DDMA Level II

Quantitative Modelling Skills flashcards

Read the question, say the answer to yourself, then turn the card to check. The first 10 of 50 cards are free; the rest come with the subject.

Card 1 of 50

Jump to a card

Complete Flashcard Reference

Review every card in this deck. Open any card to reveal its answer. The first 10 are free; the other 40 come with the subject.

What is a model, and what makes a model quantitative?

A model is a simplified representation of a real system, built to understand, predict or optimise its behaviour. A quantitative model is expressed in mathematical terms, using numbers, variables and equations rather than qualitative description.

How does a linear model differ from a probabilistic (stochastic) model?

A linear model represents a relationship as a straight-line function of the inputs and gives one deterministic answer. A probabilistic model incorporates randomness explicitly and produces a distribution of possible outcomes rather than one fixed answer.

What does regression analysis estimate, and what are its three forms?

The relationship between a dependent variable and one or more independent (predictor) variables. Linear regression: a straight line, one predictor. Multiple linear regression: two or more predictors. Non-linear regression: a relationship that does not follow a straight line, for example exponential or polynomial.

In the least-squares line y = a + bx, how are the slope b and the intercept a calculated?

b = (nΣXY - ΣXΣY) / (nΣX² - (ΣX)²) a = mean of Y - b × mean of X The line minimises the sum of squared differences between the observed and predicted values.

What are the three components of a constrained optimisation (linear programming) model?

Decision variables: the quantities being decided, for example how many units of two products to produce. Objective function: the linear expression to be maximised or minimised, for example total profit. Constraints: the linear limits the decision variables must satisfy, including non-negativity.

What are the four assumptions of a linear programming model?

Proportionality: doubling a decision variable doubles its contribution. Additivity: contributions from different variables simply add up. Divisibility: variables can take fractional values unless restricted to whole numbers. Certainty: all coefficients are known exactly.

What is the difference between simulation and modelling?

Simulation imitates the operation of a real system over time, to study its behaviour without building or disrupting the real thing. Modelling builds the representation (the model) that a simulation then runs against.

What is the difference between verifying and validating a simulation model?

Verification checks the model is built correctly: it does what it was designed to do ('did we build the model right'). Validation checks it accurately represents the real system ('did we build the right model'). A model can be verified but still invalid if it was designed on a flawed understanding of the real system.

What does Monte Carlo (risk analysis) simulation do?

It repeatedly samples random inputs according to their probability distributions to see the range of possible outcomes. It uses repeated random sampling rather than modelling time directly.

What does input-output analysis model, and where is it common?

How the outputs of one part of a system become inputs to another. It is common in economic sector analysis.

What are the steps of the modelling methodology a quantitative model is built through?