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 YÌ‚
  • To find the minimum value of SSE
  • To find the value of YÌ‚ 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 YÌ‚ and setting it equal to zero?

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

What is the value of YÌ‚ that minimizes the sum of the squared errors?

<p>The mean of the data (B)</p>
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What is the purpose of rewriting equation (3) as equation (4)?

<p>To isolate the error on the left-hand side (D)</p>
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What is the relationship between the sum of squared errors and the mean squared error?

<p>MSE is the average of SSE (D)</p>
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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 (D)</p>
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What is the assumption about the underlying process in the context of calculating the mean?

<p>The underlying process is stationary (C)</p>
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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 (A)</p>
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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 (C)</p>
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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 (C)</p>
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What is the main limitation of using the simple method of calculating the mean?

<p>It assumes an underlying constant process (D)</p>
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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 (A)</p>
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What is the purpose of stage 5 in the forecasting scenario?

<p>To appraise the forecasting method's suitability for various data patterns (B)</p>
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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 (A)</p>
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What is the primary difference between the mean and simple moving averages methods?

<p>The method of calculating the forecast (D)</p>
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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 (C)</p>
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What is the number of data points in each average in the moving averages method?

<p>It remains constant (C)</p>
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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. (B)</p>
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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. (D)</p>
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What is the algebraic formula for a moving average forecast of order k?

<p>Ft+1 = (Yt + Yt-1 +... + Yt-k+1) / k (A)</p>
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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. (D)</p>
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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. (B)</p>
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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. (C)</p>
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What do the deviations (Mi − M̄) represent?

<p>Deviation in units of miles per gallon (B)</p>
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How are the squared deviations and the mean squared deviation (MSD) related?

<p>They are equal (A)</p>
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What information can be obtained by taking the square root of variance and mean squared deviation (MSD)?

<p>Standard deviation (C)</p>
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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 (C)</p>
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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 (D)</p>
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Approximately how many of the observations are within 1 standard deviation of the mean according to the useful rule of thumb?

<p>Two-thirds (A)</p>
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