These notes provide a thorough overview of quantitative analysis techniques used in data evaluation and decision-making. Topics include statistical methods, regression analysis, probability, hypothesis testing, and data modeling. The material covers essential concepts such as descriptive and infere...
1. Basic mathematical techniques
Functions
- Functions, equations and graphs: Linear, quadratic, cubic, exponential and logarithmic
- Application of mathematical functions in solving business problems
Matrix algebra
- Types and operations (addition, subtraction, multiplication, transposition, and inversion)
- Application of matrices: statistical modelling, Markov analysis, input- output analysis and
general applications
Calculus
- Differentiation
• Rules of differentiation (general rule, chain, product, quotient)
• Differentiation of exponential and logarithmic functions
• Higher order derivatives: Turning points (maxima and minima)
• Ordinary derivatives and their applications
• Partial derivatives and their applications
- Integration
• Rules of integration
• Applications of integration to business problems
2. Probability
Set theory
- Types of sets
- Set description: Enumeration and descriptive properties of sets
- Operations of sets: Union, intersection, complement and difference
- Venn diagram
Probability theory and distribution Probability theory
- Definitions: Event, outcome, experiment, sample space
- Types of events: Elementary, compound, dependent, independent, mutually exclusive,
exhaustive, mutually inclusive
- Laws of probability: Additive and multiplicative rules - Baye's Theorem
- Probability trees
- Expected value, variance, standard deviation and coefficient of variation using frequency and
probability
Probability distributions
- Discrete and continuous probability distributions (uniform, normal, binomial, poisson and
exponential)
- Application of probability to business problems
3. Hypothesis testing and estimation
- Hypothesis tests on the mean (when population standard deviation is unknown)
- Hypothesis tests on proportions
- Hypothesis tests on the difference between means (independent samples)
- Hypothesis tests on the difference between means (matched pairs)
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, QUANTITATIVE ANALYSIS
- Hypothesis tests on the difference between two proportions
4. Correlation and regression analysis
Correlation analysis
• Scatter diagrams
• Measures of correlation -product moment and rank correlation coefficients (Pearson and
Spearman)
Regression analysis
• Assumptions of linear regression analysis
• Coefficient of determination, standard error of the estimate, standard error of the slope, t
and F statistics
• Computer output of linear regression
• T-ratios and confidence interval of the coefficients
• Analysis of Variances (ANOVA)
• Simple and multiple linear regression analysis
5. Time series
- Definition of time series
- Components of time series (circular, seasonal, cyclical, irregular/ random, trend)
- Application of time series
- Methods of fitting trend: free hand, semi-averages, moving averages, least squares methods
- Models- additive and multiplicative models
- Measurement of seasonal variation using additive and multiplicative models
- Forecasting time series value using moving averages, ordinary least squares method and
exponential smoothing
- Comparison and application of forecasts for different techniques
6. Linear programming
- Definition of decision variables, objective function and constraints
- Assumptions of linear programming
- Solving linear programming using graphical method
- Solving linear programming using simplex method
- Sensitivity analysis and economic meaning of shadow prices in business situations
- Interpretation of computer assisted solutions
- Transportation and assignment problems
7. Decision theory
- Decision process
- Decision making environment - deterministic situation (certainty), analytical hierarchical
approach (AHA), risk and uncertainty, stochastic situations (risk), situations of uncertainty
- Decision making under uncertainty - maximin, maximax, minimax regret, Hurwicz decision
rule, Laplace decision rule
- Decision making under risk - expected monetary value, expected opportunity loss,
minimising risk using coefficient of variation, expected value of perfect information
- Decision trees - sequential decision, expected value of sample information
- Limitations of expected monetary value criteria
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, QUANTITATIVE ANALYSIS
8. Game theory
- Assumptions of game theory
- Zero sum games
- Pure strategy games (saddle point)
- Mixed strategy games (joint probability approach)
- Dominance, graphical reduction of a game
- Value of the game.
- Non zero sum games
- Limitations of game theory
9. Network planning and analysis
- Basic concepts - network, activity, event
- Activity sequencing and network diagram
- Critical path analysis (CPA)
- Float and its importance
- Crashing of activity/project completion time
- Project evaluation and review technique (PERT)
- Resource scheduling (levelling) and Gantt charts
- Limitations and advantages of CPA and PERT
10. Queuing theory
- Components/elements of a queue: arrival rate, service rate, departure, customer behaviour,
service discipline,' finite and infinite queues, traffic intensity
- Elementary single server queuing systems
- Finite capacity queuing systems
- Multiple server queues
11. Simulation
- Types of simulation
- Variables in a simulation model
- Construction of a simulation model
- Monte Carlo simulation
- Random numbers selection
- Simple queuing simulation: Single server, single channel "first come first served" (FCFS)
model
- Application of simulation models
12. Current developments
- Role of advancement in information technology in solving quantitative analysis problems
13. Emerging issues and trends
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