 1, and a seasonal index is the comparison of a season of inte rest with that average season. The following variations can be performed to foreca st things with seasonal indices: Deseasonalized data : Dividing the data by the seasonal index removes the seasonal effect; then , a forecast using deseasonalized data is made and finally, the seasonal index is multiplied back in to the forecasts, restoring the effect of seasons in the forecasts. Decomposition: In decomposition, li ke converting to deseasonalized data, data is divided by the seasonal index to show a liner trend without seasonal effect, in the general form of Ŷ = b0 + b1X, as can be seen in the example of Fi gure 5.5 on page 171 of the textbook. Note in the table’s gra ph how rises and falls of the data were removed when the se asonal effect was divided out. A line Ŷ = b0 + b1X can be found for the deseasonalized data, which is then multiplied across all terms by the seasonal index to determine the equation for the season al forecast. Below are two ways to find the seasonal index: 1. If the data has no trend present, you divide the average of a given season by the average of all the data from all seasons. You may recall that if the seasonal index is 1, then the time interval is having an “average” season, as a value divided by 1 remains the same value. 2. If the data includes the effect of a trend, the main challenge is that a data’s change could be due either to a trend or a seasonal change, or both or neither! So analysts comp ute a centered moving – average (CMA) to use in calculations so a trend is not mistaken for a season. This CMA is an average of just enough data to take seasons into account (e.g. , four quarters if qua rters are running seasonally). As noted on page 170 of th e text book , the steps for computing with a CMA include the following : Compute a CMA for each observation, except in cases where there is not enough data left to average . Find seasonal ratios . Each seasonal ratio = observation data / observation’s CMA. Aver age the seasonal ratios to get seasonal indices. If seasonal indices do not yet add up to equal the number of seasons, multiply each seasonal index by the value (number of seasons / sum of the indices ). MSL 5080, Methods of Analysis for Business Operations 4 UNIT x STUDY GUIDE Title And , after eight u nits of quantitative analysis, you can see why s killed analysts draw high salaries! Having the practice and experience to be able to identify the problem, choose a fitting model, and calculate accurately are attributes that cont ribute to the decision process. You have the quantitative anal ysis approach steps and the ranks of equations to he lp you be effective in this role. A nd remember that a leader’s outlook toward challenges provides energy to effort s and is decisive toward successes. Reference Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2015). Quantitative analysis for management (12th ed.). Upper Saddle River, NJ: Pearson. Suggested Reading The links below will direct you to a PowerPoint view of the Ch apter 5 Presentation. This will summarize and reinforce the information from this chapter in your textbook. Click here to access a PowerPoint presentation for Chapter 5. Click here to access the PDF view of the presentation. For an overview of the chapte r equations, r ead the “Key Equations” on page 178 –179 of the textbook. Learning Activities (Non -Graded) Complete Solved Problems 5 -1 and 5 -2 on pages 179 –180; and Self -test problems 1 -14 on pages 180 –181 (use the key in the back of the book in Appendix H to check your answers). For the Solved Problems, the problem is presented first, followed by its solution. Challenge yourself to apply what you have learned , and see if you can work out the problems without first looking at the solution , onl y using the so lution to check your own work. Non -graded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information.

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