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Multilingual Demographic Dictionary, second unified edition, English volume

Method of least squares

Multilingual Demographic Dictionary, second unified edition, English vol.
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Method of least squares  (METHOD of least squares)

It is occasionally desirable to replace a series of figures by another series that shows greater regularity. This process is known as graduation 1 or smoothing 1, and it generally consists of passing a smooth curve through a number of points in the time series or other series, such as the number of persons distributed by reported age. If a free-hand curve is drawn the process is called graphic graduation 2. When analytical mathematical methods are used, this is called curve fitting 3. A mathematical curve is fitted to the data, possibly by the method of least squares 4, which minimizes the sum of the squares of the differences between the original and the graduated series. Other methods include moving averages 5 or involve the use of the calculus of finite differences 6. Some of these procedures may be used for interpolation 7, the estimation of values of the series at points intermediate between given values, or for extrapolation 8, the estimation of values outside of the range for which it was given.

  • 1. Graduation, n. - graduate, v. - graduated, adj. Smoothing, n. - smooth, v. - smoothed, adj.
  • 7. Interpolation, n. - interpolate, v. - interpolated, adj.
  • 8. Extrapolation, n. - extrapolate, v. - extrapolated, adj.