Showing posts with label quantitative approarches. Show all posts
Showing posts with label quantitative approarches. Show all posts

Sunday, March 16, 2008

Nonlinear Regression *

Nonlinear regression is a method of finding a nonlinear model of the relationship between the dependent variable and a set of independent variables. Unlike traditional linear regression, which is restricted to estimating linear models, nonlinear regression can estimate models with arbitrary relationships between independent and dependent variables. This is accomplished using iterative estimation algorithms. Note that this procedure is not necessary for simple polynomial models of the form Y = A + BX^2. By defining W = X^2, we get a simple linear model, Y = A + BW, which can be estimated using traditional methods such as the Linear Regression procedure.

Implementation

  • Can population be predicted based on time? A scatter plot shows that there seems to be a strong relationship between population and time, but the relationship is nonlinear, so it requires the special estimation methods of the Nonlinear Regression procedure. By setting up an appropriate equation, such as a logistic population growth model, we can get a good estimate of the model, allowing us to make predictions about population for times that were not actually measured.
  • An internet service provider (ISP) is determining the effects of a virus on its networks. As part of this effort, they have tracked the (approximate) percentage of infected e-mail traffic on its networks over time, from the moment of discovery until the threat was contained. We can use Nonlinear Regression to model the rise and decline of the infection.

Linear Regression

Linear regression is used to model the value of a dependent scale variable based on its linear relationship to one or more predictors. It estimates the coefficients of the linear equation, involving one or more independent variables that best predict the value of the dependent variable. For example, you can try to predict a salesperson's total yearly sales (the dependent variable) from independent variables such as age, education, and years of experience.
Implementation

  • An automotive industry group keeps track of the sales for a variety of personal motor vehicles. In an effort to be able to identify over- and underperforming models, you want to establish a relationship between vehicle sales and vehicle characteristics. We can use linear regression to identify models that are not selling well.
  • Is the number of games won by a basketball team in a season related to the average number of points the team scores per game? A scatter plot indicates that these variables are linearly related. The number of games won and the average number of points scored by the opponent are also linearly related. These variables have a negative relationship. As the number of games won increases, the average number of points scored by the opponent decreases. With linear regression, you can model the relationship of these variables. A good model can be used to predict how many games teams will win.
  • The Nambe Mills company has a line of metal tableware products that require a polishing step in the manufacturing process. To help plan the production schedule, the polishing times for 59 products were recorded, along with the product type and the relative sizes of these products, measured in terms of their diameters. We can use linear regression to determine whether the polishing time can be predicted by product size.

Tuesday, March 4, 2008

Analytic Nertwork Process

Super Decisions Software for Decision-Making

The Super Decisions software implements the Analytic Network Process developed by Dr. Thomas Saaty. The program was written by the ANP Team, working for the Creative Decisions Foundation.

Getting The Software

There are a few simple steps to go through to get the Super Decisions software.

Screen Shots

Here is a screen shoot of the software running with a fairly famous burger model.

screenShoot

Other links to AHP

Wikipedia;
AHP


Some MCDA Methods

Excel Resources
Excel and Database

Friday, February 29, 2008

Menghitung NPV, IRR, xNPV dan xIRR dng Excel

Menghitung NPV, IRR, xNPV dan xIRR dng Ms Excel

  1. NPV (Net Present Value)
    NPV adalah selisih antara present value dari investasi dengan nilai sekarang dari penerimaan-penerimaan kas bersih di masa yang akan datang. Untuk menghitung nilai sekarang perlu ditentukan tingkat bunga yang relevan.
  2. IRR (Internal Rate of Return)
    Metode IRR ini digunakan untuk mencari tingkat bunga yang menyamakan nilai sekarang
    dari arus kas yang diharapkan di masa datang, atau penerimaan kas, dengan mengeluarkan investasi awal. Caranya, dengan menghitung nilai sekarang dari arus kas
    suatu investasi dengan menggunakan suku bunga yang wajar, misalnya 10 %. kemudian
    di bandingkan dengan biaya investasi, jika nilai investasi lebih kecil, maka di coba lagi
    dengan penghitungan suku bunga yang lebih tinggi demikian seterusnya sampai biaya
    investasi menjadi sama besar. Apabila dengan suku bunga wajar tadi nilai investasi lebih
    besar, maka harus di coba lagi dengan suku bunga yang lebih rendah sampai
    mendapatkan nilai investasi yang sama besar dengan nilai sekarang.
File Excel contoh perhitungan dapat di download disini

Some NPV resources

Sunday, February 10, 2008

Microsoft Excel Menu Commands

Menu commands

The menus in Excel 2000 are similar to menus in other Windows applications. However, as with all the Microsoft Office 2000 products there is a small difference from earlier versions: when you open a menu item an abbreviated version is displayed (Figure 2.)

Figure 2

Getting Started with Excel 3


Figure 3

The menu shows the commonly used and the most recently used commands. The entire menu is displayed if you click on the down arrow at the bottom of the menu. If your version of Excel is so configured, the full menu will also appear after a short delay. To configure Excel, either use the command Tools|Customize or right click on the menu bar and select the Customize item. In either case, the Customize dialog box is opened. If you move to the Option tag, the dialog box resembles Figure 3. To have all the commands displayed, clear the check mark from the Menus show recently used commands first box. Beaware that this action will affect other Microsoft Office 2000 application on your PC.

Menu commands may be accessed by clicking on the required item. Alternatively, you may hold down the A key and press the key corresponding to the underscored letter in the menu item. Thus the File menu is opened with A+F. A third method is available for other commands. If you open the File menu you will see to the right of the Save item the shortcut CTRL+S. This means that the key commination C+S will save the current file – there is no need to open the File menu for this to work. The shortcuts for copy and paste (C+C and C+V) are very useful to know.

Student resources for Quantitative Approaches in Business Studies

Student resources
Excel supplement
The Excel supplement is a tutorial for Microsoft Excel. It was written by Bernard V Liengme specially as a supplement to Quantitative Approaches in Business Studies by Clare Morris.

The table below explains how the units of the tutorial link to the chapters of Quantitative Approaches in Business Studies. The student is advised to read the first two units carefully. The other units may be read in any order.

The units are in Adobe Acrobat format (PDF). The Adobe Acrobat Reader is available FREE from Adobe Systems Incorporated. The workbooks named below are in Excel 97/2000 format. Right-click on any file and choose Save As to save the file to your hard disk.

Tutorial Units Quantitative Approaches in Business Studies Chapters
1 Getting Started with Microsoft Excel 2 Spreadsheets and other computer-based resources
2 Formulas and Functions 2 Spreadsheets and other computer-based resources
3 Solving Equations 1 Tools of the Trade
19 Linear Programming
4 Creating Charts 5 Presenting the Figures
5 Regression Analysis 13 Looking for Connections
14 Spotting the Relationship
15 Multiple Regression
6 Financial Calculations 18 Allowing for Interest
7 Descriptive Statistics
Workbook: STATISTICS1
6 Summarising the Figures
8 Statistical Distributions
Workbooks: PROBABILITY, NORMALDISTA, NORMALDISTB & NORMALDISTC
9 Patterns of Probability
9 Hypothesis Testing
Workbooks: HYPOTHESIS and CHISQUARED
10 Estimating from Samples
11 Checking a Theory

Every effort has been made to be accurate but if you believe you have found an error please let the author of the supplement, Bernard Liengme, know. As stated above, the workbooks are in Excel 97/2000 format; files in Excel 5/95 format are available from the author upon request. The author will be pleased to answer questions on Excel but please make them clear and specific.

Bernard V Liengme



Copyright © 1995-2008, Pearson Education, Inc. Legal and Privacy Terms

Getting Started with Microsoft Excel- The Workspace

The Workspace

Figure 1 shows the Microsoft Excel 2000 window. Yours may not be exactly the same

because the user can customize the window. The main parts of the window are:

  • Starting at the top we have the Title bar. When Excel is started a new workbook is opened with the name Book1.
  • Below the title bar is the Menu bar. You can issue commands from the menu bar including such actions as saving the data to a file, printing a worksheet, changing the appearance of some text, etc. As with all Windows applications, menu commands may be executed by clicking an item or by typing the underscored letter while holding down the A key.
  • Next come the Toolbars which provide a way of accessing some of the most used commands. The toolbars contain a subset of the complete set of menu commands. There are many toolbars but generally we have only two displayed: the Standard and the Formatting toolbars. By default, Excel 2000 displays the two docked together. We explain later how to separate them. You can specify which toolbars are visible with the menu command View|Toolbars. If you let the mouse pointer linger over a tool icon, Excel will display a tooltip. This makes it easy to learn the purpose of each tool.
  • The Formula bar displays the current cell’s address in the Name box and either the value or the formula in that cell.
  • The Worksheet window is the main working area. The space is ruled horizontally and vertically by gridlines, dividing the space into rows and columns. The smallest unit of space, where a row and a column intersect, is called a cell. At the top of the worksheet are the 256 column headings starting with A and ending with IV. To the left are the row headings numbered 1 to 65536 (or 16384 in versions prior to Excel 97). The letters (A, B, etc) at the top of the worksheet window are the column headers and the numbers to the left are the row headers.
  • At the bottom of the worksheet window are the sheet tabs. A workbook is made up of worksheets and, optionally, chart sheets. Excel 2000 opens a new workbook with three empty worksheets.
  • Finally at the bottom of the window is the Status bar. To the left is the message area. Most of the time this displays the word Ready. When you begin to enter something in a cell it displays Enter to remind you to complete the entry. At other times it may display Edit. To the right are some sculptured boxes called the Keyboard indicators. Press the c key a few times and watch the text “CAPS” appear and disappear.

2 Getting Started with Excel

Figure 1

The active cell is the cell with a border around it. To move to another cell and make it active, (a) use the keyboard arrow keys; (b) use the T key or the combination of S+T; or (c) simply click the mouse on the required cell. A quick way to return to cell A1 is the combination C+h.

Sources: Bernard V Liengme specially as a supplement to Quantitative Approaches in Business Studies by Clare Morris.

Saturday, February 9, 2008

Quantitative Research

Quantitative research is the systematic scientific investigation of properties and phenomena and their relationships. The objective of quantitative research is to develop and employ mathematical models, theories and/or hypotheses pertaining to natural phenomena. The process of measurement is central to quantitative research because it provides the fundamental connection between empirical observation and mathematical expression of quantitative relationships.

Quantitative research is widely used in both the natural sciences and social sciences, from physics and biology to sociology and journalism. It is also used as a way to research different aspects of education. The term quantitative research is most often used in the social sciences in contrast to qualitative research.

Quantitative research is generally approached using scientific methods, which include:

  • The generation of models, theories and hypotheses
  • The development of instruments and methods for measurement
  • Experimental control and manipulation of variables
  • Collection of empirical data
  • Modeling and analysis of data
  • Evaluation of results

Quantitative research is often an iterative process whereby evidence is evaluated, theories and hypotheses are refined, technical advances are made, and so on. Virtually all research in physics is quantitative whereas research in other scientific disciplines, such as taxonomy and anatomy, may involve a combination of quantitative and other analytic approaches and methods.

In the social sciences particularly, quantitative research is often contrasted with qualitative research which is the examination, analysis and interpretation of observations for the purpose of discovering underlying meanings and patterns of relationships, including classifications of types of phenomena and entities, in a manner that does not involve mathematical models. Approaches to quantitative psychology were first modelled on quantitative approaches in the physical sciences by Gustav Fechner in his work on psychophysics, which built on the work of Ernst Heinrich Weber. Although a distinction is commonly drawn between qualitative and quantitative aspects of scientific investigation, it has been argued that the two go hand in hand. For example, based on analysis of the history of science, Kuhn (1961, p. 162) concludes that “large amounts of qualitative work have usually been prerequisite to fruitful quantification in the physical sciences”. Qualitative research is often used to gain a general sense of phenomena and to form theories that can be tested using further quantitative research. For instance, in the social sciences qualitative research methods are often used to gain better understanding of such things as intentionality (from the speech response of the researchee) and meaning (why did this person/group say something and what did it mean to them?).

Although quantitative investigation of the world has existed since people first began to record events or objects that had been counted, the modern idea of quantitative processes have their roots in Auguste Comte’s positivist framework..

Statistics in quantitative research

Statistics is the most widely used branch of mathematics in quantitative research outside of the physical sciences, and also finds applications within the physical sciences, such as in statistical mechanics. Statistical methods are used extensively within fields such as economics, social sciences and biology. Quantitative research using statistical methods typically begins with the collection of data based on a theory or hypothesis, followed by the application of descriptive or inferential statistical methods. Causal relationships are studied by manipulating factors thought to influence the phenomena of interest while controlling other variables relevant to the experimental outcomes. In the field of health, for example, researchers might measure and study the relationship between dietary intake and measurable physiological effects such as weight loss, controlling for other key variables such as exercise. Quantitatively based opinion surveys are widely used in the media, with statistics such as the proportion of respondents in favor of a position commonly reported. In opinion surveys, respondents are asked a set of structured questions and their responses are tabulated. In the field of climate science, researchers compile and compare statistics such as temperature or atmospheric concentrations of carbon dioxide.

Empirical relationships and associations are also frequently studied by using some form of General linear model, non-linear model, or by using factor analysis. A fundamental principle in quantitative research is that correlation does not imply causation. This principle follows from the fact that it is always possible a spurious relationship exists for variables between which covariance is found in some degree. Associations may be examined between any combination of continuous and categorical variables using methods of statistics.

Measurement in quantitative research

Views regarding the role of measurement in quantitative research are somewhat divergent. Measurement is often regarded as being only a means by which observations are expressed numerically in order to investigate causal relations or associations. However, it has been argued that measurement often plays a more important role in quantitative research. For example, Thomas Kuhn (1961) argued that results which appear anomalous in the context of accepted theory potentially lead to the genesis of a search for a new, natural phenomenon. He believed that such anomalies are most striking when encountered during the process of obtaining measurements, as reflected in the following observations regarding the function of measurement in science:

When measurement departs from theory, it is likely to yield mere numbers, and their very neutrality makes them particularly sterile as a source of remedial suggestions. But numbers register the departure from theory with an authority and finesse that no qualitative technique can duplicate, and that departure is often enough to start a search (Kuhn, 1961, p. 180).

In classical physics, the theory and definitions which underpin measurement are generally deterministic in nature. In contrast, probabilistic measurement models known as the Rasch model and Item response theory models are generally employed in the social sciences. Psychometrics is the field of study concerned with the theory and technique for measuring social and psychological attributes and phenomena. This field is central to much quantitative research that is undertaken within the social sciences.

Quantitative research may involve the use of proxies as stand-ins for other quantities that cannot be directly measured. Tree-ring width, for example, is considered a reliable proxy of ambient environmental conditions such as the warmth of growing seasons or amount of rainfall. Although scientists cannot directly measure the temperature of past years, tree-ring width and other climate proxies have been used to provide a semi-quantitative record of average temperature in the Northern Hemisphere back to 1000 A.D. When used in this way, the proxy record (tree ring width, say) only reconstructs a certain amount of the variance of the original record. The proxy may be calibrated (for example, during the period of the instrumental record) to determine how much variation is captured, including whether both short and long term variation is revealed. In the case of tree-ring width, different species in different places may show more or less sensitivity to, say, rainfall or temperature: when reconstructing a temperature record there is considerable skill in selecting proxies that are well correlated with the desired variable.

Quantitative methods

Quantitative methods are research techniques that are used to gather quantitative data - information dealing with numbers and anything that is measurable. Statistics, tables and graphs, are often used to present the results of these methods. They are therefore to be distinguished from qualitative methods.

In most physical and biological sciences, the use of either quantitative or qualitative methods is uncontroversial, and each is used when appropriate. In the social sciences, particularly in sociology, social anthropology and psychology, the use of one or other type of method has become a matter of controversy and even ideology, with particular schools of thought within each discipline favouring one type of method and pouring scorn on to the other. Advocates of quantitative methods argue that only by using such methods can the social sciences become truly scientific; advocates of qualitative methods argue that quantitative methods tend to obscure the reality of the social phenomena under study because they underestimate or neglect the non-measurable factors, which may be the most important. The modern tendency (and in reality the majority tendency throughout the history of social science) is to use eclectic approaches. Quantitative methods might be used with a global qualitative frame. Qualitative methods might be used to understand the meaning of the numbers produced by quantitative methods. Using quantitative methods, it is possible to give precise and testable expression to qualitative ideas. This combination of quantitative and qualitative data gathering is often referred to as mixed-methods research.

Examples of quantitative research

  • Research that consists of the percentage amounts of all the elements that make up Earth’s atmosphere
  • Survey that concludes that the average patient has to wait two hours in the waiting room of a certain doctor before being selected.
  • An experiment in which group x was given two tablets of Aspirin a day and Group y was given two tablets of a placebo a day where each participant is randomly assigned to one or other of the groups.

The numerical factors such as two tablets, percent of elements and the time of waiting make the situations and results quantitative.

Features of Qualitative & Quantitative Research

Qualitative

Quantitative

“All research ultimately has
a qualitative grounding”
- Donald Campbell

“There’s no such thing as qualitative data.
Everything is either 1 or 0″
- Fred Kerlinger

The aim is a complete, detailed description.

The aim is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

Researcher may only know roughly in advance what he/she is looking for.

Researcher knows clearly in advance what he/she is looking for.

Recommended during earlier phases of research projects.

Recommended during latter phases of research projects.

The design emerges as the study unfolds.

All aspects of the study are carefully designed before data is collected.

Researcher is the data gathering instrument.

Researcher uses tools, such as questionnaires or equipment to collect numerical data.

Data is in the form of words, pictures or objects.

Data is in the form of numbers and statistics.

Subjective - individuals’ interpretation of events is important ,e.g., uses participant observation, in-depth interviews etc.

Objective – seeks precise measurement & analysis of target concepts, e.g., uses surveys, questionnaires etc.

Qualitative data is more ‘rich’, time consuming, and less able to be generalized.

Quantitative data is more efficient, able to test hypotheses, but may miss contextual detail.

Researcher tends to become subjectively immersed in the subject matter.

Researcher tends to remain objectively separated from the subject matter.

(the two quotes are from Miles & Huberman (1994, p. 40). Qualitative Data Analysis)

Main Points

  • Qualitative research involves analysis of data such as words (e.g., from interviews), pictures (e.g., video), or objects (e.g., an artifact).

  • Quantitative research involves analysis of numerical data.

  • The strengths and weaknesses of qualitative and quantitative research are a perennial, hot debate, especially in the social sciences. The issues invoke classic ‘paradigm war’.

  • The personality / thinking style of the researcher and/or the culture of the organization is under-recognized as a key factor in preferred choice of methods.

  • Overly focusing on the debate of “qualitative versus quantitative” frames the methods in opposition. It is important to focus also on how the techniques can be integrated, such as in mixed methods research. More good can come of social science researchers developing skills in both realms than debating which method is superior.

  • source: James Neill

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