ISYE 6501 FINAL EXAM QUESTIONS
WITH 100% CORRECT ANSWERS
Backward Elimination - Answer-We start with a model that includes all factors and at
each step, we find the worst factor and remove it from the model. We continue until
there's no factor bad enough to remove, and the model doesn't have any more factors
than we want.
Stepwise Regression - Answer-Multiple different forms, but essentially a combination of
forward selection and backwards elimination. Since in each step these models look at
only the best current option and don't take future possibilities into account it is known as
the Greedy Algorithm
Lasso Approach - Answer-We add a constraint to the standard regression equation. The
goal is still to minimize SSE given the regression a budget t to use on coefficients.
It'll use that budget on the most important coefficients which means all the rest of the
factors will have zero coefficient and so those factors won't be part of the model.
Elastic Net - Answer-Elastic net is effectively a combination of LASSO and Ridge
Regressions that trades some bias in order to reduce variance and ultimately reduce
total prediction error. Constrains a combination of the absolute value of the coefficients
and their squares.
Elastic Net Pros/Cons - Answer-Pros: Variable selection benefits of LASSO
Predictive Benefits of Ridge Regression
Cons: Arbitrarily rules out some correlated variables
Underestimate coefficients of very predictive variables
A/B Testing - Answer-Analytic method used to pick the best out of several alternatives.
Best used when data can be collected quickly, from a representative population, and the
amount of data is small relative to the whole population.
Factorial Design Tests - Answer-Design of experiment method used to test a multitude
of combinations. E.g 2 fonts x 2 wordings x 2 backgrounds to compare efficacy
multi-armed bandit - Answer-Design of experiment approach that starts with no
information and k alternatives. Over time, while performing tests, the probability of which
alternative is best is updated and we become more likely to chose the better
alternatives in testing. This approach helps balance exploration vs exploitation so less
value is lost testing suboptimal alternatives.
Bernoulli Distribution - Answer--a distribution of a single Binary event, has two possible
outcomes where the positive is p and the negative is 1-p
, Binomial Distribution - Answer-Distribution of the possible number of successful
outcomes in a given number of trials in each of which there is the same probability of
success. Binomial distribution converges to a normal distribution.
Geometric Distribution - Answer-The number of Bernoulli trials until the first success
occurs. Such as how many times can you hit a window before it breaks. Can also be
used to answer whether a series of trials are actually independent from one another.
Poisson Distribution - Answer-Probability distribution good for modeling arrivals per unit
of time. Gives the probability that x people do arrive given the average arrival rate
lambda. Assumes arrivals are independent of one another and have the same
distribution. Time between arrivals follows exponential distribution.
Exponential Distribution - Answer-A probability distribution associated with the time
between arrivals
Weibull Distribution - Answer-A probability distribution that is often used to model the
amount of time it takes for something to fail. Similar to geometric, except geometric
measures trials whereas this measures time. For example how long until a tire blows.
can model situations where failure rate decreases or increases over time.
Deterministic Simulations - Answer-Simulations that never vary. Given the same inputs
the outputs will always be the same
Stochastic Simulations - Answer-Simulation that includes some randomness. Therefor
for the same inputs the outputs may vary
Continuous Time Simulations - Answer-Simulations where changes happen
continuously not discretely, such as chemical reactions and propagation of diseases.
Discrete event simulation - Answer-A simulation method that describes how a system
evolves over time by using events that occur at discrete points in time. Call center
simulations are a good example.
Discrete event stochastic simulation - Answer-Simulation technique used when systems
have high variability and you wish to understand the variance as well as the averages.
Prescriptive Simulation - Answer-Using simulation to answer questions for what a
decision maker should do, and how changing parameters change the expected
outcomes.
Markov Chains - Answer-Mathematical system that experiences transitions from one
state to another according to certain probabilistic rules. The defining characteristic of a
Markov chain is that no matter how the process arrived at its present state, the possible
future states are fixed. They are memoryless.
WITH 100% CORRECT ANSWERS
Backward Elimination - Answer-We start with a model that includes all factors and at
each step, we find the worst factor and remove it from the model. We continue until
there's no factor bad enough to remove, and the model doesn't have any more factors
than we want.
Stepwise Regression - Answer-Multiple different forms, but essentially a combination of
forward selection and backwards elimination. Since in each step these models look at
only the best current option and don't take future possibilities into account it is known as
the Greedy Algorithm
Lasso Approach - Answer-We add a constraint to the standard regression equation. The
goal is still to minimize SSE given the regression a budget t to use on coefficients.
It'll use that budget on the most important coefficients which means all the rest of the
factors will have zero coefficient and so those factors won't be part of the model.
Elastic Net - Answer-Elastic net is effectively a combination of LASSO and Ridge
Regressions that trades some bias in order to reduce variance and ultimately reduce
total prediction error. Constrains a combination of the absolute value of the coefficients
and their squares.
Elastic Net Pros/Cons - Answer-Pros: Variable selection benefits of LASSO
Predictive Benefits of Ridge Regression
Cons: Arbitrarily rules out some correlated variables
Underestimate coefficients of very predictive variables
A/B Testing - Answer-Analytic method used to pick the best out of several alternatives.
Best used when data can be collected quickly, from a representative population, and the
amount of data is small relative to the whole population.
Factorial Design Tests - Answer-Design of experiment method used to test a multitude
of combinations. E.g 2 fonts x 2 wordings x 2 backgrounds to compare efficacy
multi-armed bandit - Answer-Design of experiment approach that starts with no
information and k alternatives. Over time, while performing tests, the probability of which
alternative is best is updated and we become more likely to chose the better
alternatives in testing. This approach helps balance exploration vs exploitation so less
value is lost testing suboptimal alternatives.
Bernoulli Distribution - Answer--a distribution of a single Binary event, has two possible
outcomes where the positive is p and the negative is 1-p
, Binomial Distribution - Answer-Distribution of the possible number of successful
outcomes in a given number of trials in each of which there is the same probability of
success. Binomial distribution converges to a normal distribution.
Geometric Distribution - Answer-The number of Bernoulli trials until the first success
occurs. Such as how many times can you hit a window before it breaks. Can also be
used to answer whether a series of trials are actually independent from one another.
Poisson Distribution - Answer-Probability distribution good for modeling arrivals per unit
of time. Gives the probability that x people do arrive given the average arrival rate
lambda. Assumes arrivals are independent of one another and have the same
distribution. Time between arrivals follows exponential distribution.
Exponential Distribution - Answer-A probability distribution associated with the time
between arrivals
Weibull Distribution - Answer-A probability distribution that is often used to model the
amount of time it takes for something to fail. Similar to geometric, except geometric
measures trials whereas this measures time. For example how long until a tire blows.
can model situations where failure rate decreases or increases over time.
Deterministic Simulations - Answer-Simulations that never vary. Given the same inputs
the outputs will always be the same
Stochastic Simulations - Answer-Simulation that includes some randomness. Therefor
for the same inputs the outputs may vary
Continuous Time Simulations - Answer-Simulations where changes happen
continuously not discretely, such as chemical reactions and propagation of diseases.
Discrete event simulation - Answer-A simulation method that describes how a system
evolves over time by using events that occur at discrete points in time. Call center
simulations are a good example.
Discrete event stochastic simulation - Answer-Simulation technique used when systems
have high variability and you wish to understand the variance as well as the averages.
Prescriptive Simulation - Answer-Using simulation to answer questions for what a
decision maker should do, and how changing parameters change the expected
outcomes.
Markov Chains - Answer-Mathematical system that experiences transitions from one
state to another according to certain probabilistic rules. The defining characteristic of a
Markov chain is that no matter how the process arrived at its present state, the possible
future states are fixed. They are memoryless.
