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**INSTRUCTOR INTRODUCTIOON**

DR. MUHAMMAD IFTIKHAR UL HUSNAIN ASSISTANT PROFESOR ,DEPARTMENT OF MANAGEMENT SCIENCES COMSATS, ISLAMABAD SINCE 2012 LECTURER IN ECONOMICS PUNJAB HIGHER EDUCATION DEPARTMENT AREAS OF INTERST MICRO ECONOMICS MACRO ECONOMICS MATHEMATICAL ECONOMICS STATISTICS PUBLIC FINANCE

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**Course: MGT 605 Quantitative Techniques**

Instructor: Dr. Muhammad Iftikhar ul Husnain Course overview Definition of Quantitative Techniques Nature and Scope of Quantitative Techniques Data Sampling Simple regression Multiple regression Multicollinearity Auto correlation Hetrosekasdicity Dummy variables. Logit model Probit model Panel data

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**Quantitative Methods for Business by Anderson Sweeny and Williams**

Course Overview …. Books Quantitative Methods for Business by Anderson Sweeny and Williams Quantitative analysis for management by Render, Stair, Hanna Johnston, J. and J. DiNardo (n.d). Econometric Methods (4th Eds.) The McGraw Hill Companies. Maddala, G. S. (1992). Introduction to Econometrics, (2nd Edition), Macmillan Publishing Company, New York. J. Wooldridge, Introductory Econometrics, 4th Edition, South Western College Press

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**Introduction Back Ground Definition**

Quantitative tools have been used for thousands of years (Taylor and Frederick) Quantitative analysis can be applied to a wide variety of problems acrossdescipline It’s not enough to just know the mathematics of a technique One must understand the specific applicability of the technique, its limitations, and its assumptions Definition Quantitative Technique: Any procedure, formulae, instrument, model that helps in analyzing any hypothesis, theory, statement is called quantitative techniques. In Quantitative analysis, we may be interested in predicting Y with X, or with the casual effect of X on Y. Quantitative analysis is a scientific approach to decision making whereby raw data are processed and manipulated resulting in meaningful information. Raw data--application of QT----Meaningful information

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**Qualitative versus quantitative analysis**

It gives a general and unspecified view Focus on words Subjective Case studies fewer respondents No standardized data analysis Explores impact (why) It gives clear, specific and numerical prediction of the problem Focus on number Objective Statistical Analysis higher number of respondents Standardized data analysis Suggests/quantify the impact

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**Quantitative vs. Qualitative factors**

Quantitative factors Might be different investment levels, interest rates, inventory levels, demand, or labor cost Qualitative factors such as the weather, state and federal legislation, and technology breakthroughs should also be considered. Political instability Information may be difficult to quantify but can affect the decision-making process Why Study Quantitative Techniques In your everyday life, it will help you make sense of what to heed and what to ignore in statistical information provided in news reports, surveys, political campaigns, advertisements From house to stock market

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**Advantages of Quantitative Analysis**

1- It can accurately represent reality 2- It can help a decision maker formulate problems 3- It can give us insight and information 4- It can save time and money in decision making and problem solving 5- It may be the only way to solve large or complex problems in a timely fashion 6- It can be used to communicate problems and solutions to others 7- it can help in forecasting the future on the basis of available information

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**How the Quantitative Approach Works**

It is a systematic process 1- Define the problem It is a starting point Develop a clear and concise statement. Most important and difficult step selecting the right problems is very important Specific and measurable objectives may have to be developed In the real world, quantitative analysis models can be complex, expensive and time consuming.

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**2- Developing a Mathematical Model**

What a Model is? A model is simply a set of mathematical equations. A model is a mathematical representation of a theory/reality. Single equation model If a model has only one equation it is called a single-equation model. Multiple-equation model If it has more than one equation Models generally contain variables, and parameters Parameters are unknown quantities but there value is fixed.

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**How to Develop a Quantitative Model….**

An important part of the quantitative analysis approach Mathematical Models have two major types. Mathematical models that do not involve risk are called deterministic models. We know all the values used in the model with complete certainty. Mathematical models that involve risk, chance, or uncertainty are called probabilistic models In this course our concern is with the probabilistic model. Example: Demand function Profit function

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**3- Speciﬁcation of the probabilistic/econometric Model**

Mathematical model assumes that there is an exact relationship between the variables. However it is not of much interest in social sciences But relationships between variables are generally inexact in social sciences. The introduction of error term It captures the effect of unquantifiable forces.

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**4- Significance of the stochastic term Ui**

Error term is proxy for all the omitted variables but collectively affect Y. - Why not introduce all the variable explicitly? Unavailability of data Core versus peripheral variables- joint effect of many variable is so small that for practical consideration and cost effectiveness it does not pay to introduce them explicitly in the model. Randomness in Human Behavior Poor Proxy Variable Principle of parsimony Wrong functional form

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4- Acquiring data To estimate the Statistical model given/ obtain the numerical values of β1 and β2 , we need data. Data may come from a variety of sources such as company reports, company documents, interviews. The quality data is extremely important. The reliability of results is directly proportional to quality of data. Data collecting is an art. Data is collected only on the required variables.

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**5. Estimation of the Statistical Model**

To estimate the values of the parameters we need some techniques. Common techniques are Solving equations Trial and error – trying various approaches and picking the best result

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**6- Hypothesis Testing/testing the solution**

Model should be tested for accuracy before analysis and implementation. Whether the results are according to the theory . Results should be logical, consistent, and represent the real situation. We use statistical inference (hypothesis testing) to know the significance of the parameter.

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**7- Forecasting or Prediction**

If the chosen model does not refute the hypothesis or theory under consideration, we may use it to predict the future value(s) of the dependent variable Y on the basis of known variables. 8- implementing the results/ policy Implementation can be very difficult People can resist changes Many quantitative analysis efforts have failed because a good, workable solution was not properly implemented

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**Possible Problems in the Quantitative Analysis Approach**

Problems are not easily identified Conflicting viewpoints-linear or non linear relationship Beginning assumptions Fitting the textbook models Understanding the model Validity of data Hard-to-understand mathematics and statistics

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**Variables and their Types**

Ratio scale Two values of a variable say X1 and X2, (i)X1/X2 (ii)(X1-X2) (iii) X1≤ X2 and vice versa are meaningful quantities. Most economic variable are ratio scale. Interval Scale Satisfies last two properties. Distance b/w two time periods ( ) is meaningful. But 1990/2012 is senseless. Ordinal Scale Only it satisfies the third property of ratio scale. Grades, A,B,C,D. Upper, Middle, Lower. Example: Indifference curve in Economics Nominal Scale: None of the feature of ratio scale. Gender, male, female, marital status, single, married, divorced, unmarried simply denote categories

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Probability A probability is a numerical statement about the chance that an event will occur. Two basic rules regarding the probability 1- The probability, p, of any event is greater than or equal to 0 and less than or equal to ≤p≤1 A- 0 means that an event is never expected to occur b- 1 means that an event is always to occur. 2- The sum of the simple probabilities for all possible outcomes of an activity must be equal to 1. Examples: Quantity Demanded Number of days p=40/200 (.20) p=80/200 (.40) p=(50/200) (.25)

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**Types of probability Two different ways to determine the probability**

Objective p(event)= number of occurrence of the event /total number of events Examples: tossing of a fair coin- it is based on the previous logic. Subjective: logic and history are not appropriate. So subjectivity arises. Examples what is the probability that floods will come? What is the probability that depression will come in an economy? For this opinion polls are conducted and then probabilities are found.

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**Mutually exclusive and collectively exhaustive events**

Mutually exclusive events : If only one of the event can occur on any one trial. Collectively exhaustive events: They are said to be mutually exhaustive if the list include all the possible outcomes i.e. A U B= S. Not mutually exclusive The occurrence of one event does not restrict the occurrence of the other event. Examples: Drawing a 5 and drawing a diamond from a deck of cards- it can be both 5 and diamond

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**Adding mutually exclusive events**

We are interested in whether one event or second event will occur. When events are mutually exclusive the law of addition is simply as follows. P(event A or event B)= p(event A)+ p(event B) Drawing spade or drawing a club out of a deck card are mutually exclusive. 13/52+13/52=1/2 Venn diagram Addition of not mutually exclusive events. P(A or B)= P(A)+P(B)-P(A and B) Examples: In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student? P(girl or A)= P(girl)+ P(A)- P(girl and A)= 13/30+9/30-5/30=17/30

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**Some Basic Concepts in Mathematics**

Derivatives Definition Maxima Minima Rules of Derivatives 1- Constant function rule 2- Power function rule 3- Sum difference rule 4- Product rule 5- Quotient rule 6- Chain rule 7- Inverse function rule

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**Notation Dependent variable Independent variable**

Explained variable Explanatory variable Predictand Predictor Regressand Regressor Response Stimulus Endogenous Exogenous Outcome Covariate Controlled variable Control variable LHS RHS

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