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Test: Correlation And Regression- 6

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Correlation And Regression- 6

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Attempt Test: Correlation And Regression- 6 | 40 questions in 40 minutes | Mock test for CA Foundation preparation | Free important questions MCQ to study Quantitative Aptitude for CA CPT for CA Foundation Exam | Download free PDF with solutions

QUESTION: 1

Correlation coefficient is dependent of the choice of both origin & the scale of observations

A.
True
B.
False
C.
Both
D.
None

Solution:

QUESTION: 2

Given below the information about the capital employed and profit earned by a company over the last twenty five years:

Correlation coefficient between capital and profit =0.92. The sum of the regression coefficient for the above data would be:

A.
1.871
B.
2.358
C.
1.968
D.
2.346

Solution:

QUESTION: 3

Given the following data:

Coefficient of correlation = 0.6
What is the most likely value of y when x = 90?

A.
90
B.
103
C.
104
D.
107

Solution:

QUESTION: 4

If high values of one tend to low values of the other, they are said to be

A.
Negatively correlated
B.
Inversely correlated
C.
Both
D.
None

Solution:

QUESTION: 5

___________ is concerned with the measurement of the “strength of association” between variables.

A.
Correlation
B.
Regression
C.
Both
D.
None

Solution:

QUESTION: 6

The two lines of regression are given by
8x+10y=25 and 16x+5y=12 respectively
If the variance of x is 25, what is the standard deviation of y?

A.
16
B.
8
C.
64
D.
4

Solution:

QUESTION: 7

The regression equation of y on x for the following data:

Is given by

A.
y=1.2x - 15
B.
y=1.2x+15
C.
y=0.93x -14.64
D.
y=1.5x-10.89

Solution:

QUESTION: 8

The two regression coefficients for the following data:

are

A.
1.2 and 0.4
B.
1.6 and 0.8
C.
1.7 and 0.8
D.
1.8 and 0.3

Solution:

QUESTION: 9

The coefficient of correlation between cost of advertisement and sales of a product on the basis of the following data:

is:

A.
0.85
B.
0.89
C.
0.95
D.
0.98

Solution:

QUESTION: 10

_________ gives the mathematical relationship of the variables.

A.
Correlation
B.
Regression
C.
Both
D.
None

Solution:

QUESTION: 11

What is the coefficient of concurrent deviations for the following data:

A.
-0.43
B.
0.43
C.
0.5
D.
none

Solution:

QUESTION: 12

If y=3x+4 is the regression line of y on x and the arithmetic mean of x is -1, what is the arithmetic mean of y?

A.
1
B.
-1
C.
7
D.
None of these

Solution:

QUESTION: 13

Given that for twenty pairs of observations, ?xu=525, ?x=129, ?u=97, ?x²=687, ?u²=427 and y=10-3u, the coefficient of correlation between x and y is

A.
-0.7
B.
0.74
C.
-0.74
D.
0.75

Solution:

QUESTION: 14

What is the coefficient of correlation between the ages of husbands and wives from the following data?

A.
0.58
B.
0.98
C.
0.89
D.
0.92

Solution:

QUESTION: 15

The following results relate to bivariate date on (x, y):
Σxy=414, ∑x=120, ∑y=90, ∑x²=600, ∑y²=300, n=30. Later or, it was known that two pairs of observations (12, 11) and (6, 8) were wrongly taken, the correct pairs of observations being (10,9) and (8, 10). The corrected value of the correlation coefficient is

A.
0.752
B.
0.768
C.
0.846
D.
0.953

Solution:

QUESTION: 16

What is the value of Rank correlation coefficient between the following marks in physics and Chemistry:

A.
0.782
B.
0.696
C.
0.932
D.
0.857

Solution:

QUESTION: 17

Eight contestants in a musical contest were ranked by two judges A and B in the following manner:

The rank correlation coefficient

A.
0.65
B.
0.63
C.
0.6
D.
0.57

Solution:

QUESTION: 18

The following table provides the distribution of items according to size groups and also the number of defectives:

The correlation coefficient between size and defectives is

A.
0.25
B.
0.12
C.
0.14
D.
0.07

Solution:

QUESTION: 19

If u = 2x+5 and v=-3y-6 and regression coefficient of y on x is 2.4, what is the regression coefficient of v on u?

A.
3.6
B.
-3.6
C.
2.4
D.
-2.4

Solution:

QUESTION: 20

What is the coefficient of correlation from the following data?

A.
0.75
B.
-0.75
C.
-0.85
D.
0.82

Solution:

QUESTION: 21

Following are the marks of 10 students in Botany and Zoology:

The coefficient of rank correlation between marks in Botany and Zoology is

A.
0.65
B.
0.70
C.
0.72
D.
0.75

Solution:

QUESTION: 22

If 4y-5x=15 is the regression line of y on x and the coefficient of correlation between x and y is 0.75, what is the value of the regression coefficient of x on y?

A.
0.45
B.
0.9375
C.
0.6
D.
None of these

Solution:

QUESTION: 23

For two variables x and y, it is known that cov (x, y)=80, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is

A.
7
B.
8
C.
9
D.
10

Solution:

ANSWER :- d

Solution :- Covariance between X and Y is: C(X,Y)=80

Variance of X is: V(X)=16

Variance of Y is: V(Y)=E(Y−E(Y))^2=250/n

The Coefficient of correlation between X and Y is:

ρ(X,Y)=C(X,Y)/[√V(X)√V(Y)

= 80/√16*√250/n

=80√n/(√16*√250)

=√=80n/20*√10)

=4√n/10

Check that 4√n10 > 1 ∀n∈N,but the coefficient of correlation must always be less than or equal to 1.

QUESTION: 24

The coefficient of correlation between x and y where

is:

A.
0.655
B.
0.68
C.
0.73
D.
0.758

Solution:

QUESTION: 25

f(x) = x²/e^xthen f’(1) is equal to _________.

A.
-1/e
B.
1/e
C.
e
D.
None of these

Solution:

QUESTION: 26

If f(x) = x^k and f’(1) = 10 the value of k is

A.
10
B.
-10
C.
1/10
D.
None of these

Solution:

QUESTION: 27

If f(x) = then the values of x for which f’(x) = 0 is

A.
B.
C.
2
D.
None of these

Solution:

QUESTION: 28

If y= then y y₁ (where y₁= dy/dx) is equal to

A.
-x
B.
x
C.
1/x
D.
None of these

Solution:

QUESTION: 29

If y = e^x+ e^-x then is equal to

A.
1
B.
-1
C.
0
D.
None of these

Solution:

QUESTION: 30

Given f(x) = 4x³+ 3x²- 2x + 5 and is

A.
x⁴+ x³- x²+ 5x
B.
x⁴+ x³- x²+ 5x + k
C.
12x²+ 6x - 2x²
D.
None of these

Solution:

QUESTION: 31

If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?

A.
More than 100
B.
More than 10
C.
Less than 10
D.
More than 1.25

Solution:

QUESTION: 32

What are the limits of the two regression coefficients?

A.
No limit
B.
Must be positive
C.
One positive and the other negative
D.
Product of the regression coefficient must be numerically less than unity

Solution:

QUESTION: 33

If the coefficient of correlation between two variables is 0.7 then the percentage of variation unaccounted for is

A.
70%
B.
30%
C.
51%
D.
49%

Solution:

Step-by-step explanation:

Given: the coefficient of correlation between two variables is 0.7.

then the percentage of variation accounted for is given by

= square of coefficient of correlation

= 0.7^2 = 0.49

then the percentage of variation unaccounted for is = 1-0.49 =0.51

hence option c is correct

Read more on Brainly.in - https://brainly.in/question/13170464#readmore

QUESTION: 34

If y = a+bx, then what is the coefficient of correlation between x and y?

A.
1
B.
-1
C.
1 or -1 according as b > 0 or b < 0
D.
None of these

Solution:

QUESTION: 35

If there are two variables x and y, then the number of regression equations could be

A.
1
B.
2
C.
Any number
D.
3

Solution:

QUESTION: 36

If cov(x, y) = 15, what restrictions should be put for the standard deviations of x and y?

A.
No restriction
B.
The product of the standard deviations should be more than 15
C.
The product of the standard deviations should be less than 15
D.
The sum of the standard deviation should be less than 15

Solution:

QUESTION: 37

The regression coefficient remain unchanged due to a

A.
Shift of origin
B.
Shift of scale
C.
Both (a) and (b)
D.
(a) or (b).

Solution:

QUESTION: 38

The regression line of y on is derived by

A.
The minimization of vertical distances in the scatter diagram
B.
The minimization of horizontal distances in the scatter diagram
C.
Both (a) and (b)
D.
(a) or (b)

Solution:

QUESTION: 39

If the coefficient of correlation between two variables is -0.9, then the coefficient of determination is

A.
0.9
B.
0.81
C.
0.1
D.
0.19

Solution:

QUESTION: 40

The two lines regression become identical when

A.
r = 1
B.
r =-1
C.
r = 0
D.
(a) or (b)

Solution:

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Test: Correlation And Regression- 6

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Correlation And Regression- 6

Correlation coefficient is dependent of the choice of both origin & the scale of observations

Given below the information about the capital employed and profit earned by a company over the last twenty five years:

Correlation coefficient between capital and profit =0.92. The sum of the regression coefficient for the above data would be:

Given the following data:

Coefficient of correlation = 0.6
What is the most likely value of y when x = 90?

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