Standard Deviation and Variance Calculation

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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?

The mean of the data Signup and view all the answers

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

To isolate the error on the left-hand side Signup and view all the answers

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

MSE is the average of SSE Signup and view all the answers

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

To search for the optimum values of parameters in the model Signup and view all the answers

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

The underlying process is stationary Signup and view all the answers

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

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

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

When the process has no noticeable trend and no seasonality Signup and view all the answers

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

Only the most recent forecast and the most recent observation Signup and view all the answers

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

It assumes an underlying constant process Signup and view all the answers

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

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

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

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

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

To reduce the influence of past data on the mean Signup and view all the answers

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

The method of calculating the forecast Signup and view all the answers

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

It is dropped and replaced by the new observation Signup and view all the answers

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

It remains constant Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

The storage requirements for the data are reduced. Signup and view all the answers

What do the deviations (Mi − M̄) represent?

Deviation in units of miles per gallon Signup and view all the answers

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

They are equal Signup and view all the answers

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

Standard deviation Signup and view all the answers

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

They measure the average deviation of the observations from their mean Signup and view all the answers

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

Because spread-out observations will be far from the mean 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?

Two-thirds Signup and view all the answers