curve-fitting

APPLIED MATHEMATICS

SE Computer Sceience and Engineering

M.C.Q.on Curve Fitting

Mr. S.S. Salgare

Department of Mathematics

Sanjay Ghodawat Group of Institutions,

Atigre

Mr. S.S. Salgare Department of Mathematics

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M.C.Q. on Curve Fitting

1) The range of the correlation coefficient is?





A) (−1, 1)





A) (−1, 1)

B) (0, 1)





A) (−1, 1)

B) (0, 1)

C) [−1, 1]





A) (−1, 1)

B) (0, 1)

C) [−1, 1]

D) None of these





A) (−1, 1)

B) (0, 1)

C) [−1, 1]

D) None of these




2) For estimating value of variable X





A) Regression equation of Y on

X is used






X is used

B) Regression equation of X on

Y is used






X is used


Y is used

C) Both regression equations of

Y on X and X on Y are used






X is used


Y is used



D) None of these






X is used


Y is used



D) None of these




3) Which of the following can not be the possible value of a

correlation coefficent?






A) r= 1.99






A) r= 1.99

B) r= 0






A) r= 1.99

B) r= 0

C) r= - 0.73






A) r= 1.99

B) r= 0

C) r= - 0.73

D) r= - 1.0






A) r= 1.99

B) r= 0

C) r= - 0.73

D) r= - 1.0




4) Which of the following indicates a strong negative correlation?





A) r= - 0.846





A) r= - 0.846

B) r= - 0.793





A) r= - 0.846

B) r= - 0.793

C) r= 0.913





A) r= - 0.846

B) r= - 0.793

C) r= 0.913

D) r= 0.45





A) r= - 0.846

B) r= - 0.793

C) r= 0.913

D) r= 0.45




5) Which of the following indicates a negative correlation of lower

degree ?





degree ?

A) r= - 0.23





degree ?

A) r= - 0.23

B) r= - 0.58





degree ?

A) r= - 0.23

B) r= - 0.58

C) r= - 0.99





degree ?

A) r= - 0.23

B) r= - 0.58

C) r= - 0.99

D) r= - 0.09





degree ?

A) r= - 0.23

B) r= - 0.58

C) r= - 0.99

D) r= - 0.09




6) With the help of correlation coefficient one can study





A) Relationship between any

two attributes






two attributes

B) Relationship between any

two Variables






two attributes


two Variables

C) Relationship of more than

two variables






two attributes


two Variables


two variables

D) None of these






two attributes


two Variables


two variables

D) None of these




7) In a scatter diagram, all the points lie on a rising straight line





A) Perfect positive correlation






B) Perfect negative correlation







C) no correlation







C) no correlation

D) None of the above







C) no correlation

D) None of the above




8) If equation of the line of regression of y on x is with positive

slope





slope

A) correlation coefficient is

positive





slope


positive

B) correlation coefficient is

negative





slope


positive


negative

C) no correlation between x and

y





slope


positive


negative


y

D) none of these





slope


positive


negative


y

D) none of these




9) If equation of the line of regression of y on x is with negative

slope





slope


positive





slope


positive


negative





slope


positive


negative


y





slope


positive


negative


y

D) none of these





slope


positive


negative


y

D) none of these




10) If the regression coefficient of X on Y and Y on X are -0.5 and

-0.5 respectivly then the correlation coefficent between X and Y is






A) 1






A) 1

B) 0.5






A) 1

B) 0.5

C) - 0.5






A) 1

B) 0.5

C) - 0.5

D) - 0.25






A) 1

B) 0.5

C) - 0.5

D) - 0.25




11) If regression coefficients are negative then






positive






positive


negative






positive


negative

C) correlation coefficient is

positive and negative






positive


negative



D) none of these






positive


negative



D) none of these




12) If regression coefficients are positive then






positive






positive


negative






positive


negative








positive


negative



D) none of these






positive


negative



D) none of these




13) The correlation measures the strength and direction of the non

linear relationship between two variables






A) Totally True






A) Totally True

B) Totally False






A) Totally True

B) Totally False

C) Partially true






A) Totally True

B) Totally False

C) Partially true

D) Partially False






A) Totally True

B) Totally False

C) Partially true

D) Partially False




14) Which of the following indicate negative correlation





A) Number of accidents and number of motor vechicals in a city.






B) price and sale of the commodity







C) Rainfall and production of cars








D) Advertising and sales








D) Advertising and sales




15) Which of the following indicate positive correlation





A) Both variables change in the

same direction






same direction

B) Both variables change in the

opposite direction






same direction


opposite direction

C) The graph is a horizontal

line






same direction


opposite direction


line

D) Sign of the correlation

coefficient is negative






same direction


opposite direction


line












same direction






same direction


opposite direction






same direction


opposite direction


line






same direction


opposite direction


line








same direction


opposite direction


line






17) Two variables X and Y are linearly related





A) If the value correlation

coefficient is 0 one







B) If the value correlation

coefficient is 0.2








coefficient is 0.2

C) If the value correlation

coefficient is ±1








coefficient is 0.2


coefficient is ±1

D) None of these








coefficient is 0.2


coefficient is ±1

D) None of these




18) Two variables X and Y are not linearly correlated














coefficient is 0.2








coefficient is 0.2


coefficient is ±1








coefficient is 0.2


coefficient is ±1

D) None of these








coefficient is 0.2


coefficient is ±1

D) None of these




19) In a scatter diagram, all the points are at random linearly

correlated





correlated






correlated







correlated



C) No correlation





correlated



C) No correlation

D) None of these





correlated



C) No correlation

D) None of these




20) In a scatter diagram, all the points lie on horizotal line


















C) No correlation







C) No correlation

D) None of these







C) No correlation

D) None of these




21) If two variables X and Y are independent of each other then

they have





they have






they have







they have



C) No correlation





they have



C) No correlation

D) None of these





they have



C) No correlation

D) None of these




22) The correlation coefficient r = ±1.23 will be





A) Possible





A) Possible

B) Some times possible





A) Possible


C) Not possible





A) Possible


C) Not possible

D) None of these





A) Possible


C) Not possible

D) None of these




23) The coefficient of correlation will have value zero then





A) X increasing and Y also

increasing






increasing

B) X decresing and Y also

decresing






increasing


decresing

C) X and Y be have randomly

Correlation






increasing


decresing


Correlation

D) None of these






increasing


decresing


Correlation

D) None of these




24) If the value of coefficient of correlation coefficient is nearer to

zero then the two variables under study have






A) Correlation






A) Correlation

B) No correlation






A) Correlation

B) No correlation

C) Correlation of lower degree






A) Correlation

B) No correlation


D) None of these






A) Correlation

B) No correlation


D) None of these




25) The value of coefficient of correlation can be positive, negative

and zero is





and zero is

A) Possible





and zero is

A) Possible

B) Not possible





and zero is

A) Possible

B) Not possible

C) Partially possible





and zero is

A) Possible

B) Not possible


D) None of these





and zero is

A) Possible

B) Not possible


D) None of these




26) A measure of the linear relationship between two variables is





A) correlation coefficient






B) regression coefficient







C) both I and II







C) both I and II

D) None of these







C) both I and II

D) None of these




27) The correlation measures the strength and direction of the







A) Totally True






A) Totally True

B) Totally False






A) Totally True

B) Totally False

C) Partially true






A) Totally True

B) Totally False

C) Partially true

D) Partially False






A) Totally True

B) Totally False

C) Partially true

D) Partially False




28) Regression means





A) A method of estimating the value of one variable when other is

known






known

B) A method of estimating the value of one variable when other is

unknown






known


unknown

C) First two options are true






known


unknown


D) Partially False






known


unknown


D) Partially False




29) The law y = ax 2 + bx converted to linear form as





A) Y = ax + b where Y = x y






B) Y = aX + b where Y = log y, X = log x







C) Y = ax + b where Y = y x








D) None of these








D) None of these




30) The principal of least squares state that





A) The sum of square of all

points from curve is

minimum







minimum

B) The sum of square of all


maximum







minimum



maximum

C) The sum of square root of

all points from curve is

minimum







minimum



maximum



minimum

D) The sum of square root of


maximum







minimum



maximum



minimum

D) The sum of square root of


maximum




31) To fit the straight line y = mx + c to n observations, the

normal equations are






A) ∑ y = n ∑ x + ∑ cm

∑ xy = c

∑ x 2 + c ∑ x






A) ∑ y = n ∑ x + ∑ cm

∑ xy = c

∑ x 2 + c ∑ x

B) ∑ y = m ∑ x + nc

∑ xy = m

∑ x 2 + c ∑ x






A) ∑ y = n ∑ x + ∑ cm

∑ xy = c

∑ x 2 + c ∑ x

B) ∑ y = m ∑ x + nc

∑ xy = m

∑ x 2 + c ∑ x

C) ∑ y = c ∑ x + m ∑ n

∑ xy = c

∑ x 2 + m ∑ x






A) ∑ y = n ∑ x + ∑ cm

∑ xy = c

∑ x 2 + c ∑ x

B) ∑ y = m ∑ x + nc

∑ xy = m

∑ x 2 + c ∑ x

C) ∑ y = c ∑ x + m ∑ n

∑ xy = c

∑ x 2 + m ∑ x

D) None of these






A) ∑ y = n ∑ x + ∑ cm

∑ xy = c

∑ x 2 + c ∑ x

B) ∑ y = m ∑ x + nc

∑ xy = m

∑ x 2 + c ∑ x

C) ∑ y = c ∑ x + m ∑ n

∑ xy = c

∑ x 2 + m ∑ x

D) None of these




32) To fit y = ab x by least squares method, normal equations are:





A) ∑ Y = nA + B ∑ x

∑ xY = A

∑ x + B

∑ x 2 ,

Y = log y, A =

log a, B log b





A) ∑ Y = nA + B ∑ x

∑ xY = A

∑ x + B

∑ x 2 ,

log a, B log b

Y = log y, A =

log a, B log b

B) ∑ Y = nB + A ∑ x

∑ xY = B

∑ x + A

∑ x 2 ,

Y = log y, A =





A) ∑ Y = nA + B ∑ ∑ ∑

x

∑ xY = A x + B x 2 ,

Y = log y, A =

log a, B log b

B) ∑ Y = nB + A ∑ ∑ ∑

x

∑ xY = B x + A x 2 ,

Y = log y, A =

log a, B log b

C) ∑ Y = nA + B ∑ x 2

∑ xY = A

∑ x + B

∑ x 2 ,

where Y = log y, A =

log a, B log b





A) ∑ Y = nA + B ∑ ∑ ∑

x

∑ xY = A x + B x 2 ,

Y = log y, A =

log a, B log b

B) ∑ Y = nB + A ∑ ∑ ∑

x

∑ xY = B x + A x 2 ,

Y = log y, A =

log a, B log b

C) ∑ Y = nA + B ∑ x 2

∑ xY = A

∑ x + B

∑ x 2 ,


log a, B log b

D) None of these





A) ∑ Y = nA + B ∑ ∑ ∑

x

∑ xY = A x + B x 2 ,

Y = log y, A =

log a, B log b

B) ∑ Y = nB + A ∑ ∑ ∑

x

∑ xY = B x + A x 2 ,

Y = log y, A =

log a, B log b

C) ∑ Y = nA + B ∑ x 2

∑ xY = A

∑ x + B

∑ x 2 ,


log a, B log b

D) None of these




33) Given

x 0 1 2

y 0 1.1 2.1

then the straight line of best fit y = a + bx then a = · · · and

b = · · ·




33) Given

x 0 1 2

y 0 1.1 2.1


b = · · ·

A) a = 1.0167, b = 0.05




33) Given

x 0 1 2

y 0 1.1 2.1


b = · · ·

A) a = 1.0167, b = 0.05

B) a = 0.0167, b = 1.05




33) Given

x 0 1 2

y 0 1.1 2.1


b = · · ·

A) a = 1.0167, b = 0.05

B) a = 0.0167, b = 1.05

C) a = 0.0167, b = 0.05




33) Given

x 0 1 2

y 0 1.1 2.1


b = · · ·

A) a = 1.0167, b = 0.05

B) a = 0.0167, b = 1.05

C) a = 0.0167, b = 0.05

D) a = 1.0167, b = 1.05




33) Given

x 0 1 2

y 0 1.1 2.1


b = · · ·

A) a = 1.0167, b = 0.05

B) a = 0.0167, b = 1.05

C) a = 0.0167, b = 0.05

D) a = 1.0167, b = 1.05




34) If r = 1, the regression coefficeents are:





A) 1, 1





A) 1, 1

B) −1, −1





A) 1, 1

B) −1, −1

C) 1, 1





A) 1, 1

B) −1, −1

C) 1, 1

D) None of these





A) 1, 1

B) −1, −1

C) 1, 1

D) None of these




35) The equations of regression line are y = 0.5x + a and

x = 0.4y + b then the correlation coefficient is






A) √ 0.2






A) √ 0.2

B) 0.45






A) √ 0.2

B) 0.45

C) − √ 0.2






A) √ 0.2

B) 0.45

C) − √ 0.2

D) 0.63






A) √ 0.2

B) 0.45

C) − √ 0.2

D) 0.63




36) If the correlation coefficient is zero, the two regression lines are





A) Parallel





A) Parallel

B) Perpendicular





A) Parallel

B) Perpendicular

C) coincident





A) Parallel

B) Perpendicular

C) coincident

D) inclined at 45 0





A) Parallel

B) Perpendicular

C) coincident

D) inclined at 45 0




37) Ifr 1 and r 2 are two regression coefficients, then sign of r 1 and

r 2 depends on





r 2 depends on

A) Lines of regression





r 2 depends on


B) correlation coefficient





r 2 depends on



C) coincident lines





r 2 depends on



C) coincident lines

D) None of these





r 2 depends on



C) coincident lines

D) None of these




38) If y = x + 1 and x = 3y − 7 are the two lines of regression the

values of ¯x, ȳ, r is






A) 2. 3, 3






A) 2. 3, 3

B) 2, 3, 1






A) 2. 3, 3

B) 2, 3, 1

C) 2, 3, √ 3






A) 2. 3, 3

B) 2, 3, 1

C) 2, 3, √ 3

D) √ 3, 3, √ 3






A) 2. 3, 3

B) 2, 3, 1

C) 2, 3, √ 3

D) √ 3, 3, √ 3




39) If the regression lines are perpendicular to each other, the

value of coefficient of correlation is






A) 0






A) 0

B) 1






A) 0

B) 1

C) -1






A) 0

B) 1

C) -1

D) 0.56






A) 0

B) 1

C) -1

D) 0.56




40) The minimum value of correlation coefficient is





A) 0





A) 0

B) 1





A) 0

B) 1

C) -1





A) 0

B) 1

C) -1

D) 0.56





A) 0

B) 1

C) -1

D) 0.56




41) The point of intersection of the two regression lines is





A) (¯x, 0)





A) (¯x, 0)

B) (0, ȳ)





A) (¯x, 0)

B) (0, ȳ)

C) (0, 0)





A) (¯x, 0)

B) (0, ȳ)

C) (0, 0)

D) (¯x, ȳ)





A) (¯x, 0)

B) (0, ȳ)

C) (0, 0)

D) (¯x, ȳ)




42) The equation of the line of regression of y on x is





A) (y − ȳ) = b xy (x − ¯x)





A) (y − ȳ) = b xy (x − ¯x)

B) (ȳ − y) = b yx (¯x − x)





A) (y − ȳ) = b xy (x − ¯x)

B) (ȳ − y) = b yx (¯x − x)

C) (x − ¯x) = b xy (y − ȳ)





A) (y − ȳ) = b xy (x − ¯x)

B) (ȳ − y) = b yx (¯x − x)

C) (x − ¯x) = b xy (y − ȳ)

D) (x − ¯x) = b yx (y − ȳ)





A) (y − ȳ) = b xy (x − ¯x)

B) (ȳ − y) = b yx (¯x − x)

C) (x − ¯x) = b xy (y − ȳ)

D) (x − ¯x) = b yx (y − ȳ)




43) Correlation coefficient is · · · mean between regression

coefficient





coefficient

A) Arithmetic

A.M.= x 1 + x 2 + · · · + x n

n





coefficient

A) Arithmetic

A.M.= x 1 + x 2 + · · · + x n

n

B) Harmonic

n

H,M.=

1

x 1

+ 1 x 2

+ · · · + 1 x n





coefficient

A) Arithmetic

A.M.= x 1 + x 2 + · · · + x n

n

B) Harmonic

n

H,M.=

1

x 1

+ 1 x 2

+ · · · + 1 x n

C) Geometric

G.M.=(x 1 .x 2 . · · · x n ) 1 n





coefficient

A) Arithmetic

A.M.= x 1 + x 2 + · · · + x n

n

B) Harmonic

n

H,M.=

1

x 1

+ 1 x 2

+ · · · + 1 x n

C) Geometric

G.M.=(x 1 .x 2 . · · · x n ) 1 n

D) None of These





coefficient

A) Arithmetic

A.M.= x 1 + x 2 + · · · + x n

n

B) Harmonic

n

H,M.=

1

x 1

+ 1 x 2

+ · · · + 1 x n

C) Geometric

G.M.=(x 1 .x 2 . · · · x n ) 1 n

D) None of These




44) When the variables are independent the two lines of regression

are





are

A) parallel





are

A) parallel

B) Perpendicular





are

A) parallel

B) Perpendicular

C) coincident





are

A) parallel

B) Perpendicular

C) coincident

D) inclined at 45 0





are

A) parallel

B) Perpendicular

C) coincident

D) inclined at 45 0




45) Arithmetic mean of the coefficient of regressions . . . than the

coefficient of correlation






A) Grater






A) Grater

B) Less






A) Grater

B) Less

C) Equal






A) Grater

B) Less

C) Equal

D) None of these






A) Grater

B) Less

C) Equal

D) None of these




46) If one of the regression coefficient is greater than unity, then

other must be





other must be

A) Equal to unity





other must be

A) Equal to unity

B) Grater then unity





other must be

A) Equal to unity


C) less then unity





other must be

A) Equal to unity


C) less then unity

D) None of these





other must be

A) Equal to unity


C) less then unity

D) None of these




47) The correlation between volume and pressure of the perfect

gas is





gas is

A) Positive





gas is

A) Positive

B) Negative





gas is

A) Positive

B) Negative

C) 0





gas is

A) Positive

B) Negative

C) 0

D) None of these





gas is

A) Positive

B) Negative

C) 0

D) None of these




48) The correlation between income and expenditure is





A) Positive





A) Positive

B) Negative





A) Positive

B) Negative

C) 0





A) Positive

B) Negative

C) 0

D) None of these





A) Positive

B) Negative

C) 0

D) None of these




49) Which of the following indicates a strong positive correlation?





A) r = 0





A) r = 0

B) r = −0.793





A) r = 0

B) r = −0.793

C) r = 0.913





A) r = 0

B) r = −0.793

C) r = 0.913

D) r = 0.45





A) r = 0

B) r = −0.793

C) r = 0.913

D) r = 0.45




50) If two regression coefficient are -0.1 and -0.9, the value of r is





A) 0.3





A) 0.3

B) -0.3





A) 0.3

B) -0.3

C) 0.5





A) 0.3

B) -0.3

C) 0.5

D) 0.5





A) 0.3

B) -0.3

C) 0.5

D) 0.5




51) Which method gives a unique set of values to the constants in

the equation of the fitting curves?






A) Horners method






A) Horners method

B) Method of least squares






A) Horners method


C) Interpolation






A) Horners method


C) Interpolation

D) Newtons Method






A) Horners method


C) Interpolation

D) Newtons Method




52) The line obtained by the method of least square is known as

the line of . . .





the line of . . .

A) straight line





the line of . . .

A) straight line

B) Interpolation





the line of . . .

A) straight line

B) Interpolation

C) best fit





the line of . . .

A) straight line

B) Interpolation

C) best fit

D) polynomial equation





the line of . . .

A) straight line

B) Interpolation

C) best fit

D) polynomial equation




Thank You !



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