Probability and Statistics (3130006) MCQs

MCQs of Curve fitting by the numerical method

Showing 1 to 10 out of 18 Questions
1.

Fit a straight line for the given pairs of (x,y) which are (0,3), (1,6), (2,8), (3,11), (4,13), (5,14) .

(a)

y=2.26x

(b)

y=3.52+2.26x

(c)

y=3.52x

(d)

y=4+3x

Answer:

Option (b)

2.

The table shows the average braking distance of a car at various speeds. Use a second degree polynomial to predict the braking distance at 70 mph.

Speed (x) (miles/hr) 20 30 40 50 60
Braking distance (y) (ft) 20 45 80 125 180

 

(a)

245 ft

(b)

225 ft

(c)

285 ft

(d)

265 ft

Answer:

Option (a)

3.

Which equation represents the parabola that passes through the following points:

x 0 1 2 3 4
y 1.0 1.8 1.3 2.5 6.3

 

(a)

y=1.42x+1.07x2+0.55x3

(b)

y=1.42x3-1.07x2+0.55x

(c)

y=1.42x-1.07x2+0.55x3

(d)

y=1.55x-1.07x2+1.45x3

Answer:

Option (c)

4.

To find the constants a and b of the regression model y=aebx to fit x1,y1, x2,y2, ..., xn,yn the sum of the residuals that is minimized is _____________ .

(a)

i=1nyi-aebxi2

(b)

i=1nlnyi-lna-bxi2

(c)

i=1nyi-lna-bxi2

(d)

i=1nlnyi-lna-blnxi2

Answer:

Option (b)

5.

For data given below find xi2yi .

X 0 1 2 3 4
Y 1 0 3 10 21
(a)

435

(b)

436

(c)

437

(d)

438

Answer:

Option (d)

6.

If the normal equations for a straight line y=ax+b are 26=4a+6b and 34=6a+4b then fit the above straight line.

(a)

y=5x-b

(b)

y=5x+b

(c)

y=x+5b

(d)

y=x-5b

Answer:

Option (b)

7.

Fit the curve y=aebx if their normal equations are 13.1991=4a+10b and 30.7134=10a+30b .

(a)

y=-0.4569e4.4419x

(b)

y=-404419e0.4569

(c)

y=4.4419e-0.4569x

(d)

y=1

Answer:

Option (c)

8.

In the least square method we use ____________ to find the value of unknowns.

(a)

Regression equations

(b)

Normal equations

(c)

General equations

(d)

Auxiliary equations

Answer:

Option (b)

9.

The normal equation for fitting of a parabola y=a+bx+cx2 is __________ .

(a)

axi+bxi2+axi3

(b)

axi+bxi2+cxi3

(c)

axi+bxi3+cxi4

(d)

axi+bxi3+cxi2

Answer:

Option (b)

10.

Fit the parabola y=a+bx+cx2 , if their normal equations are 9a+60c=11 , 60b=51 and 60a+708c=-9 .

(a)

y=0.5599+0.85x-0.2673x2

(b)

y=-0.5599+0.85x2-0.2673x3

(c)

y=-0.5599+0.85x-0.2673x2

(d)

y=-0.5599x2+0.85x-0.2673

Answer:

Option (c)

Showing 1 to 10 out of 18 Questions