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OMIS2010_Quiz2_Crash-Notes.pdf

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Department
Marketing
Course
MKTG 2030
Professor
Ben Kelly
Semester
Winter

Description
By: Jessica Gahtan 1 Omis Quiz 2 Notes th Hey! So, just a reminder th vote for UBC elections from Monday March 17 at 8:00AM until Wednesday March 19 at 11:59PM at evote.yorku.ca I know my shameless promotion is annoying but like… none of you guys will remember otherwise since I’m pretty sure you are all studying your guts out for this quiz. GOOOD LUCK ON THE QUIZZ!!!!!!!!! - Jess   By: Jessica Gahtan 2 Omis Quiz 2 Notes Chapter  11  –  Time  Series  Forecasting   -­‐ A time series is a set/series of observations on a quantitative variable collected over time ▯ ▯ ▯▯ -­‐ Focus on: 𝑀𝑆𝐸 = ▯( ▯ ▯) *Remember that you want the MSE to be SMALL ▯ ▯ ▯ -­‐ A moving average calculates the average of the past ‘k’ observations – since we don’t know the best value of k – we should try different ones to see which gives the best results -­‐ A weighted moving average is a variation of the moving average that assigns weights to the data being average – Use solver to determine the value of k and w that mi nimize MSE -­‐ Exponential smoothing is for stationary data – allows weights to be assigned to past data – more recent data = higher weight -­‐ Seasonality refers to the regular, repeating patterns in the data -­‐ Additive seasonal effects tend to be on the same order of magnitude each time a given season is encountered -­‐ Multiplicative seasonal effects tend to have an increasing effect each time a given season is encountered -­‐ Stationary data with Additive Seasonal Effects: 𝑌▯▯▯ = 𝐸 ▯ 𝑆 ▯▯▯▯▯ 𝐸 ▯ 𝛼 𝑌 − ▯ ▯▯▯ + (1 − 𝛼)𝐸 ▯▯▯ 𝑆▯= 𝛽 𝑌 − ▯ ▯ + (1 − 𝛽)𝑆 ▯▯▯ 0 ≤ 𝛼 ≤ 1  𝑎𝑛𝑑  0 ≤ 𝛽 ≤ 1 E teps the expected level of the time series in period t S teps the seasonal factor for period t The constant p reps the # of seasonal periods in the data The forecast for time period t+n is simply the expected level of the time series at period t adjusted upward or downward by the seasonal factor S t+n-p In order to use the eq’ns, it’s necessary to initialize the estimated levels & seasonal factors for the first p periods ▯ ▯▯ 𝐸 ▯ ▯▯▯ ▯ ,𝑡 = 1,2,…,𝑝 𝑆▯= 𝑌 −▯𝐸 ,𝑡 ▯ 1,2,…,𝑝 -­‐ Stationary data with Multiplicative Seasonal Effects: 𝑌▯▯▯ = 𝐸 ▯𝑆 ▯▯▯▯▯ 𝐸 ▯ 𝛼 𝑌 /𝑆▯ ▯▯▯ + (1 − 𝛼)𝐸 ▯▯▯ 𝑆▯= 𝛽 𝑌 /𝐸▯ ▯ + (1 − 𝛽)𝑆 ▯▯▯ 0 ≤ 𝛼 ≤ 1  𝑎𝑛𝑑  0 ≤ 𝛽 ≤ 1 E tepresents the expected level of the time series in period t Strepresents the seasonal factor for period t The constant p represents the number of seasonal period in the data The forecast for time period t+n is simply the expected level of the time series at period t multiplied by the seasonal factor St+n-p In order to use the equations, necessary to initialize the estimated levels and seasonal factors for the first p periods ▯ ▯▯ ▯▯ 𝐸 ▯ ▯▯▯ ,𝑡 = 1,2,…,𝑝 𝑆▯= ,𝑡 = 1,2,…,𝑝 ▯ ▯▯ -­‐ Trend is a long-term sweep or general direction of movement in a time series – reflect net influence of long-term factors that affect the time series in a fairly consistent and gradual way over time -­‐ Consistent underestimation of the actual values if there’s an upward trend (and vice versa) -­‐ Double exponential smoothing is often an effective forecasting tool for time series data that exhibits a linear trend After observing the value of the time series at period t (Y ), tompute an estimate of the base, or expected, level of the time series (E t and the expected rate of increase or decrease (trend) per period (T ) t 𝑌▯▯▯ = 𝐸 ▯ 𝑛𝑇 ▯ 𝐸 = 𝛼𝑌 + (1 − 𝛼)(𝐸 + 𝑇 ) ▯ ▯ ▯▯▯ ▯▯▯ 𝑇 = 𝛽 𝐸 − 𝐸 + (1 − 𝛽)𝑇 ▯ ▯ ▯▯▯ ▯▯▯ By: Jessica Gahtan 3 Omis Quiz 2 Notes Chapter  12  –  Intro  to  Simulation  using  Risk  Solver  Platform   -­‐ Random variable is any variable whose value can’t be predicted w/certainty -­‐ Amount of risk involved in a given decision making situation – is a function of the uncertainty in the outcome of the decision and the magnitude of the potential loss (Uncertainty -> risk -> potential for loss) -­‐ Different ways to analyze risk: 1. Best-Case / Worst-Case Analysis -­‐ Calculate values of the most pessimistic and optimistic scenarios -­‐ Doesn’t tell you about the distribution of the possible values w/i n the range or probability 2. What-If Analysis -­‐ Can change values of uncertain input variables to see what happens to the company’s bottom line – shows sensitivity to changes to the input variable -­‐ 3 problems with it: (1) manager can manipulate the values selec ted for the independent variables; (2) to get a good idea of underlying variability in the bottom -line you’d need to do hundreds or thousands of what-if scenarios; (3) insight gained from playing out random scenarios isn’t very valuable when recommending something to top management 3. Simulation -­‐ Measures and describes various characteristics of the bottom -line performance measure of a model when one or more values for the independent variables are uncertain – Goal is to describe the distribution and characteristics of the possible values of Y (the performance measure) given the possible values/behaviors of the independent (X) variables -­‐ To perform simulation in a spreadsheet, first you need to place a random number generator (RNG) formula in each cell that reps a random, or uncertain, independent variable – each RNG provides a sample observation from an appropriate distribution that reps the range and frequency of possible values for the variable -­‐ It’s important to distinguish b/w discrete and continuous variables *** -­‐ When preparing the model for Simulation: either use the available historic data on the uncertain variables to determine appropriate RNGs for the variables OR use sample the historic data itself -­‐ Risk Solver Platform also has the ability to identity probability distributions that fit with the historical data pretty well -­‐ Running the simulation: Need to recalculate the spreadsheet 100s/1000s times and record the resulting values generated for the output cells – Risk Solver Platform will do this if you tell it how many times you want it to replicate the model. (1) Identify output cell, (2) indicate number of replications to perform (3) run simulation -­‐ To analyze the data – you can look at the best/worst case scenarios, view the distribution of the output cells, look at the cumulative distribution of the output cells, obtain other cumulative probabilities, analyze sensitivity – which variables have the largest impact -­‐ Sampling is inherently the best you can do is take a random sample and hope for the best! • Constructing a confidence interval for a population proportion By: Jessica Gahtan 4 Omis Quiz 2 Notes o May want to construct a confidence interval for the true proportion of a population that fall below (or above) some value o Let p denote the proportion of observations in a sample of size n that falls below some value Y p o Assuming n is sufficiently large (n≥30) o The Central Limit Theorem tell us that the lower and upper limits of a 95% confidence interval for the true proportion of the population falling belop Y are represented by  95%  𝐿𝑜𝑤𝑒𝑟  𝐶𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒  𝐿𝑖𝑚𝑖𝑡 = 𝑝 − 1.96× ▯(▯▯▯) ▯ ▯(▯▯▯)  95%  𝑈𝑝𝑝𝑒𝑟  𝐶𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒  𝐿𝑖𝑚𝑖𝑡 = 𝑝 + 1.96× ▯ • As the number of replications (n) increases, the width of the confidence in terval decreases -­‐ Interactive Simulation • The Simulate icon on the Risk Solver Platform tab is on (or the light bulb is illuminated), Risk Solver Platform is in interactive simulation mode o Anytime you make a change to your workbook that requires the spreads heet to recalculate (or manually recalculate by pressing F9), Risk Solver Platform performs a complete simulation of your model • PsiTarget (cell, target value) returns the cumulative probability of a specified distribution or output cell being less than or equal to a given target value By: Jessica Gahtan 5 Omis Quiz 2 Notes Chapter  13:  Queuing  Theory     -­‐ Queuing theory is a mgmt. science term referring to the body of knowledge dealing with waiting times -­‐ Objective is usually to find the optimal service level that achieves an acceptable balance b /w the cost of providing service and customer satisfaction -­‐ System configurations: o Single-queue, single-server system: Customers enter system, wait in line, FIFO basis until they receive service (@ which pt they exit the system) o Single-queue, multi-server system: Customers enter the system and join a FIFO queue -> Upon reaching the front of the line, a customer is serviced by the next available server o Collection of single-queue, single-server systems: Customers arrive and choose one of the queues, waits in the line to receive service -> Can often be analyzed as a independent, single- queue, single-server systems Characteristics of Queuing Systems: -­‐ Need to make some assumptions about the way customers arrive in the system, amt. of time it takes them to receive the service -­‐ Arrival rate - # of arrivals that happen in a period of time reps a random variable o Appropriate to model the arrival process in a qu
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