30 Questions
What is the primary goal of the store manager in minimizing the mean squared error?
To find the value of Ŷ that minimizes the sum of squared errors
What is the notation used to denote the ith customer?
i 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
What is the value of Ŷ that minimizes the sum of the squared errors?
The mean of the data
What is the purpose of rewriting equation (3) as equation (4)?
To isolate the error on the left-hand side
What is the relationship between the sum of squared errors and the mean squared error?
MSE is the average of SSE
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
What is the assumption about the underlying process in the context of calculating the mean?
The underlying process is stationary
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
In Pegels' classification, under what conditions would the simple averaging method produce good results?
When the process has no noticeable trend and no seasonality
How many items need to be stored recursively for the calculation of the mean?
Only the most recent forecast and the most recent observation
What is the main limitation of using the simple method of calculating the mean?
It assumes an underlying constant process
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
What is the purpose of stage 5 in the forecasting scenario?
To appraise the forecasting method's suitability for various data patterns
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
What is the primary difference between the mean and simple moving averages methods?
The method of calculating the forecast
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
What is the number of data points in each average in the moving averages method?
It remains constant
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.
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.
What is the algebraic formula for a moving average forecast of order k?
Ft+1 = (Yt + Yt-1 +... + Yt-k+1) / k
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.
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.
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.
What do the deviations (Mi − M̄) represent?
Deviation in units of miles per gallon
How are the squared deviations and the mean squared deviation (MSD) related?
They are equal
What information can be obtained by taking the square root of variance and mean squared deviation (MSD)?
Standard deviation
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
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
Approximately how many of the observations are within 1 standard deviation of the mean according to the useful rule of thumb?
Two-thirds
This quiz covers the concept of standard deviation and variance, including their mathematical properties and calculations. Learn how to convert squared deviations into meaningful units and how standard deviation is defined as the square root of variance.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
