MCQs of Curve fitting by the numerical method (Probability and Statistics - 3130006)

Probability and Statistics (3130006) MCQs

MCQs of Curve fitting by the numerical method

Showing 1 to 10 out of 18 Questions

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)	$y = 2.26 x$
(b)	$y = 3.52 + 2.26 x$
(c)	$y = 3.52 x$
(d)	$y = 4 + 3 x$

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

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)	$y = 1.42 x + 1.07 x^{2} + 0.55 x^{3}$
(b)	$y = 1.42 x^{3} - 1.07 x^{2} + 0.55 x$
(c)	$y = 1.42 x - 1.07 x^{2} + 0.55 x^{3}$
(d)	$y = 1.55 x - 1.07 x^{2} + 1.45 x^{3}$

To find the constants a and b of the regression model $y = {ae}^{bx}$ to fit $(x_{1,} y_{1}), (x_{2,} y_{2}), . . ., (x_{n,} y_{n})$ the sum of the residuals that is minimized is _____________ .

(a)	$\sum_{i = 1}^{n} {(y_{i} - {ae}^{{bx}_{i}})}^{2}$
(b)	$\sum_{i = 1}^{n} {(\ln (y_{i}) - \ln (a) - {bx}_{i})}^{2}$
(c)	$\sum_{i = 1}^{n} {(y_{i} - \ln (a) - {bx}_{i})}^{2}$
(d)	$\sum_{i = 1}^{n} {(\ln (y_{i}) - \ln (a) - bln (x_{i}))}^{2}$

For data given below find $\sum_{} x_{i}^{2} y_{i}$ .

X	0	1	2	3	4
Y	1	0	3	10	21

(a)	435
(b)	436
(c)	437
(d)	438

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

(a)	$y = 5 x - b$
(b)	$y = 5 x + b$
(c)	$y = x + 5 b$
(d)	$y = x - 5 b$

Fit the curve $y = {ae}^{bx}$ if their normal equations are $13.1991 = 4 a + 10 b$ and $30.7134 = 10 a + 30 b$ .

(a)	$y = - 0.4569 e^{4.4419 x}$
(b)	$y = - 404419 e^{0.4569}$
(c)	$y = 4.4419 e^{- 0.4569 x}$
(d)	$y = 1$

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

The normal equation for fitting of a parabola $y = a + bx + {cx}^{2}$ is __________ .

(a)	$a \sum_{} x_{i} + b \sum_{} x_{i}^{2} + a \sum_{} x_{i}^{3}$
(b)	$a \sum_{} x_{i} + b \sum_{} x_{i}^{2} + c \sum_{} x_{i}^{3}$
(c)	$a \sum_{} x_{i} + b \sum_{} x_{i}^{3} + c \sum_{} x_{i}^{4}$
(d)	$a \sum_{} x_{i} + b \sum_{} x_{i}^{3} + c \sum_{} x_{i}^{2}$

10.

Fit the parabola $y = a + bx + {cx}^{2}$ , if their normal equations are $9 a + 60 c = 11$ , $60 b = 51$ and $60 a + 708 c = - 9$ .

(a)	$y = 0.5599 + 0.85 x - 0.2673 x^{2}$
(b)	$y = - 0.5599 + 0.85 x^{2} - 0.2673 x^{3}$
(c)	$y = - 0.5599 + 0.85 x - 0.2673 x^{2}$
(d)	$y = - 0.5599 x^{2} + 0.85 x - 0.2673$

Showing 1 to 10 out of 18 Questions