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QUESTION: 1

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

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:

Solution:

QUESTION: 3

Given the following data:

Coefficient of correlation = 0.6

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

Solution:

QUESTION: 4

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

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QUESTION: 5

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

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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?

Solution:

QUESTION: 7

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

Is given by

Solution:

QUESTION: 8

The two regression coefficients for the following data:

are

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QUESTION: 9

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

is:

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QUESTION: 10

_________ gives the mathematical relationship of the variables.

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QUESTION: 11

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

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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?

Solution:

QUESTION: 13

Given that for twenty pairs of observations, ?xu=525, ?x=129, ?u=97, ?x^{2}=687, ?u^{2}=427 and y=10-3u, the coefficient of correlation between x and y is

Solution:

QUESTION: 14

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

Solution:

QUESTION: 15

The following results relate to bivariate date on (x, y):

Σxy=414, ∑x=120, ∑y=90, ∑x^{2}=600, ∑y^{2}=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

Solution:

QUESTION: 16

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

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QUESTION: 17

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

The rank correlation coefficient

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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

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?

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QUESTION: 20

What is the coefficient of correlation from the following data?

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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

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?

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

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:

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QUESTION: 25

f(x) = x^{2}/e^{x }then f’(1) is equal to _________.

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QUESTION: 26

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

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QUESTION: 27

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

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QUESTION: 28

If y= then y y_{1} (where y_{1 }= dy/dx) is equal to

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QUESTION: 29

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

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QUESTION: 30

Given f(x) = 4x^{3 }+ 3x^{2 }- 2x + 5 and is

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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?

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QUESTION: 32

What are the limits of the two regression coefficients?

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QUESTION: 33

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

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

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QUESTION: 34

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

Solution:

QUESTION: 35

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

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QUESTION: 36

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

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QUESTION: 37

The regression coefficient remain unchanged due to a

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QUESTION: 38

The regression line of y on is derived by

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QUESTION: 39

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

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QUESTION: 40

The two lines regression become identical when

Solution:

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