Standard Deviation and Variance Calculation
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Questions and Answers

What is the primary goal of the store manager in minimizing the mean squared error?

  • To find the average value of Yi
  • To find the maximum value of Ŷ
  • To find the minimum value of SSE
  • To find the value of Ŷ that minimizes the sum of squared errors (correct)

    • What is the notation used to denote the ith customer?

  • i subscript (correct)
  • ei subscript
  • Yb subscript
  • Y subscript

    • What is the result of taking the derivative of the sum of squared errors with respect to Ŷ and setting it equal to zero?

  • 12 X (Yi - Ŷ) = 0 (correct)
  • 12 X (Yi + Ŷ) = 0
  • 12 X (Yi × Ŷ) = 0
  • 12 X (Yi / Ŷ) = 0

    • What is the value of Ŷ that minimizes the sum of the squared errors?

    <p>The mean of the data</p> Signup and view all the answers

    What is the purpose of rewriting equation (3) as equation (4)?

    <p>To isolate the error on the left-hand side</p> Signup and view all the answers

    What is the relationship between the sum of squared errors and the mean squared error?

    <p>MSE is the average of SSE</p> Signup and view all the answers

    Why is it necessary to modify the initialization process in the stage of model development?

    <p>To search for the optimum values of parameters in the model</p> Signup and view all the answers

    What is the assumption about the underlying process in the context of calculating the mean?

    <p>The underlying process is stationary</p> Signup and view all the answers

    What is the primary objective of using past history data in averaging methods?

    <p>To make use of past data to develop a forecasting system for future periods</p> Signup and view all the answers

    In Pegels' classification, under what conditions would the simple averaging method produce good results?

    <p>When the process has no noticeable trend and no seasonality</p> Signup and view all the answers

    How many items need to be stored recursively for the calculation of the mean?

    <p>Only the most recent forecast and the most recent observation</p> Signup and view all the answers

    What is the main limitation of using the simple method of calculating the mean?

    <p>It assumes an underlying constant process</p> Signup and view all the answers

    What is the formula to calculate the forecast for time t + 2 when a new observation becomes available?

    <p>Ft+2 = (1/(t+1)) * Σ Yi from i=1 to t+1</p> Signup and view all the answers

    What is the purpose of stage 5 in the forecasting scenario?

    <p>To appraise the forecasting method's suitability for various data patterns</p> Signup and view all the answers

    What is the purpose of specifying a fixed number of past observations in the moving averages method?

    <p>To reduce the influence of past data on the mean</p> Signup and view all the answers

    What is the primary difference between the mean and simple moving averages methods?

    <p>The method of calculating the forecast</p> Signup and view all the answers

    What happens to the oldest observation when a new observation becomes available in the moving averages method?

    <p>It is dropped and replaced by the new observation</p> Signup and view all the answers

    What is the number of data points in each average in the moving averages method?

    <p>It remains constant</p> Signup and view all the answers

    What is the primary effect of using a large value for k in a moving average forecasting system?

    <p>The forecasting system requires more data points to be stored.</p> Signup and view all the answers

    How do moving average forecasts of order k behave when k is small?

    <p>They provide predictions that are highly responsive to changes in the pattern.</p> Signup and view all the answers

    What is the algebraic formula for a moving average forecast of order k?

    <p>Ft+1 = (Yt + Yt-1 +... + Yt-k+1) / k</p> Signup and view all the answers

    What is the adjustment made to the forecast Ft+1 to obtain the forecast Ft+2?

    <p>The (1/k)th of the difference between Yt+1 and Yt-k+1.</p> Signup and view all the answers

    What is the effect of using a moving average forecasting system with a high order k?

    <p>The forecasts are highly smoothed and do not change much over time.</p> Signup and view all the answers

    What is the primary advantage of using a moving average forecasting system with a small order k?

    <p>The storage requirements for the data are reduced.</p> Signup and view all the answers

    What do the deviations (Mi − M̄) represent?

    <p>Deviation in units of miles per gallon</p> Signup and view all the answers

    How are the squared deviations and the mean squared deviation (MSD) related?

    <p>They are equal</p> Signup and view all the answers

    What information can be obtained by taking the square root of variance and mean squared deviation (MSD)?

    <p>Standard deviation</p> Signup and view all the answers

    Why are both the Mean Absolute Deviation (MAD) and standard deviation (S) considered measures of spread?

    <p>They measure the average deviation of the observations from their mean</p> Signup and view all the answers

    Why do MAD and S tend to be large when the data are spread out?

    <p>Because spread-out observations will be far from the mean</p> Signup and view all the answers

    Approximately how many of the observations are within 1 standard deviation of the mean according to the useful rule of thumb?

    <p>Two-thirds</p> Signup and view all the answers

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