# 1. Show that EWMA smoothing is equivalent to an ARIMA{O, 1,1) model with no constant, as described in Chapter 8, “Advanced Analytica l Theory and Methods: Time Series Analysis.” 2. Develop and test a user-defined aggregate to calculate n factorial {n!), where n is an integer. 3. From a SQL table or query, randomly select 10% of the rows. Hint: Most SQL implementations have a random() function that provides a uniform random number between 0 and 1. 4. Discuss possible reasons to randomly sample records from a SQL table. 5. Describe four common deliverables for an analytics project. 6. What is the focus of a presentation for a project sponsor? 7. Give examples of appropriate charts to create in a presentation for other data analysts and data scientists as part of a final presentation. Explain why the charts are appropriate to show each audience. 8. Explain what types of graphs would be appropriate to show data changing over time and why. 9. As part of operationalizing an analytics project, which deliverable would you expect to provide to a Business Intelligence analyst? Purchase the answer to view it

Chapter 8 of “Advanced Analytical Theory and Methods: Time Series Analysis” discusses the equivalence between EWMA smoothing and an ARIMA(0, 1, 1) model with no constant. The Exponentially Weighted Moving Average (EWMA) smoothing technique is widely used in time series analysis to remove noise and highlight underlying trends. On the other hand, ARIMA models are a class of models commonly used to analyze and forecast time series data.

To establish the equivalence between EWMA smoothing and an ARIMA(0, 1, 1) model, we need to show that the two approaches produce the same results under certain conditions. EWMA smoothing calculates the weighted average of past observations, where the emphasis on older observations decays exponentially. The weights are determined by a smoothing factor, typically denoted as alpha. The choice of alpha determines the level of smoothing, with smaller values resulting in more smoothing.

In an ARIMA(0, 1, 1) model, the differencing order is set to 1, indicating that the differenced series is used. Differencing is a technique used to remove trends and make the time series stationary, which is often required for modeling purposes. The MA(1) component in the ARIMA(0, 1, 1) model represents a moving average term of order 1. It captures the dependence between the current observation and the previous error term.

To establish the equivalence, we can show that the EWMA smoothing equation is mathematically equivalent to the equation used to estimate the MA(1) parameter in the ARIMA(0, 1, 1) model. This involves manipulating the equations to express the parameters and observations in terms of each other. Once the equivalence is established, we can conclude that applying EWMA smoothing or fitting an ARIMA(0, 1, 1) model with no constant produces the same results.

Moving on to the next question, the development and testing of a user-defined aggregate to calculate n factorial (n!) where n is an integer requires a combination of programming skills and knowledge of factorial calculations. A user-defined aggregate is a powerful feature in many programming languages and database management systems, allowing the creation of custom aggregate functions that can be used in SQL queries.

To calculate n factorial, we need to define the algorithm for factorial calculation and implement it in a user-defined aggregate function. The function should take an integer input parameter (n) and return the factorial result. It should handle cases where n is a non-negative integer.

Testing the user-defined aggregate involves evaluating its performance, accuracy, and error handling capabilities. Test cases can be created to compare the results of the user-defined aggregate with known factorial values for different input values of n. The aggregate should also be tested with edge cases, such as handling large values of n or negative values.

The next questions discuss randomly selecting a sample from a SQL table, possible reasons for doing so, and the deliverables for an analytics project.

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