Midterm Quiz 2 - GT Students and Verified MM Learners Introduction to Analytics Modeling

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GTx: ISYE6501x Introduction to Analytics Modeling Help khoi32 Course Midterm Quiz 2 - Spring 2020 Midterm Quiz 2 Midterm Quiz 2 - GT Students and Verified MM Learners Midter... m Quiz 2 - GT Students and Verified MM Learners 90 Minute Time Limit Instructions Work alone. Do not collaborate with or copy from anyone else. You may use any of the following resources: One sheet (both sides) of handwritten (not photocopied or scanned) notes If any question seems ambiguous, use the most reasonable interpretation (i.e. don't be like Calvin): Good Luck! This the beginning of Midterm Quiz 2. Please make sure that you submit all your answers before the time runs out. Once you submit an answer to a question, you cannot change it. There is no overall Submit button. Information for Question 1 There are five questions labeled "Question 1." Answer all five questions. For each of the following five questions, select the probability distribution that could best be used to model the described scenario. Each distribution might be used, zero, one, or more than one time in the five questions. Question 1 1.4/1.4 points (graded) Number of days in a year where the temperature is more than 3 degrees higher than forecast Binomial You have used 1 of 1 attempt Question 1 1.4/1.4 points (graded) Number of phone calls made by a telemarketer until one is answered Geometric You have used 1 of 1 attempt Question 1 1.4/1.4 points (graded) Time from the beginning of Fall until the first snowflake is seen Weibull You have used 1 of 1 attempt Question 1 1.4/1.4 points (graded) Time from when a house is put on the market until the first offer is received Weibull You have used 1 of 1 attempt Question 1 1.4/1.4 points (graded) Time from when a generator is turned on until it fails You have used 1 of 1 attempt Questions 2a, 2b 5.0/10.0 points (graded) Five classification models were built for predicting whether a neighborhood will soon see a large rise in home prices, based on public elementary school ratings and other factors. The training data set was missing the school rating variable for every new school (3% of the data points). Because ratings are unavailable for newly-opened schools, it is believed that locations that have recently experienced high population growth are more likely to have missing school rating data. Model 1 used imputation, filling in the missing data with the average school rating from the rest of the data. Model 2 used imputation, building a regression model to fill in the missing school rating data based on other variables. Model 3 used imputation, first building a classification model to estimate (based on other variables) whether a new school is likely to have been built as a result of recent population growth (or whether it has been built for another purpose, e.g. to replace a very old school), and then using that classification to select one of two regression models to fill in an estimate of the school rating; there are two different regression models (based on other variables), one for neighborhoods with new schools built due to population growth, and one for neighborhoods with new schools built for other reasons. Model 4 used a binary variable to identify locations with missing information. Model 5 used a categorical variable: first, a classification model was used to estimate whether a new school is likely to have been built as a result of recent population growth; and then each neighborhood was categorized as "data available", "missing, population growth", or "missing, other reason". a. If school ratings cannot be reasonably well-predicted from the other factors, and new schools built due to recent population growth cannot be reasonably well-classified using the other factors, which model would you recommend? b. In which of the following situations would you recommend using Model 5? [All predictions and classifications below are using the other factors.] You have used 1 of 1 attempt Answers are displayed within the problem Information for Question 3 In a diet problem (like we saw in the lessons and homework), let xi be the amount of food i in the solution (xi maximum amount that can be eaten of any food. >= 0), and let M be the Suppose we added new variables yi that are binary (i.e., they must be either 0 or 1): if food i is eaten in the solution, then it is part of the solution (yi = 1); otherwise yi = 0. There are five questions labeled "Question 3." Answer all five questions. For each of the following five questions, select the mathematical constraint that best corresponds to the English sentence. Each constraint might be used, zero, one, or more than one time in the five questions. Question 3 1.4/1.4 points (graded) Select the mathematical constraint that corresponds to the following English sentence: Either cheese sauce or peanut butter (or both) must be eaten with broccoli. You have used 1 of 1 attempt Question 3 1.4/1.4 points (graded) Select the mathematical constraint that corresponds to the following English sentence: Exactly one of peanut butter and cheese sauce must be eaten. You have used 1 of 1 attempt Question 3 1.4/1.4 points (graded) Select the mathematical constraint that corresponds to the following English sentence: Broccoli, cheese sauce, and peanut butter all can't be eaten together. You have used 1 of 1 attempt Question 3 1.4/1.4 points (graded) Select the mathematical constraint that corresponds to the following English sentence: No more than two of broccoli, cheese sauce, and peanut butter may be eaten. You have used 1 of 1 attempt Question 3 1.4/1.4 points (graded) Select the mathematical constraint that corresponds to the following English sentence: Either peanut butter or cheese sauce, but not both, must be eaten. You have used 1 of 1 attempt Question 4a 5.0/5.0 points (graded) A hospital emergency department (ED) has created a stochastic discrete-event simulation model of the ED, including patient arrivals, resource usage (rooms, doctors, etc.), and treatment duration. EDs are not first-come-first-served; a patient who arrives with a more-serious condition will be treated first, ahead of even long-waiting patients with less-serious conditions. When a patient comes in, the ED will run the simulation to quickly give the patient an estimate of the expected wait time before being treated. How many times does the ED need to run the simulation for each new patient (i.e., how many replications are needed)? You have used 1 of 1 attempt Information for Question 4b The figure above shows the average of the first x simulated wait times, as new replications ("runs") are run and added into the overall average. It is not showing the wait time just for each replication. For example, after x=101 replications, the wait time of the 101st replication is not necessarily 72, but the average of those 101 replications is about 72. Question 4b 5.0/5.0 points (graded) If the goal is to report the expected wait time to within +/- 2 minutes, what can you conclude from the figure above? Select all of the answers that are correct. You have used 1 of 1 attempt Question 4c 6.0/6.0 points (graded) Suppose it is discovered that simulated wait times are 25% higher than actual wait times, on average. What would you recommend that they do? You have used 1 of 1 attempt Information for Question 5 For each of the optimization problems below, select its most precise classification. In each model, x are the variables, all other letters (a,b,c) refer to known data, and the values of c are all positive. There are seven questions labeled "Question 5". Answer all seven questions. Each classification might be used, zero, one, or more than one time in the seven questions. Question 5 1.0/1.0 point (graded) Minimize ∑? ???? subject to ∑? ????? ≥ ?? for all ? all ?? ∈ {0, 1} You have used 1 of 1 attempt Question 5 1.0/1.0 point (graded) Minimize ∑? ???? subject to ∑? ????? ≥ ?? for all ? all ?? ≥ 0 You have used 1 of 1 attempt Question 5 1.0/1.0 point (graded) Minimize ∑? ???? subject to ∑? ∑? ???????? ≥ ?? for all ? all ?? ≥ 0 You have used 1 of 1 attempt Question 5 1.0/1.0 point (graded) Minimize ∑?( log ??)?? subject to ∑? ????? ≥ ?? for all ? all ?? ≥ 0 You have used 1 of 1 attempt Question 5 1.0/1.0 point (graded) Minimize ∑? ???2 subject to ∑? ????? ≥ ?? for all ? all ?? ≥ 0 You have used 1 of 1 attempt Question 5 0.0/1.0 point (graded) Minimize ∑? ?? sin ?? subject to ∑? ????? ≥ ?? for all ? all ?? ≥ 0 Answer: General non-convex program You have used 1 of 1 attempt Answers are displayed within the problem Question 5 1.0/1.0 point (graded) Minimize ∑? ??|?? − 6| subject to ∑? ????? ≥ ?? for all ? all ?? ≥ 0 You have used 1 of 1 attempt Questions 6a,6b,6c 9.32/12.0 points (graded) A medium-sized city is analyzing the size of its judicial system, specifically the number of judges it has available for hearing cases at different times of the year. At busy times (about 10% of the times), the arrival rate is 20 new cases ready for trial per day. At other times, the arrival rate is 10 new cases ready for trial per day. Once an judge is assigned to a case (at any time), it takes an average of 0.5 days to complete. [NOTE: This is a very simplified version of the judicial system. If you have deeper knowledge of how the judicial system works, please do not use it for this question; you would end up making the question more complex than it is designed to be.] a. The first model the city tries is a queuing model with 3 judges always available. What would you expect the queuing model to show? b. The second model the city tries is a queuing model with 15 judges available during busy times and 7 judges availableduring non-busy times. What would you expect the queuing model to show? c. The third model the city tries is a Markov chain, where each state is the number of cases waiitng (e.g., 0 cases waiting, 1 case waiting, etc.). When there are at least 20 total cases waiting, the city will refer waiting caess to arbitrators who try to get the cases settled without a trial (arbitration also takes about 0.5 days per case). Once the arbitrators start hearing cases, the arbitrators continue to be assigned cases until no more cases are waiting. Select all of the following statements about the model and the memoryless property (previous states don't affect the probability of moving from one state to another) that are true. You have used 1 of 1 attempt Answers are displayed within the problem Questions 7a,7b 10.0/10.0 points (graded) A retailer is testing two different customer retention approaches. The retailer is using A/B testing: For each customer, the retailer randomly selects one approach or the other to use. The results after 2000 trials are shown below. Trials Customer loss rate 95% confidence interval Option A 1036 4.8% 3.6%-6.2% Option B 964 10.4% 8.5%-12.3% Note: Lower customer loss rates are better. a. What should the retailer do? Later, the retailer developed 7 new options, so they used a multi-armed bandit approach where each option is chosen with probability proportional to its likelihood of being the best. The results after 2000 total trials are shown below. Customer loss rate 95% confidence interval Option #1 15.9% 9.5%-22.2% Customer loss rate 95% confidence interval Option #2 12.0% 7.2%-17.4% Option #3 9.4% 5.7%-13.7% Option #4 9.1% 5.5%-13.2% Option #5 8.7% 5.2%-12.6% Option #6 6.1% 3.7%-8.9% Option #7 2.8% 1.7%-4.0% Note: Lower customer loss rates are better. b. What should the retailer do? You have used 1 of 1 attempt Information for Question 8a For each of the mathematical optimization models, select the variable-selection/regularization method it most-precisely represents (or select "none of the above" if none of the other choices are appropriate). In each model, x is the data, y is the response, a are the coefficients, n is the number of data points, m is the number of predictors, and T and ? are appropriate constants. There are four questions labeled "Question 8a". Answer all four questions. Each of the choices might be used zero, one, or more than one time in the four questions. Question 8a 1.0/1.0 point (graded) Minimize ∑? (?? − (?0 ? ?=1 ?? ??? ))2 subject to ∑? (??)2 ≤ ? You have used 1 of 1 attempt Question 8a 1.0/1.0 point (graded) Minimize ∑? (?? − (?0 ? ?=1 ?? ??? ))2 subject to ? ∑? |? | + (1 − ?) ∑? (? )2 ≤ ? ?=1 ? ?=1 ? You have used 1 of 1 attempt Question 8a 1.0/1.0 point (graded) Minimize ∑? (?? − (?0 ? ?=1 ?? ??? ))2 You have used 1 of 1 attempt Question 8a 1.0/1.0 point (graded) Minimize ∑? (?? − (?0 ? ?=1 ?? ??? ))2 subject to ∑? |??| ≤ ? You have used 1 of 1 attempt Question 8b 1/4 points (graded) Keyboard Help Rank the following regression and variable-selection/regularization methods from fewest variables selected to most variables selected. All four methods will be used (the bottom contains two equivalent spaces). You have used 1 of 1 attempts. Reset Show Answer FEEDBACK Correctly placed 1 item. Misplaced 3 items. Good work! You have completed this drag and drop problem. Final attempt was used, highest score is 1.0 Question 8c 6.0/6.0 points (graded) Select all of the following reasons that you might want to use stepwise regression, lasso, etc. to limit the number of factors in a model. You have used 1 of 1 attempt Question 8d 3.0/3.0 points (graded) In the simple linear regression model ? ? 2 ???????? ∑ (?? − (?0 + ∑ ?????)) ?=1 ?=1 i. What are the variables from an optimization perspective? ii. What are the variables from a regression perspective? You have used 1 of 1 attempt Question 8e 7/7 points (graded) Keyboard Help Put the following seven steps in order, from what is done first to what is done last. You have used 1 of 1 attempts. Reset Show Answer FEEDBACK Correctly placed 7 items. Good work! You have completed this drag and drop problem. Final attempt was used, highest score is 7.0 There are five questions labeled "Question 9". Answer all five questions. For each question, select the most appropriate model/approach to answer the question/analyze the situation described. Each model/approach might be used zero, one, or more than one time in the five questions. Question 9 1.4/1.4 points (graded) Determine the best marketing strategy, given that a competitor will react to your choice in his/her decisions. You have used 1 of 1 attempt Question 9 © All Rights Reserved [Show More]

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