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Bayesian Statistics: Techniques and Models, 1.05 (Q) Lesson 1

Lesson 1 TOTAL POINTS 8 1. Which objective of statistical modeling is best illustrated by the following example? You fit a linear regression of monthly stock values for your company. You use the estimates and recent stock history to calculate a forecast of the stock's value for the next three months. Quantify uncertainty Inference Hypothesis testing Prediction 2. Which objective of statistical modeling is best illustrated by the following example? A biologist proposes a treatment to decrease genetic variation in plant size. She conducts an experiment and asks you (the statistician) to analyze the data to conclude whether a 10% decrease in variation has occurred. Quantify uncertainty Inference Hypothesis testing Prediction 3. Which objective of statistical modeling is best illustrated by the following example? The same biologist form the previous question asks you how many experiments would be necessary to have a 95% chance at detecting a 10% decrease in plant variation. Quantify uncertainty Inference Hypothesis testing Prediction 4. Which of the following scenarios best illustrates the statistical modeling objective of inference? A venture capitalist uses data about several companies to build a model and makes recommendations about which company to invest in next based on growth forecasts. A social scientist collects data and detects positive correlation between sleep deprivation and traffic accidents. A model inputs academic performance of 1000 students and predicts which student will be valedictorian after another year of school. A natural language processing algorithm analyzes the first four words of a sentence and provides words to complete the sentence. 5. Which step in the statistical modeling cycle was not followed in the following scenario? Susan gathers data recording heights of children and fits a linear regression predicting height from age. To her surprise, the model does not predict well the heights for ages 14-17 (because the growth rate changes with age), both for children included in the original data as well as other children outside the model training data. Explore the data Use the model Fit the model Plan and properly collect relevant data 6. Which of the following is a possible consequence of failure to plan and properly collect relevant data? You will not produce enough data to make conclusions with a sufficient degree of confidence. Your analysis may produce incomplete or misleading results. You may not be able to visually explore the data. Your selected model will not be able to fit the data. 7. For Questions 6 and 7, consider the following: Xie operates a bakery and wants to use a statistical model to determine how many loaves of bread he should bake each day in preparation for weekday lunch hours. He decides to fit a Poisson model to count the demand for bread. He selects two weeks which have typical business, and for those two weeks, counts how many loaves are sold during the lunch hour each day. He fits the model, which estimates that the daily demand averages 22.3 loaves. Over the next month, Xie bakes 23 loaves each day, but is disappointed to find that on most days he has excess bread and on a few days (usually Mondays), he runs out of loaves early. Which of the following steps of the modeling process did Xie skip? Understand the problem Postulate a model Fit the model Check the model and iterate Use the model 8. What might you recommend Xie do next to fix this omission and improve his predictive performance? Abandon his statistical modeling initiative. Collect three more weeks of data from his bakery and other bakeries throughout the city. Re-fit the same model to the extra data and follow the results based on more data. Plot daily demand and model predictions against the day of the week to check for patterns that may account for the extra variability. Fit and check a new model which accounts for this. Trust the current model and continue to produce 23 loaves daily, since in the long-run average, his error is zero.



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Lesson 1 TOTAL POINTS 8 1. Which objective of statistical modeling is best illustrated by the following example? You fit a linear regression of monthly stock values for your company. You use the estimates and recent stock history to calculate a forecast of the stock's value for the next three months. Quantify uncertainty Inference Hypothesis testing Prediction 2. Which objective of statistical modeling is best illustrated by the following example? A biologist proposes a treatment to decrease genetic variation in plant size. She conducts an experiment and asks you (the statistician) to analyze the data to conclude whether a 10% decrease in variation has occurred. Quantify uncertainty Inference Hypothesis testing Prediction 3. Which objective of statistical modeling is best illustrated by the following example? The same biologist form the previous question asks you how many experiments would be necessary to have a 95% chance at detecting a 10% decrease in plant variation. Quantify uncertainty Inference Hypothesis testing Prediction 4. Which of the following scenarios best illustrates the statistical modeling objective of inference? A venture capitalist uses data about several companies to build a model and makes recommendations about which company to invest in next based on growth forecasts. A social scientist collects data and detects positive correlation between sleep deprivation and traffic accidents. A model inputs academic performance of 1000 students and predicts which student will be valedictorian after another year of school. A natural language processing algorithm analyzes the first four words of a sentence and provides words to complete the sentence. 5. Which step in the statistical modeling cycle was not followed in the following scenario? Susan gathers data recording heights of children and fits a linear regression predicting height from age. To her surprise, the model does not predict well the heights for ages 14-17 (because the growth rate changes with age), both for children included in the original data as well as other children outside the model training data. Explore the data Use the model Fit the model Plan and properly collect relevant data 6. Which of the following is a possible consequence of failure to plan and properly collect relevant data? You will not produce enough data to make conclusions with a sufficient degree of confidence. Your analysis may produce incomplete or misleading results. You may not be able to visually explore the data. Your selected model will not be able to fit the data. 7. For Questions 6 and 7, consider the following: Xie operates a bakery and wants to use a statistical model to determine how many loaves of bread he should bake each day in preparation for weekday lunch hours. He decides to fit a Poisson model to count the demand for bread. He selects two weeks which have typical business, and for those two weeks, counts how many loaves are sold during the lunch hour each day. He fits the model, which estimates that the daily demand averages 22.3 loaves. Over the next month, Xie bakes 23 loaves each day, but is disappointed to find that on most days he has excess bread and on a few days (usually Mondays), he runs out of loaves early. Which of the following steps of the modeling process did Xie skip? Understand the problem Postulate a model Fit the model Check the model and iterate Use the model 8. What might you recommend Xie do next to fix this omission and improve his predictive performance? Abandon his statistical modeling initiative. Collect three more weeks of data from his bakery and other bakeries throughout the city. Re-fit the same model to the extra data and follow the results based on more data. Plot daily demand and model predictions against the day of the week to check for patterns that may account for the extra variability. Fit and check a new model which accounts for this. Trust the current model and continue to produce 23 loaves daily, since in the long-run average, his error is zero.


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