# Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques Page 1 of 11. EduPristine CMA - Part I

Size: px
Start display at page:

Download "Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA - Part I"

## Transcription

1 Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA - Part I Page 1 of 11

2 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques Prelude Planning involves forecasting key revenue and cost drivers. Forecasting can be done using qualitative (market research, anecdotes, opinions from experts, historical analogy) and quantitative methods. Here we are focusing on following quantitative methods of forecasting: 1) Linear Regression Analysis a) Single variable and b) Multi variable 2) Learning Curve Analysis a) Cumulative Average Time Learning Model and b) Incremental Unit Time Learning Model 3) Moving Averages a) Weighted Average and b) Exponential Smoothing 4) Time Series Analysis 5) Expected Value Techniques and Sensitivity Analysis A. Understanding of a simple regression equation and the measures associated with it What is a Linear Regression Analysis? 1. Statistical tool / model to establish relationship between one variable (called dependent variable, Y) with another (or a group of another) variable (called independent variable(s), Xi) 2. The relationship is then translated into a linear regression equation and used to predict / forecast the value of dependent variable (Y) given the values of independent variable(s) 1) Types of Regression Analysis: a) A simple regression analysis uses / involves only one independent variable b) A multiple regression analysis uses / involves multiple independent variables 2) A simple linear regression line has an equation of the form Y = a + bx, where a) X is the explanatory variable b) Y is the dependent variable c) b is the slope of the line and measures change in y w.r.t unit change in x

3 d) as is the intercept (the value of y when x = 0) 3) A linear regression is fitting a straight line to data and explaining the change in one variable through changes in other variables. This is based on following assumptions: a) Linearity: Linear relationship between X and Y (Y varies directly with first power of X) b) Constant Process: Process relating the variables is constant or stationary c) No auto correlation: Dependent variable is not auto-correlated this implies the errors measured by Y(actual) Y(predicted) are normally distributed with zero mean and a constant standard deviation d) No multi-co linearity: The independent variables are independent of each other. They are not correlated with each other 4) In real life, we hardly come across a situation where these assumptions are met. We nevertheless perform regression analysis. So, it s likely that analysis doesn t yield efficient results. We therefore have various measures to test the efficiency of a regression analysis or model: a) R Squared: Also known as coefficient of determination; takes a value between 0 and 1; explains the extent to which changes in dependent variable can be explained by changes in dependent variables; a statistical measure of how close the data are to the fitted regression line; i) 0 indicates that the model explains none of the variability of the response data around its mean. ii) 1 indicates that the model explains all the variability of the response data around its mean. b) T value: Measure of strength of relationship between the independent and dependent variable: i) A value of 0 means no significant relationship between the two and hence the independent variable should be removed from the regression analysis ii) should be more than 2 to indicate a strong relationship between the dependent and independent variables c) Standard Error (SE): A measure of the accuracy of predictions; a measure of dispersion around the regression line i) ~68% of observations should fall within ± 1 x SE ii) ~95% of observations should be within ± 2 x SE Regression Fit with Low R squared value Regression Fit with High R squared Value Graphical Representation of Standard Error

4 B. A multiple regression equation and when it is an appropriate tool to use for forecasting Multiple Linear Regression Equation: y = α + β 1x 1 + β 2x 2 + β 3x 3 + β 4x 4 Interpretation of the variables and measure of efficiency of the regression model remain as per single linear regression equation (intercept, slope, R squared, T value, standard error) When Multiple Regression is an appropriate tool to use for forecasting: 1. When a single independent variable is not able to explain the dependent variable in entirety. This implies the entire change in dependent variable is not explained by a single independent variable (R squared less than 1) 2. When the dependent variable is not expected to be impacted by seasonality, cyclicality or unexpected trend 3. When we know that an outcome is actually impacted by more than one input / variable C. Calculate the result of a simple regression equation Better explained by an example. A marketing research firm has undertaken regression analysis on the historical sales data of Alpha Beta Corporation and has come up with following linkage between the monthly quantity sold (Q) and the sales price (P): Q = x P. Sonali Sundaram is preparing the sales budget for the company. What will be the budgeted annual revenue for the company if the sales price is budget at Rs. 50 / unit? Solution: Monthly quantity as predicted by regression price of Rs. 50 / unit = x 50 = 24,500. Hence, Annual Quantity = 12 x = 2,94,000. Budgeted Revenue = Sales Price x Annual Quantity = Rs. 1,47,00,000 = Rs Cr D. An understanding of learning curve analysis 1. As an individual, group or organization completes a job, task or an activity; he /she / it tends to gain experience and learning. As a result when the same task is performed for the second time, the time and the cost involved should be lower than what they were previously. 2. This is the effect of learning and hence a plot of time/cost required per unit of production against cumulative units of production is called learning curve. 3. Learning curve analysis is thus a tool that helps us estimate the time / cost of production at different production levels.

5 Learning curve analysis is thus a tool that helps us estimate the time / cost of production at different production levels. The graph on the right hand side depicts the time taken to complete the nth unit. For example, if time required to make 1 st unit was 10 hours then time required to complete the 4 th unit should be 8.10 hours as per 90% learning curve. The curve levels off after a certain point. E. Calculate the results under a cumulative average-time learning model and under an incremental unit-time learning model Two models used to capture different forms of learning are: 1. Incremental unit-time learning model: The incremental time needed to produce the last unit declines by a constant percentage each time the cumulative quantity of units produced doubles. Example: Calculate the time required to produce the nth unit at a cumulative production level of n assuming the learning rate of 90% and 10 hours requirement to make the first unit. Cumulative Production Level (n) Time required to produce nth unit (hours) Formula = x 90% = 9.00 x 90% = 8.10 x 90% = 7.29 x 90% 2. Cumulative average-time learning model: The cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced doubles. Example: Calculate the total time required to produced n units, assuming the learning rate of 90% and 10 hours requirement to make the first unit. Cumulative Production Level (n) Average Time required to produce n unit (hours) Total time required to produce n units (hours) Inferences from learning Curve Models: 1. Resource (Time or cost) required to make the next unit is lower than that required to make the previous unit

6 2. Rate of reduction is faster to begin with and slows down subsequently 3. The curve levels off ultimately implying learning and experience don t lower the quantum of resource required significantly after a point. F. Understanding of Moving Averages, Weighted Moving Averages & Exponential Smoothing and Calculate Forecasts A time series data is a compilation of behaviour of a variable at a particular time interval (say daily, monthly, quarterly, hourly etc.) over a period of time An analysis of time series tells us many underlying behaviour of the variable but also exposes many noises (cyclicality, seasonality, irregularity etc. explained in the subsequent LOS) Smoothing techniques are used to reduce irregularities (random fluctuations) in time series data. They provide a clearer view of the true underlying behaviour of the series. Smoothing is usually done to help us better see patterns, trends for example, in time series. One should generally smooth out the irregular roughness to see a clearer signal. Techniques of Smoothing: 1. Moving Averages: Average of recent most set of data for the given fixed time frame. With every time period, last data point moves out and the recent most data moves in. Example: Three months moving average of Sales 2. Weighted Moving Averages: Similar to moving average method, but higher weights are assigned to recent data than the older data; assumes that recent observation will be a better predictor. 3. Exponential Smoothing: Forecast value is a weighted combination of the observed value at time t and the forecasted value at time t as shown by equation below: F t+1 = α x D t + (1 α) x F t where α is the smoothing constant Although the method is called a smoothing method, it s principally used for short run forecasting. Sl. No. Parameter Moving Averages Exponential Smoothing 1. Effective 2. Data Requirement 3. Weights Effective in smoothing out sudden fluctuations in demand pattern in order to provide stable estimates Useful if forecast is assumed to stay fairly steady over time Requires maintaining extensive records of past data; requires historical data Equal or more weightage to recent data Work well when the time series is stable without any significant trends, cyclicality or seasonality. Good for forecasting large number of dependent variables, Requires little record keeping of past data; minimal data requirement Smoothing constant ranges from 0 to 1; subjectively chosen; Smaller constant gives more smoothing, larger constant gives less smoothing

7 Actual Sales of Alpha Beta Corporation in first 3 months of the years were as tabulated alongside. Sales Forecasts for March was Rs. 108 Cr. Calculate the sales forecasts for April based on moving averages, weighted moving averages (use weights of 20%, 30% and 50% for Jan, Feb and March data respectively) and Exponential Smoothing with constant of Solution: Moving average forecast = ( ) / 3 = Sl. No. Month Sales (Rs. Cr) 1. Jan Feb Mar 98 Weighted Moving average forecast = (20% x % x % x 98) / 3 = Exponential Smoothing Forecast = 0.92 x 98 + (1 0.92) x 108 = G. Understanding of Time Series Analysis including objectives and patterns 1. A time series data is a compilation of behaviour of a variable at a particular time interval (say daily, monthly, quarterly, hourly etc.) over a period of time. 2. An analysis of time series tells us many underlying behaviour of the variable but also exposes many noises / patterns: Sl. No. Pattern Remarks 1. Trends 2. Cyclical 3. Seasonal 4. Irregular Variations 1. Depicts a gradual shift to a higher (upward sloping) or lower (downward sloping) values 2. Due to change in population, technology, customer preference, pricing, competition etc. 3. Forecasts for dependent variable can be made based on trend line using regression analysis (time as independent variable) 4. Informed decision-making on expansion related decisions 1. Repetitive pattern of data points lying above or below the trend line 2. Can last for more than a year 3. Result of macro-economic conditions 4. Improved decision-making in the light of macro-economic conditions 1. Peak and Trough pattern during a year 2. Can occur due to seasonal change in preference and activities 3. Assists in inventory management 1. Any outlier data points which don t form a trend, seasonality or cyclical pattern 2. Can occur due to non-recurring, extraordinary event 3. Such factors cannot be accounted for in the forecasts

8 H. List the benefits and shortcomings of regression analysis, learning curve analysis and time series analysis Regression Analysis Learning Curve Analysis Time Series Analysis Benefits 1. Simple and most frequently used tool for forecasting 2. Can be used to trace the relationship and the strength of relationship with multiple variables at a time 3. Can handle large set of data as well to derive conclusions 4. Forces user to look at the relationship between the variable graphically and predict the trend intuitively Shortcomings 1. Outliers can distort the results of regression analysis. Should be checked to ensure that any data recording error or an extraordinary event is not impacting the analysis 2. May not be a suitable tool if assumptions (linear relationship, stable process, no multi collinearity, no autocorrelation) don t hold true 3. Regression analysis should not be used for forecasting if independent variable lies outside the historical data set 1. Important technique for predicting how long it will take to undertake future tasks. 2. Helps you take into account the impact of learning for resource planning, staffing, control and decision-making. 3. Emphasises the fact that initial resource requirements usually do not accurately represent future requirements. 1. Applies only for laborintensive operations 2. Assumption of constant learning rate may not be valid and hence induce errors in forecasting 3. Productivity improvement can be due to factors other than learning so unreliable conclusions 1. A time series analysis clearly depicts all kinds of trends and noises and help managers take informed decision 1. Uses historical data for forecasting. Past patterns are expected to occur in future 2. Extraordinary or nonrecurring events cannot be factored for forecasting I. Expected Value of Random Variables 1. For sake of simplicity, a random variable is a variable that can take any possible value. There always exists a finite probability for every possible outcome it can show. 2. For such a probabilistic situation, a random variable is quantified by its expected value given by sum total of its probability weighted values: 3. X = p 1x 1 + p 2x 2 + p 3x 3 + p nx n 4. Where X is the expected value of the variable x; x 1, x 2, x n are n different outcomes / value it can take and p 1, p 2, p n are the respective probabilities of these outcomes / values

9 Example: Sales of Alpha Beta Corporation can take any of the three values depending upon the state of economy. Calculate the expected value of sales forecasts? Economic Condition Sales Estimate (Rs. Cr) Good 5, Bad 2, Average 4, Probability Expected value of sales forecasts = 5,000 x ,000 x ,000 x 0.70 = Rs. 3,850 J. Benefits and Shortcomings of Expected Value Techniques Benefits 1. A method to forecast a variable even if it has too much of uncertainties associated with it 2. Aids in decision making to do or not do 3. Considers all the possible states / outcomes / before decision making Key Issues: 1. Estimation and probabilities assigned under different conditions can be subjective 2. Decision cannot be made in case of unreliable estimates 3. Expected value method assumes the decision maker is risk neutral. Will not be suitable for risk-taker or risk-averse decision makers K. Use probability values to estimate future cash flows Alpha Beta Corporation is planning to introduce a new product in its portfolio. The cost of introducing the product is Rs. 50 Cr. The product once introduced can fetch different level of revenues depending upon the state of economy next year. The gross margin is roughly 50% and fixed operating costs will be Rs. 10 Cr per annum. What is the expected break even period for this product? Solution: All financials in Rs. Cr Sl. No. State Probability Revenue Sl. No. 1. State Highly buoyant Probability 10% Buoyant 20% Most likely 30% Pessimistic 40% 20 Variable Cost Fixed Costs Total expenses 1. Highly buoyant 10% Buoyant 20% Most likely 30% Pessimistic 40% Expected cash flow per annum (Rs. Cr) = 15 x 10% + 10 x 20% + 5 x 30% + 0 x 40% = 5 Expected payback period = 50 / 5 = 10 years Revenue (Rs. Cr) Cash Flow

10 L. Uses of sensitivity analysis An output or a dependent variable is typically dependent upon several independent / input variables. Sensitivity Analysis tells us: 1. How sensitive the outcome / output is to a particular input? 2. The outcomes corresponding to different values of inputs? 3. Identify the variable(s) which significantly or weakly impact(s) the output / outcome M. Perform a sensitivity analysis with different values for the probabilities of the states of nature and / or the payoffs Example: Alpha Beta Corporation has assigned different probabilities to the sales estimates under three macroeconomic scenarios. However two other estimates of probabilities are also available as depicted below. Find out the sensitivity of sales w.r.t economic conditions. Economic Condition Sales Estimate (Rs. Cr) Expected Probabilities Alternate Probabilities 1 Good 5, Bad 2, Average 4, Alternate Probabilities 2 Expected sales under expected probabilities will be (Rs. Cr) = 5,000 x ,000 x ,000 x 0.70 = Rs. 3,850 Expected sales under alternate probabilities 1 will be (Rs. Cr) = 5,000 x ,000 x ,000 x 0.25 = Rs. 4,450 Expected sales under alternate probabilities 2 will be (Rs. Cr) = 5,000 x ,000 x ,000 x 0.25 = Rs. 2,800 The significant variations in the sales forecast under three scenarios shows that it is highly sensitive to the economic conditions of the country. N. Benefits & Shortcomings of Sensitivity Analysis

11 Benefits: 1. Allows a manager to do a what if / scenario analysis 2. Helps managers identify the most crucial / critical / sensitive variables in decision making and thus guides them to be very realistic and cautious in forecasting / projecting them Shortcomings 1. Independent variables may be correlated and may not impact dependent variable individually but mutually result in substantial different outcome. 2. Independent variables may be correlated, hence all of them need to be changed if forecasts are to be accurate. A manager must understand this otherwise forecasts will be grossly inaccurate.

12

### Forecasting the first step in planning. Estimating the future demand for products and services and the necessary resources to produce these outputs

PRODUCTION PLANNING AND CONTROL CHAPTER 2: FORECASTING Forecasting the first step in planning. Estimating the future demand for products and services and the necessary resources to produce these outputs

### Industry Environment and Concepts for Forecasting 1

Table of Contents Industry Environment and Concepts for Forecasting 1 Forecasting Methods Overview...2 Multilevel Forecasting...3 Demand Forecasting...4 Integrating Information...5 Simplifying the Forecast...6

### A Primer on Forecasting Business Performance

A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.

### RELEVANT TO ACCA QUALIFICATION PAPER P3. Studying Paper P3? Performance objectives 7, 8 and 9 are relevant to this exam

RELEVANT TO ACCA QUALIFICATION PAPER P3 Studying Paper P3? Performance objectives 7, 8 and 9 are relevant to this exam Business forecasting and strategic planning Quantitative data has always been supplied

### Exponential Smoothing with Trend. As we move toward medium-range forecasts, trend becomes more important.

Exponential Smoothing with Trend As we move toward medium-range forecasts, trend becomes more important. Incorporating a trend component into exponentially smoothed forecasts is called double exponential

### Demand forecasting & Aggregate planning in a Supply chain. Session Speaker Prof.P.S.Satish

Demand forecasting & Aggregate planning in a Supply chain Session Speaker Prof.P.S.Satish 1 Introduction PEMP-EMM2506 Forecasting provides an estimate of future demand Factors that influence demand and

### Demand Forecasting When a product is produced for a market, the demand occurs in the future. The production planning cannot be accomplished unless

Demand Forecasting When a product is produced for a market, the demand occurs in the future. The production planning cannot be accomplished unless the volume of the demand known. The success of the business

### CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression

Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the

### Module 6: Introduction to Time Series Forecasting

Using Statistical Data to Make Decisions Module 6: Introduction to Time Series Forecasting Titus Awokuse and Tom Ilvento, University of Delaware, College of Agriculture and Natural Resources, Food and

### 2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or

Simple and Multiple Regression Analysis Example: Explore the relationships among Month, Adv.\$ and Sales \$: 1. Prepare a scatter plot of these data. The scatter plots for Adv.\$ versus Sales, and Month versus

### 4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4

4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Non-linear functional forms Regression

### FORECASTING. Operations Management

2013 FORECASTING Brad Fink CIT 492 Operations Management Executive Summary Woodlawn hospital needs to forecast type A blood so there is no shortage for the week of 12 October, to correctly forecast, a

### Smoothing methods. Marzena Narodzonek-Karpowska. Prof. Dr. W. Toporowski Institut für Marketing & Handel Abteilung Handel

Smoothing methods Marzena Narodzonek-Karpowska Prof. Dr. W. Toporowski Institut für Marketing & Handel Abteilung Handel What Is Forecasting? Process of predicting a future event Underlying basis of all

### Ch.3 Demand Forecasting.

Part 3 : Acquisition & Production Support. Ch.3 Demand Forecasting. Edited by Dr. Seung Hyun Lee (Ph.D., CPL) IEMS Research Center, E-mail : lkangsan@iems.co.kr Demand Forecasting. Definition. An estimate

### TIME SERIES ANALYSIS & FORECASTING

CHAPTER 19 TIME SERIES ANALYSIS & FORECASTING Basic Concepts 1. Time Series Analysis BASIC CONCEPTS AND FORMULA The term Time Series means a set of observations concurring any activity against different

### CALL VOLUME FORECASTING FOR SERVICE DESKS

CALL VOLUME FORECASTING FOR SERVICE DESKS Krishna Murthy Dasari Satyam Computer Services Ltd. This paper discusses the practical role of forecasting for Service Desk call volumes. Although there are many

### CHAPTER 6 FINANCIAL FORECASTING

TUTORIAL NOTES CHAPTER 6 FINANCIAL FORECASTING 6.1 INTRODUCTION Forecasting represents an integral part of any planning process that is undertaken by all firms. Firms must make decisions today that will

### 16 : Demand Forecasting

16 : Demand Forecasting 1 Session Outline Demand Forecasting Subjective methods can be used only when past data is not available. When past data is available, it is advisable that firms should use statistical

### Production Planning. Chapter 4 Forecasting. Overview. Overview. Chapter 04 Forecasting 1. 7 Steps to a Forecast. What is forecasting?

Chapter 4 Forecasting Production Planning MRP Purchasing Sales Forecast Aggregate Planning Master Production Schedule Production Scheduling Production What is forecasting? Types of forecasts 7 steps of

### Integrated Resource Plan

Integrated Resource Plan March 19, 2004 PREPARED FOR KAUA I ISLAND UTILITY COOPERATIVE LCG Consulting 4962 El Camino Real, Suite 112 Los Altos, CA 94022 650-962-9670 1 IRP 1 ELECTRIC LOAD FORECASTING 1.1

### Slides Prepared by JOHN S. LOUCKS St. Edward s University

s Prepared by JOHN S. LOUCKS St. Edward s University 2002 South-Western/Thomson Learning 1 Chapter 18 Forecasting Time Series and Time Series Methods Components of a Time Series Smoothing Methods Trend

### Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480

1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500

### TIME SERIES ANALYSIS. A time series is essentially composed of the following four components:

TIME SERIES ANALYSIS A time series is a sequence of data indexed by time, often comprising uniformly spaced observations. It is formed by collecting data over a long range of time at a regular time interval

### Theory at a Glance (For IES, GATE, PSU)

1. Forecasting Theory at a Glance (For IES, GATE, PSU) Forecasting means estimation of type, quantity and quality of future works e.g. sales etc. It is a calculated economic analysis. 1. Basic elements

### 2) The three categories of forecasting models are time series, quantitative, and qualitative. 2)

Exam Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) Regression is always a superior forecasting method to exponential smoothing, so regression should be used

### MGT 267 PROJECT. Forecasting the United States Retail Sales of the Pharmacies and Drug Stores. Done by: Shunwei Wang & Mohammad Zainal

MGT 267 PROJECT Forecasting the United States Retail Sales of the Pharmacies and Drug Stores Done by: Shunwei Wang & Mohammad Zainal Dec. 2002 The retail sale (Million) ABSTRACT The present study aims

### Time series Forecasting using Holt-Winters Exponential Smoothing

Time series Forecasting using Holt-Winters Exponential Smoothing Prajakta S. Kalekar(04329008) Kanwal Rekhi School of Information Technology Under the guidance of Prof. Bernard December 6, 2004 Abstract

### Outline: Demand Forecasting

Outline: Demand Forecasting Given the limited background from the surveys and that Chapter 7 in the book is complex, we will cover less material. The role of forecasting in the chain Characteristics of

### Regression Analysis: A Complete Example

Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

### 2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

### Conditional guidance as a response to supply uncertainty

1 Conditional guidance as a response to supply uncertainty Appendix to the speech given by Ben Broadbent, External Member of the Monetary Policy Committee, Bank of England At the London Business School,

### Factors Influencing Price/Earnings Multiple

Learning Objectives Foundation of Research Forecasting Methods Factors Influencing Price/Earnings Multiple Passive & Active Asset Management Investment in Foreign Markets Introduction In the investment

### Simple Methods and Procedures Used in Forecasting

Simple Methods and Procedures Used in Forecasting The project prepared by : Sven Gingelmaier Michael Richter Under direction of the Maria Jadamus-Hacura What Is Forecasting? Prediction of future events

### Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables

### Part 1 : 07/27/10 21:30:31

Question 1 - CIA 593 III-64 - Forecasting Techniques What coefficient of correlation results from the following data? X Y 1 10 2 8 3 6 4 4 5 2 A. 0 B. 1 C. Cannot be determined from the data given. D.

### Simple linear regression

Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between

### Forecasting Methods. What is forecasting? Why is forecasting important? How can we evaluate a future demand? How do we make mistakes?

Forecasting Methods What is forecasting? Why is forecasting important? How can we evaluate a future demand? How do we make mistakes? Prod - Forecasting Methods Contents. FRAMEWORK OF PLANNING DECISIONS....

### Forecasting in supply chains

1 Forecasting in supply chains Role of demand forecasting Effective transportation system or supply chain design is predicated on the availability of accurate inputs to the modeling process. One of the

### CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA

We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical

### Paper No 19. FINALTERM EXAMINATION Fall 2009 MTH302- Business Mathematics & Statistics (Session - 2) Ref No: Time: 120 min Marks: 80

Paper No 19 FINALTERM EXAMINATION Fall 2009 MTH302- Business Mathematics & Statistics (Session - 2) Ref No: Time: 120 min Marks: 80 Question No: 1 ( Marks: 1 ) - Please choose one Scatterplots are used

### Module 5: Multiple Regression Analysis

Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

### Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

### Example: Boats and Manatees

Figure 9-6 Example: Boats and Manatees Slide 1 Given the sample data in Table 9-1, find the value of the linear correlation coefficient r, then refer to Table A-6 to determine whether there is a significant

### Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

### Predicting the US Real GDP Growth Using Yield Spread of Corporate Bonds

International Department Working Paper Series 00-E-3 Predicting the US Real GDP Growth Using Yield Spread of Corporate Bonds Yoshihito SAITO yoshihito.saitou@boj.or.jp Yoko TAKEDA youko.takeda@boj.or.jp

### Trend and Seasonal Components

Chapter 2 Trend and Seasonal Components If the plot of a TS reveals an increase of the seasonal and noise fluctuations with the level of the process then some transformation may be necessary before doing

### Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics

Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in

### 2013 MBA Jump Start Program. Statistics Module Part 3

2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just

### Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

### INCORPORATION OF LEARNING CURVES IN BREAK-EVEN POINT ANALYSIS

Delhi Business Review Vol. 2, No. 1, January - June, 2001 INCORPORATION OF LEARNING CURVES IN BREAK-EVEN POINT ANALYSIS Krishan Rana Suneel Maheshwari Ramchandra Akkihal T HIS study illustrates that a

### The Strategic Role of Forecasting in Supply Chain Management and TQM

Forecasting A forecast is a prediction of what will occur in the future. Meteorologists forecast the weather, sportscasters and gamblers predict the winners of football games, and companies attempt to

Business Valuation Review Regression Analysis in Valuation Engagements By: George B. Hawkins, ASA, CFA Introduction Business valuation is as much as art as it is science. Sage advice, however, quantitative

### Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

### Accurately and Efficiently Measuring Individual Account Credit Risk On Existing Portfolios

Accurately and Efficiently Measuring Individual Account Credit Risk On Existing Portfolios By: Michael Banasiak & By: Daniel Tantum, Ph.D. What Are Statistical Based Behavior Scoring Models And How Are

### Simple Predictive Analytics Curtis Seare

Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

Review for Exam 2 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems You are not responsible for any topics that are not covered in the lecture note

### 17. SIMPLE LINEAR REGRESSION II

17. SIMPLE LINEAR REGRESSION II The Model In linear regression analysis, we assume that the relationship between X and Y is linear. This does not mean, however, that Y can be perfectly predicted from X.

### VIANELLO FORENSIC CONSULTING, L.L.C.

VIANELLO FORENSIC CONSULTING, L.L.C. 6811 Shawnee Mission Parkway, Suite 310 Overland Park, KS 66202 (913) 432-1331 THE MARKETING PERIOD OF PRIVATE SALES TRANSACTIONS By Marc Vianello, CPA, ABV, CFF 1

### Forecasting DISCUSSION QUESTIONS

4 C H A P T E R Forecasting DISCUSSION QUESTIONS 1. Qualitative models incorporate subjective factors into the forecasting model. Qualitative models are useful when subjective factors are important. When

### 8. Time Series and Prediction

8. Time Series and Prediction Definition: A time series is given by a sequence of the values of a variable observed at sequential points in time. e.g. daily maximum temperature, end of day share prices,

### Part 2: Analysis of Relationship Between Two Variables

Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable

### VIANELLO FORENSIC CONSULTING, L.L.C.

VIANELLO FORENSIC CONSULTING, L.L.C. 6811 Shawnee Mission Parkway, Suite 310 Overland Park, KS 66202 (913) 432-1331 THE MARKETING PERIOD OF PRIVATE SALE TRANSACTIONS Updated for Sales through 2010 By Marc

### Summary. Chapter Five. Cost Volume Relations & Break Even Analysis

Summary Chapter Five Cost Volume Relations & Break Even Analysis 1. Introduction : The main aim of an undertaking is to earn profit. The cost volume profit (CVP) analysis helps management in finding out

### http://www.jstor.org This content downloaded on Tue, 19 Feb 2013 17:28:43 PM All use subject to JSTOR Terms and Conditions

A Significance Test for Time Series Analysis Author(s): W. Allen Wallis and Geoffrey H. Moore Reviewed work(s): Source: Journal of the American Statistical Association, Vol. 36, No. 215 (Sep., 1941), pp.

### Introduction to time series analysis

Introduction to time series analysis Margherita Gerolimetto November 3, 2010 1 What is a time series? A time series is a collection of observations ordered following a parameter that for us is time. Examples

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

### CHAPTER 11: ARBITRAGE PRICING THEORY

CHAPTER 11: ARBITRAGE PRICING THEORY 1. The revised estimate of the expected rate of return on the stock would be the old estimate plus the sum of the products of the unexpected change in each factor times

### 5. Linear Regression

5. Linear Regression Outline.................................................................... 2 Simple linear regression 3 Linear model............................................................. 4

### WEB APPENDIX. Calculating Beta Coefficients. b Beta Rise Run Y 7.1 1 8.92 X 10.0 0.0 16.0 10.0 1.6

WEB APPENDIX 8A Calculating Beta Coefficients The CAPM is an ex ante model, which means that all of the variables represent before-thefact, expected values. In particular, the beta coefficient used in

### AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

### Answers to Text Questions and Problems. Chapter 22. Answers to Review Questions

Answers to Text Questions and Problems Chapter 22 Answers to Review Questions 3. In general, producers of durable goods are affected most by recessions while producers of nondurables (like food) and services

### Analysis of Bayesian Dynamic Linear Models

Analysis of Bayesian Dynamic Linear Models Emily M. Casleton December 17, 2010 1 Introduction The main purpose of this project is to explore the Bayesian analysis of Dynamic Linear Models (DLMs). The main

### Exercise 1.12 (Pg. 22-23)

Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

### Experiment #1, Analyze Data using Excel, Calculator and Graphs.

Physics 182 - Fall 2014 - Experiment #1 1 Experiment #1, Analyze Data using Excel, Calculator and Graphs. 1 Purpose (5 Points, Including Title. Points apply to your lab report.) Before we start measuring

### CHAPTER 10 In-Class QUIZ

CHAPTER 10 In-Class QUIZ 1. A mixed cost function has a constant component of \$20,000. If the total cost is \$60,000 and the independent variable has the value 200, what is the value of the slope coefficient?

### Factors affecting online sales

Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4

### Time series forecasting

Time series forecasting 1 The latest version of this document and related examples are found in http://myy.haaga-helia.fi/~taaak/q Time series forecasting The objective of time series methods is to discover

### Overview... 2. Accounting for Business (MCD1010)... 3. Introductory Mathematics for Business (MCD1550)... 4. Introductory Economics (MCD1690)...

Unit Guide Diploma of Business Contents Overview... 2 Accounting for Business (MCD1010)... 3 Introductory Mathematics for Business (MCD1550)... 4 Introductory Economics (MCD1690)... 5 Introduction to Management

### Quarterly Wholesale/Retail Price Report

Quarterly Wholesale/Retail Price Report February 29 Contents Overview 3 Summary of analysis 1. Customer bills, wholesale costs and margins 5 Electricity Gas 2. Scenario analysis: Impact of retail price

### TIME SERIES ANALYSIS AS A MEANS OF MANAGERIA DECISION MAKING IN MANUFACTURING INDUSTRY

TIME SERIES ANALYSIS AS A MEANS OF MANAGERIA DECISION MAKING IN MANUFACTURING INDUSTRY 1 Kuranga L.J, 2 Ishola James.A, and 3 Ibrahim Hamzat G. 1 Department of Statistics Kwara State Polytechnic Ilorin,Nigeria

### VI. Real Business Cycles Models

VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized

### Revenue Structure, Objectives of a Firm and. Break-Even Analysis.

Revenue :The income receipt by way of sale proceeds is the revenue of the firm. As with costs, we need to study concepts of total, average and marginal revenues. Each unit of output sold in the market

### Case, Fair and Oster Macroeconomics Chapter 11 Problems Money Demand and the Equilibrium Interest Rate

Case, Fair and Oster Macroeconomics Chapter 11 Problems Money Demand and the Equilibrium Interest Rate Money demand equation. P Y Md = k * -------- where k = percent of nominal income held as money ( Cambridge

### AN INTRODUCTION TO PREMIUM TREND

AN INTRODUCTION TO PREMIUM TREND Burt D. Jones * February, 2002 Acknowledgement I would like to acknowledge the valuable assistance of Catherine Taylor, who was instrumental in the development of this

### Uniwersytet Ekonomiczny

Uniwersytet Ekonomiczny George Matysiak Introduction to modelling & forecasting December 15 th, 2014 Agenda Modelling and forecasting - Models Approaches towards modelling and forecasting Forecasting commercial

### Linear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares

Linear Regression Chapter 5 Regression Objective: To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects

### Financial Time Series Analysis (FTSA) Lecture 1: Introduction

Financial Time Series Analysis (FTSA) Lecture 1: Introduction Brief History of Time Series Analysis Statistical analysis of time series data (Yule, 1927) v/s forecasting (even longer). Forecasting is often

### 5. Multiple regression

5. Multiple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/5 QBUS6840 Predictive Analytics 5. Multiple regression 2/39 Outline Introduction to multiple linear regression Some useful

### Lean Six Sigma Analyze Phase Introduction. TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY

TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY Before we begin: Turn on the sound on your computer. There is audio to accompany this presentation. Audio will accompany most of the online

### Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data

Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable

### A Decision-Support System for New Product Sales Forecasting

A Decision-Support System for New Product Sales Forecasting Ching-Chin Chern, Ka Ieng Ao Ieong, Ling-Ling Wu, and Ling-Chieh Kung Department of Information Management, NTU, Taipei, Taiwan chern@im.ntu.edu.tw,

### Agenda. Managing Uncertainty in the Supply Chain. The Economic Order Quantity. Classic inventory theory

Agenda Managing Uncertainty in the Supply Chain TIØ485 Produkjons- og nettverksøkonomi Lecture 3 Classic Inventory models Economic Order Quantity (aka Economic Lot Size) The (s,s) Inventory Policy Managing

### EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS TERM PAPER

EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS TERM PAPER NAME: IOANNA KOULLOUROU REG. NUMBER: 1004216 1 Term Paper Title: Explain what is meant by the term structure of interest rates. Critically evaluate

### The Short-Run Macro Model. The Short-Run Macro Model. The Short-Run Macro Model

The Short-Run Macro Model In the short run, spending depends on income, and income depends on spending. The Short-Run Macro Model Short-Run Macro Model A macroeconomic model that explains how changes in

### The Combination Forecasting Model of Auto Sales Based on Seasonal Index and RBF Neural Network

, pp.67-76 http://dx.doi.org/10.14257/ijdta.2016.9.1.06 The Combination Forecasting Model of Auto Sales Based on Seasonal Index and RBF Neural Network Lihua Yang and Baolin Li* School of Economics and

### South Carolina College- and Career-Ready (SCCCR) Probability and Statistics

South Carolina College- and Career-Ready (SCCCR) Probability and Statistics South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR)