# Numerical Analysis Questions and Answers – Approximation of Functions using Least Square Method

This set of Numerical Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Approximation of Functions using Least Square Method”.

1. Fit the straight line to the following data.

a) y=x
b) y=x+1
c) y=2x
d) y=2x+1

2. Fit the straight line to the following data.

 x 0 5 10 15 20 y 7 11 16 20 26

a) y = 0.94x + 6.6
b) y = 6.6x + 0.94
c) y = 0.04x + 5.6
d) y = 5.6x + 0.04

3. Fit the straight line curve to the following data.

 x 75 80 93 65 87 71 98 68 84 77 y 82 78 86 72 91 80 95 72 89 74

a) y = 0.9288x + 7.78155
b) y = 7.78155x + 0.9288
c) y = 0.8288x + 6.78155
d) y = 6.78155x + 0.8288

4. Fit a second degree parabola to the following data.

 x 1 2 3 4 5 6 7 8 9 y 2 6 7 8 10 11 11 10 9

a) y = -0.2673x2 + 3.5232x – 0.9286
b) y = 0.2673x2 + 3.5232x – 0.9286
c) y = 0.2673x2 + 3.5232x + 0.9286
d) y = -0.2673x2 + 3.5232x + 0.9286

5. The normal equations for a straight line y = ax + b are:
a) Σy = aΣx + nb and Σxy = aΣx2 + bΣx
b) Σxy = aΣx + nb and Σy = aΣx2 + bΣx
c) Σy = aΣx + nb and Σxy = aΣx2 + bΣxy
d) Σy = aΣx + nb and Σx2y = aΣx2 + bΣx

6.The normal equations for a second degree parabola y = ax2 + bx + c are Σy = aΣx2 + bΣx + nc, Σxy = aΣx3 + bΣx2 + cΣx and Σx2y = aΣx4 + bΣx3 + cΣx2.. Is it true or false?
a) True
b) False

7. If the equation y = aebx can be written in linear form Y=A + BX, what are Y, X, A, B?
a) Y = logy, A = loga, B=b and X=x
b) Y = y, A = a, B=b and X=x
c) Y = y, A = a, B=logb and X=logx
d) Y = logy, A = a, B=logb and X=x

8. If the equation y=abx can be written in linear form Y=A+BX, what are Y, X, A, B?
a) Y=logy, X=x, A=loga and B=logb
b) Y=y, A=a, B=b and X=x
c) Y=y, A=a, B=logb and X=logx
d) Y=logy, A=a, B=logb and X=x

9. If the equation y=axb can be written in the linear form Y=A+BX, what are Y, X, A, B?
a) Y=logy, A=loga, B=b and X=logx
b) Y=y, A=a, B=b and X=x
c) Y=y, A=a, B=logb and X=logx
d) Y=logy, A=a, B=logb and X=x

10. The parameter E which we use for least square method is called as ____________
a) Sum of residues
b) Residues
c) Error
d) Sum of errors