Correlation Test

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Correlation Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

What is the formula to calculate Spearman's rank correlation coefficient when ranks are not repeated.

A
$$R=\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

B
$$R=1-\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

C
$$R=-\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

D
$$R=1+\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

Solution

When ranks are not repeated Speraman's rank coefficient $$=R=1-\dfrac { 6\sum { { d }_{ i }^{ 2 } } }{ n({ n }^{ 2 }-1) } $$
$$'n'$$ is the number of observations
$$'{ d }_{ i }'$$ is the difference in rank for $${i}^{th}$$ observation.
So option $$B$$ is corrrect.
Question 2
1 / -0

For two variables $$x$$ and $$y$$ regression equations are given as $$7x-3y-18=0$$ and $$4x-y-11=0$$ then the correlation coefficient between $$x$$ and $$y$$ is

A
$$0.7048$$

B
$$0.7500$$

C
$$0.7638$$

D
None of the above

Solution

Let $$7x-3y-18=0$$ represents the regression line of $$y$$ on $$x$$
$$\Rightarrow y=-6+\dfrac { 7 }{ 3 } x\\ \Rightarrow { b }_{ yx }=\dfrac { 7 }{ 3 } $$
Then $$4x-y-11=0$$ is the regression line of $$x$$ on $$y$$.
$$\Rightarrow x=\frac { 11 }{ 4 } +\dfrac { y }{ 4 } \\ \Rightarrow { b }_{ xy }=\dfrac { 1 }{ 4 } $$
Both $${ b }_{ yx }$$ and $${ b }_{ yx }$$ are positive.
$$\Rightarrow r=\sqrt { { b }_{ yx }\times { b }_{ xy } } \\ \Rightarrow r=\sqrt { \dfrac { 7 }{ 3 } \times \dfrac { 1 }{ 4 } } =0.7638$$
So, option C is correct.
Question 3
1 / -0

If the covariance between x and y is $$30$$, variance of x is $$25$$ and variance of y is $$144$$, then what is the correlation coefficient?

A
$$0.4$$

B
$$0.5$$

C
$$0.6$$

D
$$0.7$$

Solution

Given:-
$$Cov(x,y)=30$$
$$V(x)=25$$
$$V(y)=144$$
As we know formula of Corelation coefficient is$$:-$$
Let $$r$$ be Corelation coefficient of $$x,y$$
Then,
$$r=\dfrac{Covariance(x,y)}{\sqrt{V(x)\times V(y)}}$$
on solving$$:-$$
$$\Rightarrow r=\dfrac{30}{\sqrt{25\times 144}}$$
$$\Rightarrow r=0.5$$
Question 4
1 / -0

Correlation coefficient is denoted by the letter________.

A
'C'

B
'L'

C
'Co'

D
'r'

Solution

The correlation coefficient is denoted by the letter 'r' so as to represent the interdependence between two variables in a set of data, i.e., how strongly they are related.
Question 5
1 / -0

Which of the following is advisable to use while interpreting the value of co-efficient correlation?

A
Square of the co-efficient of correlation

B
Probable error

C
Scatter diagram

D
Correlation graph

Solution

Square of the coefficient of correlation is advisable to use because it makes the data easy to be interpreted easily by the researcher. This value represents the variation in one variable that may be explained by another variable.
Question 6
1 / -0

The formula of Karl Pearson's co-efficient of correlation is ________.

A
$$r = 1 - \dfrac{6\Sigma{{D}_2}}{{{N}_{3}} - N}$$

B
$$r = \dfrac{{\Sigma}{x}{y}}{{N}{\sigma}{x}{\sigma}{y}}$$

C
$$ r = \dfrac {{\sigma}{x}}{{\sigma}{y}}$$

D
$$ r = \dfrac {{\sigma}{y}}{{\sigma}{x}}$$

Solution

The correct formula foe the karl pearson's coefficient if correlation is given in the option B. The value of coefficient always lies between -1 to +1 that measures the strength of linear relationship between two variables.
Question 7
1 / -0

Defects of Karl Pearson's method is/are________.

A
it consumes more time

B
the value of correlation is affected by extreme values

C
if the data are not homogeneous, the co-efficient of correlation will give a wrong picture

D
all of the above

Solution

Disadvantages of using karl pearson's method is that it is avery time consuming and lengthy process and it gets affected by extreme values and it may give a wrong image if the variables are not of same nature or homogeneous.
Question 8
1 / -0

The formula of product moment correlation is ______________.

A
$$r=\dfrac{S_{xy}}{\sqrt{S_xS_y}}$$ ; S= Standard error

B
$$ r = \dfrac {{\sigma}_{xy}}{{N}{\sigma}_{x}{\sigma}_{y}}$$ ; N=number of variables

C
$$ r = \dfrac {{-r}^2}{\sqrt{N}}$$

D
$$ r = \dfrac {{6}{\sigma}^2_{{d}}}{n({n}^2 - {1})}$$

Solution

The formula for product moment correlation given in the option A is correct and measures the linear relationship between two variables. The formula basically tries to show how strongly are the two variables (x and y in this case) are related to each other. A correlation could be weakly or strongly correlated depending on the value of 'r'.
Question 9
1 / -0

What are the assumptions of correlation co-efficient?
I. There is non-linear relationship between two variables.
II. The two variables have cause and effect relationship.
III. Each variable is affected by a large number of independent causes.
IV. If the error is reduced to minimum, the co-efficient of correlation is more reliable.

A
I, II and III

B
II, Ill and IV

C
I, II and IV

D
All of the above

Solution

For the calculation of correlation, it is assumed that there exists a cause and effect relationship between variables, every variable is affected by many factors or causes and correlation is more reliable if the error is less.
Question 10
1 / -0

Rank correlation is useful where____________.

A
we place things in an order of merit

B
the number of variables is more than 30

C
there is a need to calculate the co-efficient of frequency distribution

D
none of the above

Solution

Rank correlation technique measures the strength and direction between two variables by providing suitable ranks to the concerned variables, e.g. marks of students in a class can be easily ranked.

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Re-Attempt Weekly Quiz Competition

Correlation Test - 15

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Correlation Test - 15

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SHARING IS CARING

Question 1

$$R=\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

$$R=1-\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

$$R=-\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

$$R=1+\dfrac{6\sum d_{i}^{2}}{n(n^{2}-1)}$$

Solution

Question 2

$$0.7048$$

$$0.7500$$

$$0.7638$$

None of the above

Solution

Question 3

$$0.4$$

$$0.5$$

$$0.6$$

$$0.7$$

Solution

Question 4

'C'

'L'

'Co'

'r'

Solution

Question 5

Square of the co-efficient of correlation

Probable error

Scatter diagram

Correlation graph

Solution

Question 6

$$r = 1 - \dfrac{6\Sigma{{D}_2}}{{{N}_{3}} - N}$$

$$r = \dfrac{{\Sigma}{x}{y}}{{N}{\sigma}{x}{\sigma}{y}}$$

$$ r = \dfrac {{\sigma}{x}}{{\sigma}{y}}$$

$$ r = \dfrac {{\sigma}{y}}{{\sigma}{x}}$$

Solution

Question 7

it consumes more time

the value of correlation is affected by extreme values

if the data are not homogeneous, the co-efficient of correlation will give a wrong picture

all of the above

Solution

Question 8

$$r=\dfrac{S_{xy}}{\sqrt{S_xS_y}}$$ ; S= Standard error

$$ r = \dfrac {{\sigma}_{xy}}{{N}{\sigma}_{x}{\sigma}_{y}}$$ ; N=number of variables

$$ r = \dfrac {{-r}^2}{\sqrt{N}}$$

$$ r = \dfrac {{6}{\sigma}^2_{{d}}}{n({n}^2 - {1})}$$

Solution

Question 9

I, II and III

II, Ill and IV

I, II and IV

All of the above

Solution

Question 10

we place things in an order of merit

the number of variables is more than 30

there is a need to calculate the co-efficient of frequency distribution

none of the above

Solution

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