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ISYE 6501 MIDTERM 2 EXAM NEWEST 2025 COMPLETE 100
QUESTIONS AND CORRECT DETAILED ANSWERS (VERIFIED
ANSWERS) |ALREADY GRADED A+
what does ridge regression do when 2 predictors are highly correlated? - ANSWER-have smaller non-zero coefficients for both predictors it may underestimated the effect of the factors What is LASSO Regression? - ANSWER-Adds a constraint (T) to the standard regression equation Want to choose coefficients that minimize the sum of squared errors but add the restriction that the sum of the coefficients can't be too large Use the budget (T) on the most important coefficients give other factors 0 as coefficients and removing them from the model What is elastic net regression? - ANSWER-Almost the same as LASSO, but restrain a combination of absolute value of coefficients and their squares looks like LASSO regression plus ridge regression What is ridge regression - ANSWER-elastic net with the absolute value term removed leads to better predictive models but doesn't do variable selection choose coefficients that minimize total error, like LASSO, but constraints on the coefficients are different
What is the difference in the constraints between ridge regression and LASSO regression? - ANSWER-in Lasso regression the constraint function is a sum of absolute values which leads to a function with the smallest amount of error having some coefficients that are 0 (think error ellipse intersecting with diamond shaped restraint function) in ridge regression the constraint function is sum of squared values which leads to a function with the smallest amount of error including all the coefficients (think error ellipse intersecting with circle shaped constraint function) What is the Bias Variance Trade off? - ANSWER-When you have high bias and low variance it leads to underfitting, less fit to real patterns and less fit to random patterns When you have low bias and high variance it leads to overfitting, more fit to real patterns and more fit to random patterns Underfit - ANSWER-The less fit the model is the fewer variables we use and the smaller the coefficients get every prediction by the model gets closer to constant term a0 regardless of the value of x removing variables and shrinking coefficients creates bias in the model - model misses/minimizes real patterns in the data underfitting real effects while eliminating variance from random effects 3 Main reasons to limit number of factors/variables in model - ANSWER-Overfitting - when number of factors is close to or larger than number of data points the model will fit too closely to random effects
yes - go to step 5
- fit model with current set of factors
- remove factors with high p value (typically p value above .05)
- fit model with final set of factors What is the process for backward selection stepwise regression? - ANSWER-1) start with all the factors
- find worst current factor
- is it bad enough (high enough p value typically above .15)? yes - remove it go back to step 2 no - go to step 4
- do we have too many factors yes - remove it go back to step 2 no - go to step 5
- remove factors with high p value (typically p value above .05)
- fit model with final set of factors what is the process for combination stepwise regression? - ANSWER-1) 1) start with 0 factors
- find best new factor
- is it good enough (low enough p value typically below .15)? yes - add factor go to step 4 no - go to step 7
- fit model with current set of factors
- remove factors with high p value (typically p value above .05)
- do we have enough factors? no - go back to step 2 yes - go to step 7
- remove factors with high p value (typically p value above .05)
- fit model with final set of factors What are some metrics besides p values that should be used to determine if a factor should be added - ANSWER-R-squared valued AIC BIC
What are quick methods of variable selection? - ANSWER-forward selection backward selection stepwise regression - most common what are the pros and cons of quick variable selection methods? - ANSWER-good for initial analysis can give variables with more fit to random patterns than you'd like and appear to have a better fit often doesn't perform as well when tested on other data what are the slower methods of variable selection? - ANSWER-Lasso Elastic net what are the pros and cons of slower variable selection methods? - ANSWER-slower to compute give better predictive models recommended to do unless just doing data exploration - then do greedy methods first and use these methods to build more refined model what are the advantages of elastic net? - ANSWER-variable selection benefits of Lasso
predictive benefits of ridge what are the disadvantages of elastic net? - ANSWER-arbitrarily rules out some correlated variables like lasso underestimates coefficients of very predictive variables like ridge regression What is the relationship between comparison and control? - ANSWER-when we choose a factor to compare data points on we need to make sure the data collectively the same in all other important factors What is a blocking factor - ANSWER-something that could create variation other than what we're studying What 3 things must be true to use A/B testing? - ANSWER-1) collect data quickly
- data sample must be representative of total population
- amount of data in sample must be small compared to the whole population What is factorial design? - ANSWER-if there are lost of combinations of factors to test you can use factorial design good to use before modeling and if possible before collecting data ANOVA - ANSWER-Analysis of variance, used in factorial design to test the importance of different factors
how to update the probabilities how to pick an alternative to test based on probabilities and/or expected values no simple rule for setting parameters what are some benefits of the multi-armed bandit problem? - ANSWER-help you learn faster on the fly create more value along the way Binomial distribution models - ANSWER-probability of getting x successes out of n independent identically distributed Bernoulli trials how many trials are needed before we get an answer of a certain type What are some questions you can answer using a Binomial distribution? - ANSWER-How many interviews until first job offer How many job offers made until someone accepts How many hits until a baseball bat breaks How many good units manufactured before a defective one? Geometric distribution models - ANSWER-how many Bernoulli trials until _____ happens?
probability of having x i.i.d Bernoulli(p) failures until first success? or probability of having x i.i.d Bernoulli(1-p) successes until first failure? Can compare data to geometric distribution to see if i.i.d is true i.i.d - ANSWER-independent and identically distributed What's an example of a question that can be answered by a geometric distribution? - ANSWER- how many hits until a baseball bat breaks? Poisson Distribution model - ANSWER-good at modeling random arrivals, lambda is the average number of arrivals in a time period f(x) gives the probability that x people arrive given average arrival rate lambda assumes arrivals are i.i.d Exponential Distribution Models - ANSWER-Relates to Poisson If arrivals are Poisson(lambda) the time between arrival (inter-arrival time) is exponential lambda distribution(lambda) inter-arrival-time is 1/lambda Weibull distribution models - ANSWER-modeling the amount of time it takes for something to fail, specifically the time between failures
Poisson distribution Markov chains memoryless - ANSWER-doesn't matter what the previous states were, the only thing that matters is what state we're in now What are 5 types of simulations? - ANSWER-1) Deterministic simulations
- Stochastic simulations
- Continuous-time simulations
- Discrete-event simulations
- Discrete-event stochastic simulations Deterministic simulations - ANSWER-Same inputs give the same outputs, no randomness (never very) Stochastic simulations - ANSWER-Use when system has randomness, get different outputs every time we run the model Generally more useful in analytics Continuous-time simulations - ANSWER-Model changes that are happening continuously
Example - chemical process, propagation of diseases Often modeled with differential equations Discrete-event simulations - ANSWER-System only changes at discrete time points Example: call center simulations - someone calls, worker finishes talking to someone Discrete-event stochastic simulations - ANSWER-Valuable when systems have high variability Using average values (like we might in an optimization model) isn't good enough Example - modeling a machine in a manufacturing process Example airport baggage simulation What is replication and why is it important - ANSWER-the number of runs of a simulation 1 replication = 1 data point and 1 data point may or may not be representative. What validation issues can you encounter when you're validating your simulation - ANSWER-if the real and simulated averages don't match if the real and simulated averages match but the real and simulated variances don't match
What are some uses for Markov chains - ANSWER-web search urban sprawl population dynamics disease propagation What are some common data problems? - ANSWER-missing data wrong data patterns in the missing or wrong data for data that is more likely to be missing... - ANSWER-there is bias in the values of the data that are missing 3 ways to deal with missing data - ANSWER-1) throw away
- use categorical variables to indicate missing data
- estimate missing values Pros & cons of throwing away missing data - ANSWER-Pros Not potentially introducing errors
Easy to implement Cons Don't want to lose too many data points Potential for censored or biased missing data Pros & cons of categorical variable method for missing data - ANSWER-If attribute is categorical just add extra category called 'missing' or similar Simple for quantitative variable make all missing values 0 and add new categorical variable to show if data is missing or not but can lead to bias if some data types more likely to be missing can use interaction variables to help with bias but basically creating 2 models, 1 for missing data in this variable and one for no missing data, like a tree with 1 branch Midrange value imputation method - ANSWER-simplest Find mean or median value (numeric) mode (categorical) and use value for each data point where the factors value is missing pros and cons of Midrange value imputation method - ANSWER-Pros Hedge against being too wrong Easy to compute Cons Biased imputation EX: people with high income less likely to answer survey
Crude oil shipment planning Server farm allocation (webpage optimization) Machine shop production GPS routing for cars Shortest route from my house to airport given traffic Army recruiting asset usage Professional sports draft priority determinations Worldwide oil delivery and routing scheduling Electricity generation accounting for weather impact on atmospheric effects 3 main components of optimization models - ANSWER-variables - decisions the optimization model will find the best value for constraints - restrictions on the decisions that can be made Objective function - measure of the quality of the solution Feasible solution - ANSWER-variable values that satisfy all the constraints Optimal solution - ANSWER-feasible solution with the best objective value
Examples of ways integer variables can be used to write special features of an optimization model - ANSWER-Fixed charges in an objective function Constraints to choose among options Constraints requiring same/opposite decisions If-then constraints Why are statistical based models like linear regression more widely used than optimization models - ANSWER-Statistical models you just need the data Optimization models are hard to build for the situation/ system you're modeling Requires learning and experience Not easily automated like regression Regression Optimization - ANSWER-Variables - coefficients Constraints - none Objective Function - minimize the squared error in the models estimate Lasso Optimization - ANSWER-Variables - coefficients Constraint - the sum of the absolute value of the variables must be less than or equal to T Objective Function - minimize the squared error in the models estimate
