Index numbers are used to measure changes in economic variables over time or space. Common index numbers include the Laspeyres, Paasche, Fisher, and Törnqvist indexes. These indexes can be used to create price indexes that measure inflation, as well as quantity indexes that measure changes in output and inputs. Direct and indirect approaches can be used to calculate quantity indexes. Properties like transitivity, self-duality, and mean value are important in selecting an appropriate index number formula. Chain indexes that compare consecutive periods are commonly used for productivity measurement.
Predicting future sales is intended to control the number of existing stock, so the lack or excess stock can be minimized. When the number of sales can be accurately predicted, then the fulfillment of consumer demand can be prepared in a timely and cooperation with the supplier company can be maintained properly so that the company can avoid losing sales and customers. This study aims to propose a model to predict the sales quantity (multi-products) by adopting the Recency-Frequency-Monetary (RFM) concept and Fuzzy Analytic Hierarchy Process (FAHP) method. The measurement of sales prediction accuracy in this study using a standard measurement of Mean Absolute Percentage Error (MAPE), which is the most important criteria in analyzing the accuracy of the prediction. The results indicate that the average MAPE value of the model was high (3.22%), so this model can be referred to as a sales prediction model.
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.
REGRESSION ANALYSISPlease refer to chapter 3 of the textbook fo.docxdebishakespeare
REGRESSION ANALYSIS
Please refer to chapter 3 of the textbook for more information on regression analysis.
Also, see the link
http://www2.chass.ncsu.edu/garson/PA765/regress.htm
We will estimate a demand function using linear and log-linear regressions with lagged Q.
· Linear Regression (three independent variables): The following demand function has three regressors P, M and Qt-1 .
Qt = a + bPt + cMt + dQt-1
where: Q is the Quantity (dependent variable)
P is the Price
M is the Income
Qt-1 is the lagged Q
t is the time period
· Input or copy the data on an EXCEL sheet, clearly specifying the dependent Y variable to be the quantity (Qt) (highlight its column), and the independent Xvariables to be the price (Pt), income (Mt) and the lagged Qt-1 or as the situation warrants.. Here we have three regressors: (Pt), income (Mt) and the lagged Qt-1 (highlight all of them at the same time).
· To enter values for the lagged Qt-1, you may copy the whole data under Qt and paste it in a new column added to the given sheet under the lagged Qt-1. Pasting should start such that the first observation under Qt will be the first observation under the lagged Qt-1 starting with the second row.
· Click on Excel icon on top left, Excel Options at the bottom of pop up menu, Add-ins in the left hand column, then Analysis Toolpak, then hit ok.
·
· if it does not come up, then hit go and make sure that Analysis Toolpak is checked.
·
· then under Data, Data analysis, Regression, ok.
·
· If you have Analysis Toopak in your computer, then the road to regression is shorter. Click on Excel icon, Data, Data Analysis in the up far right then Regression.
· Go to TOOLS menu and click DATA ANALYSIS. Pick up REGRESSION from the ANALYSIS TOOLS presented in the pop up menu and click OK.
· First highlight the dependent variable (Qt) cell range from the spreadsheet starting from the second row (skip the row with the empty cell), and click OK on the REGRESSION pop up menu to insert the selected data range in the Input Y range box. Similarly select the relevant data range for all the independent variablestogether including lagged Q and insert the selected data range in the Input X range box. Double check your cell ranges.
· Click on “LABEL” to include the symbols or names of variables in the regression output.
· In the OUTPUT OPTIONS, click New Worksheet Ply and say OK. The Regression output will be available to you on a newly created worksheet.
How to add DATA ANALYSIS to your TOOLS menu?
· If the TOOLS menu in your computer does not have DATA ANALYSIS, you can add it by doing the following.
· Open TOOLS
· Click on ADD-INS
· Include ANALYSIS TOOLPACK from the pop up menu dialog box and click OK.
· Go back to TOOLS and you will find DATA ANALYSIS at the bottom of the menu.
The Questions required for the homework assignment are listed
Below:
Homework assignment: Questions
QUESTION 1:
Copy the database below into an excel sheet.
Run QX on the four regres ...
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
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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.
3. Outline Introduction Conceptual framework and notation Formulae for price index numbers Quantity index numbers Properties of index numbers 3 ECON377/477 Topic 5.1
4. Introduction Index numbers are the most commonly used instruments to measure changes in levels of various economic variables Measuring productivity changes necessarily involves measuring changes in the levels of output and the associated changes in the input usage Such changes are easy to measure in the case of a single input and a single output, but are more difficult when multi-input and multi-output cases are considered ECON377/477 Topic 5.1 4
5.
6. generating data for use in the application of DEA or in the estimation of the stochastic frontiers
7. handling panel data sets, with price and quantity data over time and space to meet some basic consistency requirements such as ‘transitivity’ and ‘base invariance’ECON377/477 Topic 5.1 5
8. Introduction The principal aim of the first part of this topic is to familiarise you with the various index numbers The main indices we shall deal with are the Laspeyres, Paasche, Fisher and Törnqvist index numbers We then focus on the construction of price and quantity index numbers Quantity index number formulae are applied to input and output data that lead to quantity index numbers that are, in turn, used in defining the TFP index in the next part ECON377/477 Topic 5.1 6
9. Conceptual framework and notation An index number is defined as a real number that measures changes in a set of related variables Conceptually, index numbers may be used for comparisons over time or space or both Price index numbers may refer to consumer prices, input and output prices, export and import prices, etc. Quantity index numbers may measure changes in quantities of outputs produced or inputs used by a firm or industry over time or across firms ECON377/477 Topic 5.1 7
10. Conceptual framework and notation Let pmjand qmj represent the price and quantity, respectively, of the m-th commodity in the M commodities being considered (m = 1,2,...,M) in the j-th period (j = s, t) Without loss of generality, s and t may refer to two firms instead of time periods, and quantities may refer to either input or output quantities All index numbers measure changes in the levels of a set of variables from a reference period ECON377/477 Topic 5.1 8
11. Conceptual framework and notation The reference period is denoted at the ‘base period’ The period for which the index is calculated is referred to as the ‘current period’ Let Istrepresent a general index number for current period, t, with s as the base period Similarly, let Vst, Pst and Qst represent value, price and quantity index numbers, respectively ECON377/477 Topic 5.1 9
12. Conceptual framework and notation The value change from period s to t is the ratio of the value of commodities in periods s and t, valued at respective prices Thus, ECON377/477 Topic 5.1 10
13. Conceptual framework and notation The index, Vst, measures the change in the value of the basket of quantities of M commodities from period s to period t It is the result of changes in the two components, prices and quantities While Vst is easy to measure, it is more difficult to disentangle the effects of price and quantity changes ECON377/477 Topic 5.1 11
14. Conceptual framework and notation If we are operating in a single-commodity world, decomposition is simple to achieve We have The ratios, pt/ps and qt/qs, measure the relative price and quantity changes and there is no index number problem ECON377/477 Topic 5.1 12
15. Conceptual framework and notation In general, when we have M 2 commodities, we have a problem of aggregation The price relative, pmt/pms, measures the change in the price level of the m-th commodity, and the quantity relative, qmt/qms, measures the change in the quantity level of the m-th commodity (m = 1,2,...,M) The problem is one of combining the M different measures of price (quantity) changes, into a single real number, called a price (quantity) index ECON377/477 Topic 5.1 13
16. Formulae for price index numbers The Laspeyres price index uses the base-period quantities as weights to define the index: The Paasche price index uses the current-period weights to define the index: ECON377/477 Topic 5.1 14
17. Formulae for price index numbers The value share of m-th commodity in the base period in the Laspeyres price index is: The value shares reflect the relative importance of each commodity in the set involved They refer to the base period ECON377/477 Topic 5.1 15
18. Formulae for price index numbers There are two alternative interpretations of the Laspeyres index: It is the ratio of two value aggregates resulting from the valuation of the base-period quantities at current- and base-period prices It is a value-share weighted average of the M price relatives ECON377/477 Topic 5.1 16
19. Formulae for price index numbers The Paasche index number, based on current-period quantities, is a natural alternative to the use of base-period quantities in the Laspeyres index The first part shows that the Paasche index is the ratio of the two value aggregates resulting from the valuation of period-t quantities at the prices prevailing in periods t and s The last part suggests it is a weighted harmonic mean of price relatives, with current-period value shares as weights ECON377/477 Topic 5.1 17
20. Formulae for price index numbers The Laspeyres and Paasche formulae represent two extremes, one formula placing emphasis on base-period quantities and the other on current-period quantities They coincide if the price relatives do not exhibit any variation, that is, if pmt/pms = c, but diverge when price relatives exhibit a large variation The extent of divergence also depends on quantity relatives and the statistical correlation between price and quantity relatives ECON377/477 Topic 5.1 18
21. Formulae for price index numbers The Fisher index is: It possesses a number of desirable statistical and economic theoretic properties It is also known as the Fisher ideal index ECON377/477 Topic 5.1 19
22. Formulae for price index numbers The Törnqvist price index is a weighted geometric average of the price relatives, with weights that are a simple average of the value shares in periods s and t: It is usually presented and applied in its log-change form ECON377/477 Topic 5.1 20
23. Formulae for price index numbers In log-change form, the Törnqvist index is a weighted average of logarithmic price changes The log-change in the price of the m-th commodity given by represents the percentage change in the price of the m-th commodity It provides an indication of the overall growth rate in prices (inflation rate) ECON377/477 Topic 5.1 21
24. Quantity index numbers: direct approach Two approaches can be used in measuring quantity changes The first approach is a direct approach, using a formula that measures overall quantity changes from individual commodity-specific quantity changes, measured by qmt/qms The Laspeyres, Paasche, Fisher and Törnqvist indices can be applied directly to quantity relatives These formulae may be defined using price index numbers by simply interchanging prices and quantities ECON377/477 Topic 5.1 22
25. Quantity index numbers: direct approach The formulae described above yield: ECON377/477 Topic 5.1 23
26. Quantity index numbers: direct approach The Törnqvist quantity index, in its multiplicative and additive (log-change) forms, is: The log-change form of the Törnqvist index is generally used for computational purposes ECON377/477 Topic 5.1 24
27. Quantity index numbers: indirect approach The second approach is an indirect approach in which price and quantity changes comprise the value change over periods s and t If price changes are measured directly using the formulae in the previous section, quantity changes can be indirectly obtained after deflating the value change for the price change This approach is commonly used for purposes of quantity comparisons over time on the premise that Vst = Pst Qst ECON377/477 Topic 5.1 25
28. Quantity index numbers: indirect approach Since Vst is defined from data directly as the ratio of values in periods t and s, Qst can be obtained as a function of Pst ECON377/477 Topic 5.1 26
29. Quantity index numbers: indirect approach The numerator in this expression corresponds to the constant price series This approach states that quantity indices can be obtained from ratios of values, aggregated after removing the effect of price movements over the period under consideration Some features and applications of indirect quantity comparisons are discussed below ECON377/477 Topic 5.1 27
30. Constant price aggregates and quantities Time series and cross-section data on price aggregates are often used as data series to estimate least-squares econometric production models and stochastic frontiers, and in DEA calculations, where it is necessary to reduce the dimensions of the output and input vectors This means that, even if index number methods are not used to measure productivity changes directly, they are regularly used to create intermediate data series ECON377/477 Topic 5.1 28
31. Self-duality of formulae The Laspeyres price index and the Paasche quantity index form a pair that exactly decompose the value change In that sense, the Paasche quantity index can be considered as the dual of the Laspeyres price index The Paasche price index and Laspeyres quantity index decompose the value index, and therefore are dual to each other ECON377/477 Topic 5.1 29
32. Self-duality of formulae The Fisher index for prices and the Fisher index for quantities form a dual pair This implies that the direct quantity index obtained using the Fisher formula is identical to the indirect quantity index derived by deflating the value change by the Fisher price index This property is sometimes referred to as the factor reversal test (see below) ECON377/477 Topic 5.1 30
36. Direct versus indirect quantity comparisons Since an index number is a scalar-valued representation of changes that are observed for different commodities, the reliability of such a representation depends upon the variabilities that are observed in the price and quantity changes for the different commodities Uniform price changes over different commodities mean the price index provides a reliable measure of the price changes A similar conclusion can be drawn for quantity index numbers ECON377/477 Topic 5.1 32
37. Direct versus indirect quantity comparisons The relative variability in the price and quantity ratios, pmt/pms and qmt/qms (m = 1, 2, ...,M) provides a useful clue as to which index is more reliable If the price ratios exhibit less variability than the quantity ratios, an indirect quantity index is advocated If quantity relatives show less variability, a direct quantity index is preferred Price changes over time tend to be more uniform across commodities than quantity changes ECON377/477 Topic 5.1 33
38. Direct versus indirect quantity comparisons If price (quantity) ratios exhibit little variability, most index number formulae lead to very similar measures of price (quantity) change There is more concurrence of results arising out of different formulae, and, therefore, the choice of a formula has less impact on the measure of price (quantity) change derived Direct quantity comparisons may offer theoretically more meaningful indices because they use the constraints underlying the production technologies ECON377/477 Topic 5.1 34
39. Direct versus indirect quantity comparisons Direct input and output quantity indices based on the Törnqvist index formula are theoretically superior under certain conditions The Fisher index performs well with respect to both theoretical and test properties Also, it is self-dual in that it satisfies the factor-reversal test (see below) Being defined using the Laspeyres and Paasche indices, the Fisher index is easier to understand and is capable of handling zero quantities in the data set ECON377/477 Topic 5.1 35
40. Direct versus indirect quantity comparisons But, under the assumption of behaviour under revenue constraints, productivity indices are best computed using indirect quantity measures Given these results, from a theoretical point of view the choice between direct and indirect quantity (input or output) comparisons should be based on the assumptions about the behaviour of the decision-making unit A decision needs to be made on pragmatic considerations as well as on pure analytical grounds ECON377/477 Topic 5.1 36
41. Properties of index numbers Tests can be used to choose a formula to construct price and quantity index numbers An alternative (yet closely related) framework is to state a number of properties, in the form of axioms, and find an index number that satisfies a given set of axioms This approach is known as the axiomatic approach to index numbers ECON377/477 Topic 5.1 37
42. Properties of index numbers Let Pst and Qst represent price and quantity index numbers, which are both real-valued functions of the prices and quantities (M commodities) observed in periods s and t, denoted by M-dimensional column vectors, ps, pt, qs and qt Some of the basic and commonly used axioms are listed on the next two slides ECON377/477 Topic 5.1 38
43. Properties of index numbers Positivity: The index (price or quantity) should be everywhere positive Continuity: The index is a continuous function of the prices and quantities Proportionality: If all prices (quantities) increase by the same proportion then Pst(Qst) should increase by that proportion Commensurability or dimensional invariance: The price (quantity) index must be independent of the units of measurement of quantities (prices) Time-reversal test: For two periods s and t: ECON377/477 Topic 5.1 39
44. Properties of index numbers Mean-value test: The price (or quantity) index must lie between the respective minimum and maximum changes at the commodity level Factor-reversal test: A formula is said to satisfy this test if the same formula is used for direct price and quantity indices and the product of the resulting indices is equal to the value ratio Circularity test (transitivity): For any three periods, s, t and r, this test requires that: ECON377/477 Topic 5.1 40
45. Properties of index numbers The following two results describe the properties of the Fisher and Törnqvist indices, and thus offer justification for the common use of these indices in the context of productivity measurement: The Fisher index satisfies all the properties listed above, with the exception of the circularity test (transitivity) The Törnqvist index satisfies all the tests listed above with the exception of the factor-reversal and circularity tests ECON377/477 Topic 5.1 41
46. Properties of index numbers In the case of temporal comparisons for productivity measurement, we are usually interested in comparing each year with the previous year Annual changes in productivity are then combined to measure changes over a given period The index constructed using this procedure is known as a chain index ECON377/477 Topic 5.1 42
47. Properties of index numbers Let I(t, t+1) define an index of interest for period t+1 with t as the base period The index can be applied to a time series with t = 0, 1, 2, ..., T A comparison between period t and a fixed base period, 0, can be made using the following chained index of comparisons for consecutive periods: I(0, t) = I(0, 1)I(1, 2)...I(t-1, t) ECON377/477 Topic 5.1 43
48. Properties of index numbers As an alternative to the chain-base index, it is possible to compare period 0 with period t using any one of the formulae described earlier This index is known as the fixed-base index From a practical angle, especially with respect to productivity measurement, a chain index is more suitable than a fixed-base index It involves comparing consecutive periods and is measuring smaller changes, so some of the approximations involved in deriving theoretically meaningful indices are more likely to hold ECON377/477 Topic 5.1 44
49. Properties of index numbers Another advantage is that comparisons over consecutive periods mean that the Laspeyres-Paasche spread is likely to be small, indicating that most index number formulae result in indices that are very similar in magnitude A drawback is that the weights used in a chain index need to be revised every year Also, the use of a chained index does not result in transitive index numbers Although transitivity is not essential for temporal comparisons, it is needed for multilateral comparisons (more on this in Topic 5.2) ECON377/477 Topic 5.1 45
50. Which index number to choose? The foregoing discussion indicates that the choice of formula is essentially between the Fisher and Törnqvist indices Both possess important properties and satisfy a number of axioms But it is likely that Laspeyres or Paasche indices are used in published aggregated data If the indices are being computed for periods that are not far apart, differences in the numerical values of the Fisher and the Törnqvist indices are likely to be minimal ECON377/477 Topic 5.1 46
51. Which index number to choose? Further, both of these indices also have important theoretical properties In practice, the Törnqvist index seems to be preferred But use of the Fisher index is recommended because of its additional self-dual property and its ability to accommodate zeros in the data ECON377/477 Topic 5.1 47