Statistical Computing (STAT-428) Due Date: 7 August 2020 Acceptable Plagiarism index 17% Task a. [Pre analysis] Use the data given in Data1, choose the suitable auxiliary variables for literacy ratio. Provide the visual and numerical method of this selection. Task b. [Simulation] Generate 4000 independent samples for simulation from the original data. The parameter of interest is the population mean of the variable literacy ratio. From generated samples, compute ratio and regression estimates. Find the percent Relative bias (PRB) and percent coefficient of variation (PCV) for both ratio and regression estimators and suggest the best estimator for this population. Task c. [Distribution Fitting] Generate an artificial data use the function fitdistr and fit an exponential distribution. Task d. [Cigarette Consumption Data] A national insurance organization wanted to study the consumption pattern of cigarettes in all 50 states and the Districts of Columbia. The variables chosen for the study are given in table below. The data from 1970 are given in DATA3, the states are given in alphabetical order. Using the R programming answer the following questions at 5% level of significance discuss each. Variable Definition Age Median age of a person living in a state HS Percentage of people over 25 years of age in a state who had completed high school Income Per capita personal income for a state (income in dollars) Black Percentage of blacks living in a state Female Percentage of females living in a state Price Weighted average price (in cents) of a pack of cigarettes in a state Sales Number of packs of cigarettes sold in a state on a per capita basis 1. Test the hypothesis that the variable Female is not needed in the regression equation relating Sales to the six predictor variables. 2. Test the hypothesis that the variables Female and HS are not needed in the above regression equation. 3. Compute the 95% confidence interval for the true regression coefficient of the variable Income. 4. What percentage of the variation in Sales can be accounted for when Income is removed from the above regression equation? Explain. 5. What percentage of the variation in Sales can be accounted for by the three variables: Price, Age, and Income? Explain. 6. What percentage of the variation in Sales that can be accounted for by the variable Income, when Sales is regressed on only Income? Explain
Task e. [Pre analysis] Use the Data2, Provide the data visualization (time series plot, box plot, histogram and ACF plot) and the descriptive statistics of log (Yt ) and d log (Yt ) . What can you spot from various plot? What is the meaning of the descriptive statistics? Task f. [Unit root/Stationarity tests] Perform tests on of log (Yt ) and d log (Yt ) . Use AIC to select the best lag length for the ADF test and use “short” lag length for the PP and KPSS test. Task g. [Model selection] Select the best ARMA (p, q) model for d log (Yt ) by AIC. Please set the maximum order as 5, i.e. p, q <= 5. Task h. [Model diagnostics] Perform model diagnostics for the residuals from the best selected model. To be specific, carry out the time series plot, ACF plot, and LjungBox test on the residuals. Comments on the results of the model diagnostics. Task i. [Forecasting] Choose the best model based on the data in the in-sample period and make forecasting for the out-of-sample period. Plot the predicted values from the best model versus the true values. Calculate the forecasting performance (MSE, MAE, MAPE) of the best model.
Assignment: Plot the Phillips Curve Your assignment is to grab data from Fred and plot out the Phillips Curve and run a regression. Things you must do: 1) Create a scatter plot of inflation and unemployment. 2) Draw a linear regression line through the chart. 3) Run a linear regression of inflation on output. What you should deliver to me: Send me your program file, a chart of your output and your regression results. You can export images out of R. Steps to install R 1) Download R for your operating system https://cloud.r-project.org/ 2) Download R Studio https://cloud.r-project.org/bin/windows/base/ 3) Install R 4) Install R Studio 5) Open R Studio 6) And run the commands in the ExtraCredit.R File
First Part: Initial Post (Instructions)
- Answer the questions for each chapter in your own words.
Chapter 07
Give an example of a business situation where regression analysis can be used for decision making
Chapter 08
Discuss the advantages of using forecasting in planning and monitoring businesses activities
Chapter 10
Why is it important to build good spreadsheet models?
Chapter 12
Do some research on the Internet and find a real-world example of linear programming applications. Relate the example you found to what is developed in class
Chapter 15
Discuss the advantages of using decision tree analysis
Second Part: Reply to student’s Post (Instructions)
- Read and reply two students’ post
- Provide a thoughtful and correct reply
Students’ Post (Chapter 7)
Student 1: Chapter 7 - Britney H
Question: Give an example of a business situation where regression analysis can be used for decision making
Post answer: Regression analysis can provide quantitative support for decisions and prevent mistakes due to manager’s intuitions. Regression analysis, however, may indicate that the increase in revenue might not be sufficient to support the rise in operating expenses due to longer working hours. Regression is not only significant for lending empirical support to management decisions but also for identifying errors in judgment. For example, a retail store manager may believe that extending shopping hours will significantly increase sales.
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Student 2: Chapter 7 - Shelby S
Question: Give an example of a business situation where regression analysis can be used for decision making
Post answer: Regression analysis can be used in almost everything when it comes to businesses and decision making. One example is the number of phone calls made at a sales company vs. the amount of sales made in dollars. This could set a standard of how many calls each worker needs to make per day to achieve the sales goal.
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Students’ Post (Chapter 8)
Student 1: Chapter 8 - Michelle W
Question: Discuss the advantages of using forecasting in planning and monitoring businesses activities
Post answer: The advantage of using forecasting is that it provides businesses with valuable information that can be used to make decisions about the future of the business. Forecasting uses qualitative data that helps businesses plan for the future. Forecasting also helps a business plan their finances and revenues along with equity and debt requirements.
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Student 2: Chapter 8 - Kyle R
Question: Discuss the advantages of using forecasting in planning and monitoring businesses activities
Post answer: Forecasting can be used to make decisions that affect all aspects of a company. Forecasting models are developed using time series data sets to predict future variables for business needs. An analyst can predict manufacturing needs by creating a time series forecast by averaging out the last few months of need materials and provide an accurate forecast of needed materials for the upcoming month. Having accurate forecasts are essential to sales, supply chain, production, and most facets of business to maximize revenues and efficiency.
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Students’ Post (Chapter 10)
Student 1: Chapter 10 - Lane S
Question: Why is it important to build good spreadsheet models
Post answer: It is very important to build good spreadsheet models because it presents viable data and information in an easy to read and understanding format that helps the user make better business decisions. Along with that a well-built spreadsheet model helps eliminate calculation errors as computer software is able to complete calculations for the users.
Overall a well-built spreadsheet eliminates mistakes, and compiles data into a user-friendly form that can lead to better business decisions, resulting in higher sales, profits, lowers costs and etc.
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Student 2: Chapter 10 - Satoru O
Question: Why is it important to build good spreadsheet models
Post answer: Spreadsheets are essential to the business world. While the complexity can vary, and can be used for different reasons, spreadsheet is for organizing and categorizing important data of the business. It is how the business can organize and analyze important data with time efficiency. In addition, by having a good spreadsheet, business can do various of things with the data, such as creating a graph. A good spreadsheet models are important in order to have efficient business.
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Students’ Post (Chapter 12)
Student 1: Chapter 12 - Tarig A
Question: Do some research on the Internet and find a real-world example of linear programming applications. Relate the example you found to what is developed in class
Post answer: Linear programming can be applied in the nutrition field to determine dietary needs planning for needy families at a low cost. Mathematical models will aid in determining the food needed to offer low-cost nutrition. Constraints, in this case, include the dietary guidelines and different cultures about food combinations and consumption van (Dooren, 2018). In the transport industry, airlines do apply linear programming for scheduling of pilots and the roots they cover. The same concept can be used by learning institutions in allocating tutors to various classes.
Dooren, C. (2018). A review of the use of linear programming to optimize diets, nutritiously, economically and environmentally. Frontiers in nutrition, 5, 48.
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Student 2: Chapter 12 - Deborah Le
Question: Do some research on the Internet and find a real-world example of linear programming applications. Relate the example you found to what is developed in class
Post answer: I am linking to an article in The Chicago Tribune that discusses how airlines use linear programming to develop their flight schedules. They use this technique to reduce fuel costs, use their labor efficiently, and have the right airplanes on the right routes (among other things). According to this article (which is, admittedly, old) American Airlines cut the number of “penalty payments” it had to make to employees from 15% of its total payroll costs to 4% between 1980-1990, saving the airline $20 million a year.
Airlines don’t just use linear programming to schedule flights, though. They also use this tool to help them schedule maintenance and even determine the order in which passengers board the aircraft. Turning a plane over so it can go to its next destination contributes to such metrics as on-time departures and arrivals (and, in turn, contributes to customer satisfaction and retention).
As it relates to this class, the examples in the text are heavily concerned with managing logistics. Linear programming helps airlines with their logistics challenges in much the same way as the hypothetical issues in the course textbook and homework.
https://www.chicagotribune.com/news/ct-xpm-1990-07-30-9003030978-story.html
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Students’ Post (Chapter 15)
Student 1: Chapter 15 - Tarig A
Question: Discuss the advantages of using decision tree analysis
Post answer: The advantages of decision tree analysis include its comprehensive nature. The method develops a detailed analysis of the consequences that follow every branch and also determines the decisions that require more investigation. Decision tree analysis is also specific as it points out the particular decision paths, eliminates ambiguity, mitigates uncertainty, and provides the financial needs of each decision that could be followed (Alsaedi, Fong, Abdelqader, Delano, & Altaie, 2019). The method is also straightforward to use as it involves the application of simple formula and offers all the alternatives to be considered in decision making for quick comparison.
Alsaedi, A., Fong, A., Abdelqader, I., Delano, M. N., & Altaie, K. (2019). Modeling Big Medical Survival Data Using Decision Tree Analysis with Apache Spark.
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Student 2: Chapter 15 - Deborah Le
Question: Discuss the advantages of using decision tree analysis
Post answer: One of the primary advantages of using decision tree analysis is that it requires an organization to consider the consequences of possible decisions. Additionally, it requires the organization to consider the likelihoods of the possible outcomes of a given decision.
A decision tree can be useful to a business in developing contingency plans for consequences it deemed undesirable or unlikely. Conversely, it can provide a tactical game-plan if the decision yields the expect (or hoped-for) results.
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