The power point presentation will help you understand Demand Estimation and Forecast in nutshell. It covers:
1) Estimation and its Methods
2) Forecast and its purpose
3) Steps to Forecast
4) Scope of Forecasting
5) Determinants for Demand Forecast
Meaning of demand forecasting , determinants and categorization of forecasting, choosing the technique of forecasting,objectives and methods of forecasting,tools used for forecasting and limitations to forecasting are discussed.
The power point presentation will help you understand Demand Estimation and Forecast in nutshell. It covers:
1) Estimation and its Methods
2) Forecast and its purpose
3) Steps to Forecast
4) Scope of Forecasting
5) Determinants for Demand Forecast
Meaning of demand forecasting , determinants and categorization of forecasting, choosing the technique of forecasting,objectives and methods of forecasting,tools used for forecasting and limitations to forecasting are discussed.
This is a presentation covering the concepts of demand forecasting. it includes the meaning of demand forecasting, purpose, scope and factors affecting demand forecasting. It also covers the methods of forecasting for both new and existing products.
In this paper we attempt to review the models, process, qualitative and quantitative methods of forecasting. We also review the needs and reasons for forecasting and what methods and approaches are employed for forecasting, requirements for forecasting, what are the shortcomings and business implications of forecasting.
ForecastingBUS255 GoalsBy the end of this chapter, y.docxbudbarber38650
Forecasting
BUS255
Goals
By the end of this chapter, you should know:
Importance of Forecasting
Various Forecasting Techniques
Choosing a Forecasting Method
2
Forecasting
Forecasts are done to predict future events for planning
Finance, human resources, marketing, operations, and supply chain managers need forecasts to plan
Forecasts are made on many different variables
Forecasts are important to managing both processes and managing supply chains
3
Key Decisions in Forecasting
Deciding what to forecast
Level of aggregation
Units of measurement
Choosing a forecasting system
Choosing a forecasting technique
4
5
Forecasting Techniques
Qualitative (Judgment) Methods
Sales force Estimates
Time-series Methods
Naïve Method
Causal Methods
Executive Opinion
Market Research
Delphi Method
Moving Averages
Exponential Smoothing
Regression Analysis
Qualitative (Judgment) methods
Salesforce estimates
Executive opinion
Market Research
The Delphi Method
Salesforce estimates: Forecasts derived from estimates provided by salesforce.
Executive opinion: Method in which opinions, experience, and technical knowledge of one or more managers are summarized to arrive at a single forecast.
Market research: A scientific study and analysis of data gathered from consumer surveys intended to learn consumer interest in a product or service.
Delphi method: A process of gaining consensus from a group of experts while maintaining their anonymity.
6
Case Study
Reference: Krajewski, Ritzman, Malhotra. (2010). Operations Management: Processes and Supply Chains, Ninth Edition. Pearson Prentice Hall. P. 42-43.
7
Case study questions
What information system is used by UNILEVER to manage forecasts?
What does UNILEVER do when statistical information is not useful for forecasting?
What types of qualitative methods are used by UNILEVER?
What were some suggestions provided to improve forecasting?
8
Causal methods – Linear Regression
A dependent variable is related to one or more independent variables by a linear equation
The independent variables are assumed to “cause” the results observed in the past
Simple linear regression model assumes a straight line relationship
9
Causal methods – Linear Regression
Y = a + bX
where
Y = dependent variable
X = independent variable
a = Y-intercept of the line
b = slope of the line
10
Causal methods – Linear Regression
Fit of the regression model
Coefficient of determination
Standard error of the estimate
Please go to in-class exercise sheet
Coefficient of determination: Also called r-squared. Measures the amount of variation in the dependent variable about its mean that is explained by the regression line. Range between 0 and 1. In general, larger values are better.
Standard error of the estimate: Measures how closely the data on the dependent variable cluster around the regression line. Smaller values are better.
11
Time Series
A time seri.
This is a presentation covering the concepts of demand forecasting. it includes the meaning of demand forecasting, purpose, scope and factors affecting demand forecasting. It also covers the methods of forecasting for both new and existing products.
In this paper we attempt to review the models, process, qualitative and quantitative methods of forecasting. We also review the needs and reasons for forecasting and what methods and approaches are employed for forecasting, requirements for forecasting, what are the shortcomings and business implications of forecasting.
ForecastingBUS255 GoalsBy the end of this chapter, y.docxbudbarber38650
Forecasting
BUS255
Goals
By the end of this chapter, you should know:
Importance of Forecasting
Various Forecasting Techniques
Choosing a Forecasting Method
2
Forecasting
Forecasts are done to predict future events for planning
Finance, human resources, marketing, operations, and supply chain managers need forecasts to plan
Forecasts are made on many different variables
Forecasts are important to managing both processes and managing supply chains
3
Key Decisions in Forecasting
Deciding what to forecast
Level of aggregation
Units of measurement
Choosing a forecasting system
Choosing a forecasting technique
4
5
Forecasting Techniques
Qualitative (Judgment) Methods
Sales force Estimates
Time-series Methods
Naïve Method
Causal Methods
Executive Opinion
Market Research
Delphi Method
Moving Averages
Exponential Smoothing
Regression Analysis
Qualitative (Judgment) methods
Salesforce estimates
Executive opinion
Market Research
The Delphi Method
Salesforce estimates: Forecasts derived from estimates provided by salesforce.
Executive opinion: Method in which opinions, experience, and technical knowledge of one or more managers are summarized to arrive at a single forecast.
Market research: A scientific study and analysis of data gathered from consumer surveys intended to learn consumer interest in a product or service.
Delphi method: A process of gaining consensus from a group of experts while maintaining their anonymity.
6
Case Study
Reference: Krajewski, Ritzman, Malhotra. (2010). Operations Management: Processes and Supply Chains, Ninth Edition. Pearson Prentice Hall. P. 42-43.
7
Case study questions
What information system is used by UNILEVER to manage forecasts?
What does UNILEVER do when statistical information is not useful for forecasting?
What types of qualitative methods are used by UNILEVER?
What were some suggestions provided to improve forecasting?
8
Causal methods – Linear Regression
A dependent variable is related to one or more independent variables by a linear equation
The independent variables are assumed to “cause” the results observed in the past
Simple linear regression model assumes a straight line relationship
9
Causal methods – Linear Regression
Y = a + bX
where
Y = dependent variable
X = independent variable
a = Y-intercept of the line
b = slope of the line
10
Causal methods – Linear Regression
Fit of the regression model
Coefficient of determination
Standard error of the estimate
Please go to in-class exercise sheet
Coefficient of determination: Also called r-squared. Measures the amount of variation in the dependent variable about its mean that is explained by the regression line. Range between 0 and 1. In general, larger values are better.
Standard error of the estimate: Measures how closely the data on the dependent variable cluster around the regression line. Smaller values are better.
11
Time Series
A time seri.
This overview discusses the predictive analytical technique known as Gradient Boosting Regression, an analytical technique that explore the relationship between two or more variables (X, and Y). Its analytical output identifies important factors ( Xi ) impacting the dependent variable (y) and the nature of the relationship between each of these factors and the dependent variable. Gradient Boosting Regression is limited to predicting numeric output so the dependent variable has to be numeric in nature. The minimum sample size is 20 cases per independent variable. The Gradient Boosting Regression technique is useful in many applications, e.g., targeted sales strategies by using appropriate predictors to ensure accuracy of marketing campaigns and clarify relationships among factors such as seasonality, product pricing and product promotions, or for an agriculture business attempting to ascertain the effects of temperature, rainfall and humidity on crop production. Gradient Boosting Regression is just one of the numerous predictive analytical techniques and algorithms included in the Assisted Predictive Modeling module of the Smarten augmented analytics solution. This solution is designed to serve business users with sophisticated tools that are easy to use and require no data science or technical skills. Smarten is a representative vendor in multiple Gartner reports including the Gartner Modern BI and Analytics Platform report and the Gartner Magic Quadrant for Business Intelligence and Analytics Platforms Report.
Case StudiesMemorial HospitalMemorial Hospital is a privately .docxtidwellveronique
Case Studies
Memorial Hospital
Memorial Hospital is a privately owned 600-bed facility. The hospital provides a broad range of health care services, including complete laboratory and X-ray facilities, an emergency room, an intensive care unit, a cardiac care unit, and a psychiatric ward. Most of these services are provided by several other hospitals in the metropolitan area. Memorial has purposely avoided getting involved in any specialized fields of medicine or obtaining very specialized diagnostic equipment because it was felt that such services would not be cost-effective. The General Hospital, located only a few miles from Memorial, is affiliated with the local School of Medicine and offers up-to-date services in those specialized areas. Instead of trying to compete with General Hospital to provide special services, Memorial Hospital has concentrated on offering high-quality general health care at an affordable price. Compared with the much larger General Hospital, Memorial stresses close personal attention to each patient from a nursing staff that cares about its work. In fact, the hospital has begun to place ads in newspapers and on television, stressing its patient-oriented care.
However, the hospital's administrator, Janice Fry, is concerned about whether the hospital can really deliver on its promises, and worries that failure to provide the level of health care patients expect could drive patients away. Janice met recently with the hospital's managerial personnel to discuss her concerns. The meeting raised some questions about how the hospital's quality of health care could be assured. Jessica Tu, director of nursing, raised the question, "How do we measure the quality of health care? Do we give patients a questionnaire when they leave, asking if they were happy here? That does not seem to answer the question because we could make a patient happy, but give them lousy health care." Several other questions were asked concerning the hospital's efforts to keep costs down. Some people were concerned that an emphasis on costs would be detrimental to quality. They argued that when a person's life is at stake, costs should not be of concern.
After the meeting, Janice began thinking about these questions. She remembered reading recently that some companies were using total quality management (TQM) to improve their quality. She liked the idea—if it could be used in a hospital.
1. Discuss some ways that a hospital might measure quality.
2. What are the potential costs of quality for Memorial Hospital? How could the value of a human life be included?
3. Are there any ideas or techniques from TQM that Janice could use to help Memorial focus on providing quality health care?
4. What measures could Memorial use to assess the quality of health care it is providing?
Forecasting
BUS255
Goals
By the end of this chapter, you should know:
Importance of Forecasting
Various Forecasting Techniques
Choosing a Forecasting Method
2
Forecasti ...
[KAIST DFMP CBA] Analyze price determinants and forecast Seoul apartment pric...경록 박
Analyzed price determinants and forecasted Seoul apartment prices with correlations, regressions (linear, decision tree, random forest, XGB), and time series models (Auto ARIMA, Holt-Winters) using Samsung Brightics Studio.
Chapter 9ReliabilityWhat is ReliabilityReliability is.docxmccormicknadine86
Chapter 9
Reliability
What is Reliability?
Reliability is concerned with questions of consistency
Other terms for reliability are:
Repeatability
Reproducibility
Stability
Consistency
Predictability
Agreement
Homogeneity
Measurement
Measurement is the assignment of number to object or events according to certain rules (Carmines and Zeller, 1979)
Measurement
Measurement is important in quantitative research because:
Quantification allows for powerful statistical analysis
Numbers are often more clearly communicated
Objectivity is increased
Efficiency may be increased
Levels of Measurement
Nominal: a label but nothing more
Categorical: identifies group membership
Ordinal: indicates an order
Interval: also in order but an estimation of distance between the scores
Ratio: order, defined distance, and a zero point
Measurement Error
The sources of error causing unreliability may be one or more of the following:
Measurement is inaccurate or inconsistent
Raters or testers are inaccurate or inconsistent
Measurement Error
The sources of error causing unreliability may be one or more of the following:
Phenomenon being measured varies from one measurement time to the next
The situation is confounding the measurement
Classic Measurement EquationX =t +eObservedTrueRandomScoreScoreError
Consistency
In order to maintain consistency of measurement there needs to be:
Interrater reliability
Intrarater reliability
Intercoder reliability
Cohen’s Kappa
A way to calculate the percent of agreement between the two coders
K = fo – fc K = kappa
N – fc fo = frequency of agreement
fc = frequency expected by chance
N = number evaluated
Test-Retest Reliability
A type of reliability that is evaluated by administering the same test to the same people or taking the same measurement on the same people after a specified period of time
The results of the two testing times are then compared statistically
Test-Retest Reliability
Factors affecting the test-retest reliability:
Assumes stability in the phenomenon being measured
May be affected by reactivity
Practice effect may also affect reliability
Test-Retest Reliability
Ways to calculate test-retest reliability include:
Pearson product moment correlation
Intraclass correlations (ICCs)
Homogeneity
Cronbach’s alpha can be used to test the homogeneity of items within a measure
It indicates the extent to which all of the items on the test are “behaving” similarly
Homogeneity
Alpha of 0.70 is acceptable for new measures
Alpha of at least 0.80 is expected for established measures
Higher alphas (at least 0.90 or higher) are desirable for use in clinical evaluation
Reliability of Physical Measures
Systematic error: a consistent error
Random error: inconsistent, unpredictable errors
Random errors can cancel each other out unless the researcher know how to detect them by using the technical error of measurement (TEM)
√ ∑ d2 d = the difference between scores of paired ...
aim of this paper is to study and analyse various aspects of the historical novel, i.e., need for fiction in a historical narrative, the defining features of historical fiction and the rise of the historical novel etc.
Power Sectors Reforms in Delhi: Implications, Promises, and the road aheadshivraj negi
Done as a requirement for CCS summer internship 2009, this ppt presents a birds eye view of power sector reforms in New Delhi, explains the power procurement procedure and then recommends some more policy changes, and the necessity of some measures for moving ahead on the reform path.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2. DEFINITION Estimation of various demand function of a firm(industry) or market through various processes. For practical purposes ,demand function for a firm or market has to be estimated from the empirical data.
3. . Broadly there are two types methods of Estimation: Simple Method of Estimation(5 steps) Statistical method of Estimation(Econometric analysis,7 Steps).
4. STEPS FOR DEMAND ESTIMATION Statement of a theory or hypothesis. Model specification. Data collection. Estimation of parameters. Checking goodness of fit. Hypothesis testing. Forecasting.
5. MODEL SPECIFICATION What variables to be included and what mathematical form to followed. Need to formulate many alternative models. Deterministic(certainity) and Statistical relationship It is assumed to begin with that the relationship is deterministic. With a simple demand curve the relationship would therefore be: Q =f (P)
11. Consumer Survey Seeking information through questionnaire , interviews etc. Asking information about their consumption behavior ie, buying habits , motives etc.
12. Consumer survey Advantages They give uptodate information about the current market scenario . Much useful information can be obtained that would be difficult to uncover in other ways; for example, if onsumersare ignorant of the relative prices of different brands, it may be concluded that they are not sensitive to price changes.This can be exploited by the firms for their best possible interest. Disadvantages Validity Reliability Sample Bias
13. Market Experiment Here consumers are studied in an artificial environment . Laboratory experiments or consumer clinics are used to test consumer reactions to changes in variables in the demand function in a controlled environment. Need to be careful in such experiments as the knowledge of being in the artificial environment can affect the consumer behavior.
14. Market experiment Advantages Direct observation of the consumers takes place rather than something of a hypothetical theoretical model . Disadvantages There is less control in this case, and greater cost; furthermore, some customers who are lost at this stage may be difficult to recover. Experiments need to be long lasting in order to reveal proper result.
15. Statistical methods These are various quantitative methods to find the exact relationship between the dependent variable and the independent variable(s). The most common method is regression Analysis : Simple (bivariate) Regression: Y = a + bX Multiple Regression: Y = a +bX1 + c X2 +dX3 +..
16. Limitations of Statistical methods They require a lot of data in order to be performed. They necessitate a large amount of computation.
17. Linear Regression – OLS Method Applicable when our model employs a linear relationship between X and Y. Find a line Ŷ = a + bX which minimizes sum of square errors Σ(Yi–Ŷi)2. Find a and b by partial differntiation.
18. Goodness of Fit Regression – type of relationshipCorrelation – strength of relationship An alternative to visual inspection Measures: Correlation coefficient (r) Coefficient of Determination (R2)
19. Correlation Coefficient Measures the degree of linear correlation Small correlation may imply weak linear, but strong non-linear relationship. Hence, visual inspection is also important. Does not talk about causation Causation may be reversed, circular, endogenic or third-party Hence, correlation cannot tell you how good a model is.
20. Correlation Coefficient It can be calculated as follows: r varies from 0 to 1. A high value of r implies that the points are very closely scattered around the regression line.
21. Coefficient of Determination (R2) The proportion of the total variation in the dependent variable that is explained by the relationship with the independent variable.
22.
23. Coefficient of Determination (R2) TD: Total DeviationED: Explained DeviationUD: Unexplained Deviation TD = ED + UD ΣTD2 = ΣED2 + ΣUD2
24. Coefficient of Determination (R2) R2 also varies from 0 to 1. Low R2 values imply that: The model is not a good fit. Perhaps a power regression model is needed? We are missing important variables. Look at Multivariate regression? R2is preferred to Correlation Coefficient (r)
25. Power Regression Mathematical form: Y=aXb Cannot directly use the OLS method. However by ignoring error terms and taking logarithm we get a linear model. log(Y) = log(a) + b*log(X)
26. Significance Testing t-test: Test of significance of a particular variable. t-stat = estimated coefficient/standard error Rule of thumb for a 95% confidence interval: >2 Implies that the independent variable truly impacts the dependent variable Specially useful in Multivariate regression F-test: Checks if variation in X explains a significant amount of the variation in Y.
27. The Pizza Dillemna Estimate the demand for Pizza by college students. Select variables for the model that you believe are: Relevant, and for which Data can be found
28. The Pizza Dillemna Average number of pizza slices consumed per month by students (Y) Average Selling Price of a Pizza slice (X1) Annual Course Fee – proxy for student income (X2) Average price of a soft drink – complementary product (X3) Location of the campus – proxy for availability of substitutes (X4) (1 for city campus, 0 for outskirts)
29. The Pizza Dillemna Y = a + b1X1 + b2X2 + b3X3 + b4X4 Results of linear regression based on actual data Y = 26.67 – 0.088 X1 + 0.138 X2 - 0.076 X3 - 0.0544 X4 (0.018) (0.087) (0.020) (0.884) R2 = 0.717 Adjusted R2 = 0.67 F= 15.8 Std Error of the Y-estimate = 1.64 (The standard errors of the coefficients are listed in parenthesis)
30. The Pizza Dillemna Values of Elasticity: Price Elasticity -0.807 Income Elasticity 0.177 Cross-price Elasticity -0.767 T-test: b2 and b4 are not significant. R2 = 0.717
31. Demand Forecasting Estimation or prediction of future demand for goods and services. Nearer it is to its true value, higher is the accuracy. Active and Passive forecasts. Short term, long term and medium term. Capacity utilization, Capacity expansion and Trade Cycles. Different forecasts needed for different conditions, markets, industries. Approaches to Forecasting: Judgmental, Experimental, Relational/Causal, Time Series Approaches.
32. Demand Forecasting Requirements for Demand Forecasting. Elements related to Consumers. Elements concerning the Suppliers. Elements concerning the Markets or Industry. Other Exogenous Elements like taxation, government policies, international economic climate, population, income etc. Estimating general conditions, estimating the total market demand and then calculating the firm’s market share. Multiple methods of forecasting, used depending upon suitability, accuracy and other factors. Subjective methods used when appropriate data is not available.
33. Demand Forecasting Subjective methods depend on intuition based on experience, intelligence, and judgment. Expert’s opinion survey, consumer’s interview method and historical analogy method. Survey Methods Using questionnaires with either complete enumeration or sample survey method. Using consumers, suppliers, employees or experts (Delphi method). Problems of survey methods. Less reliable and accurate due to subjectivity, but give quick estimates and are cost saving.
34. Demand Forecasting Historical Analogy Method. Forecasting for new product or new market/area. Difficulties in finding similar conditions. Test Marketing involves launching in a test area which can be regarded as true sample of total market. Difficulties of cost, time, variation of markets and imitation by competitors.
35. Demand Forecasting Systematic forces may show some variation in time series of sales data of a product. Basic parameters like population, technology. Business cycles, seasonal variations and then random events. Main focus is to find out the type of variation and then use it for long term forecasting. Use judgment to extrapolate the trend line obtained from sales data. OLS method to prepare a smooth curve is a better option. We may obtain a linear trend, quadratic trend, logarithmic trend or exponential trend each of which gives us a different information about the behavior of demand.
36. Demand Forecasting Linear: Y = a0 + a1(t) Quadratic: Y = a0 + a1(t) + a2(t)2 Logarithmic : Log Y = b0 + b1 log (t) Exponential : Log Y = c0 + c1 (t) Choice of the equation is based on multiple correlation coefficient (R) of OLS. Averaging is used to remove any large scale fluctuations.
37. Demand Forecasting The sales curve eventually is an S shaped ‘product life cycle curve’. Price elasticities vary in different stages. Highest in later stages as substitutes are available. All these stages give exponential shape to the curve. Trend method assumes little variations in business conditions. Knowledge of curve helps in planning marketing and planning for the product.
38. Demand Forecasting Leading Indicators or Barometric method. Time as a explanatory variable may not always show a liner relation, so we use another commodity as an indicator for sales. Regression method : Identify the demand factors for commodity and expected shape of the demand function. Use regression to fit the time series data. Higher the R2 the better is explanation. Inadequacy of data, multi-collinearity, auto-correlation, heteroscedasticity and lack of direct estimates of future values of explanatory variables.
50. Used only for short term predictions . Suitable only for demand with stationary time series sales data,i.e the one that does not reveal the long term trend.
51.
52.
53.
54.
55. One who wishes to do work with input-output systems must deal skillfully with industry classification, data estimation, and inverting very large, ill-conditioned matrices.
56.
57. Input-output model Let Xij=aijXj,i=1 to 4,j=1 to 4 or Xij/Xj=aij where aij is the output of ith industry required to produce unit output of jth industry. Thus X1=a11X1+a12X2+a13X3+a14X4+C1 X2=a21X1+a22X2+a23X3+a24X4+C2 X3=a31X1+a32X2+a33X3+a34X4+C3 X4=a41X1+a42X2+a43X3+a44X4+C4