General Principles of Least Squares MCQ

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• Find the value of N if the sums of squares of two individual residuals are given as 24.98 and 13.76 respectively. The summation of the difference between individual and the mean of the readings is 3.32 for 8 observations.
  ক

  1

  খ

  1.6

  গ

  1.7

  ঘ

  2
• Determine the arithmetic mean if the summation of the difference between individual and mean of the observations is given as 1.54 for 10 observations.
  ক

  0.154

  খ

  0.514

  গ

  0.145

  ঘ

  1.405
• When number of observations is large, the arithmetic mean will be equal to true value.
  ক

  True

  খ

  False
• In the process of least squares, sum of residuals must be equal to zero.
  ক

  False

  খ

  True
• Which of the following value must always be positive in the principle of least squares?
  ক

  (N-(∑V/n))2

  খ

  (N*(∑V/n))2

  গ

  (N+(∑V/n))2

  ঘ

  (N-(∑V/n))0
• Which of the following indicates the fundamental of least squares?
  ক

  arithmetic mean should be maximized

  খ

  arithmetic mean should be zero

  গ

  arithmetic mean should be neutralized

  ঘ

  arithmetic mean should be minimized
• If the value of number of observations is large and e is small then ∑e / n will be equal to __________
  ক

  Frequency

  খ

  True value

  গ

  Arithmetic mean

  ঘ

  Probable value
• Which of the following indicates the formula of arithmetic mean?
  ক

  ∑V * n

  খ

  ∑V – n

  গ

  ∑V + n

  ঘ

  ∑V / n
• In the principle of least squares, residual error will be__________
  ক

  Maximum

  খ

  Minimum

  গ

  Negligible

  ঘ

  Nor error occurs
• The principle of least squares can be formed from___________
  ক

  Probability equation

  খ

  Normal equation

  গ

  Celestial equation

  ঘ

  Observed equation