Least Squares Principles MCQs : This section focuses on the "Least Squares Principles". These Multiple Choice Questions (MCQs) should be practiced to improve the Least Squares Principles skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.
Question 1
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.
A. 0.154
B. 0.514
C. 0.145
D. 1.405
Question 2
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.
A. 1
B. 1.6
C. 1.7
D. 2
Question 3
If the value of number of observations is large and e is small then ∑e / n will be equal to __________
A. Frequency
B. True value
C. Arithmetic mean
D. Probable value
Question 4
In the principle of least squares, residual error will be__________
A. Maximum
B. Minimum
C. Negligible
D. Nor error occurs
Question 5
In the process of least squares, sum of residuals must be equal to zero.
A. False
B. True
Question 6
The principle of least squares can be formed from___________
A. Probability equation
B. Normal equation
C. Celestial equation
D. Observed equation
Question 7
When number of observations is large, the arithmetic mean will be equal to true value.
A. True
B. False
Question 8
Which of the following indicates the formula of arithmetic mean?
A. ∑V * n
B. ∑V – n
C. ∑V + n
D. ∑V / n
Question 9
Which of the following indicates the fundamental of least squares?
A. arithmetic mean should be maximized
B. arithmetic mean should be zero
C. arithmetic mean should be neutralized
D. arithmetic mean should be minimized
Question 10
Which of the following value must always be positive in the principle of least squares?
A. (N-(∑V/n))2
B. (N*(∑V/n))2
C. (N+(∑V/n))2
D. (N-(∑V/n))0