Tag: correlation coefficients

Questions Related to correlation coefficients

Write True/False in the following statement:
If regression coefficient are $0.8$ and $0.2$ then the value of corelation coefficient is $+0.4$

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. True

  2. False

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Correct Option: A
Explanation:

Given:-

Coefficient of regression are $0.8$ and $0.2$.
Therefore,
Coefficient of correlation $= \sqrt{0.8 \cdot 0.2} = \sqrt{0.16} = 0.4$
Hence the given statement is true.

It is perfect correlaion if

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. $0.7\lt r\lt 0.99$

  2. $-0.7\gt r\gt -0.99$

  3. $r=1$

  4. $0.5\lt r \lt0.699$

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Correct Option: C

The coefficient of correlation is always between

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. $0\ and \ 1$

  2. $-1\ and \ 1$

  3. $-\infty \ and \ \infty$

  4. $-10\ and \ 10$

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Correct Option: B
Explanation:

$\Rightarrow$  Correlation coefficients are expressed as values between $-1$ and $+1$. 

$\Rightarrow$  A coefficient of $+1$ indicates a perfect positive correlation: A change in the value of one variable will predict a change in the same direction in the second variable. 
$\Rightarrow$  A coefficient of $-1$ indicates a perfect negative correlation: A change in the value of one variable predicts a change in the opposite direction in the second variable. 

It is moderate degree of relation if 

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. $-0.7\gt r\gt -0.99$

  2. $0.7\lt r\lt 0.99$

  3. $0.5\lt r \lt0.699$

  4. $r=-1$

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Correct Option: C

It is high degree of relation if 

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. $-0.7\gt r\gt -0.99$

  2. $0.7\lt r\lt 0.99$

  3. $0.5\lt r \lt0.699$

  4. $r=1$

Show answer
Correct Option: B

The formula for correlation coeficient $r$ of two variables $x$ and $y$ is 

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. $u _i=\dfrac{x _i-a}{h}$,

  2. $\dfrac{1}{n}\sum(x-\overline x)(y-\overline y)$

  3. $\dfrac{d _xd _y}{\sqrt{{\sum d _x}^2.{\sum d _y}^2}}$

  4. $\dfrac{\sum xy}{\sigma _x \sigma _y}$

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Correct Option: C

Write True/False in the following statement:
The value of correlation coefficient lies between $-2$ to $+2$

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. True

  2. False

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Correct Option: B
Explanation:

The value of correlation coefficient lies between $-1$ to $+1$.

Hence the given statement is false.

State the following statement is true or false

The value of coefficient of correlation is greater than $1$.

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. True

  2. False

Show answer
Correct Option: B
Explanation:
Value of coeff. of correlation lies between $-1$ and $+1$.
Depending on the strength & direction of linear relationship between two variable. 
Coeff. of correlation $\ngtr   1$
$\therefore $ Given statement is false.

State the following statement is True or False
The value of correlation coefficient is always $2$.

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. True

  2. False

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Correct Option: B
Explanation:

Correlation coefficient is the measure of the degree of linear relationship between two variables, usually labelled X and Y. While in regression the emphasis is on predicting one variable from the other, in correlation the emphasis is on the degree to which a linear model may describe the relationship between two variables. In regression the interest is directional, one variable is predicted and the other is the predictor; in correlation the interest is non-directional, the relationship is the critical aspect.

$-1\le r\le 1$

Hence statement is false

Consider the following statements :
1. Two independent variables are always uncorrelated.
2. The coefficient of correlation between two variables X and Y is positive. When X decreases then Y decreases.
Which of the above statements is/are correct ?

statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

  1. 1 only

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2

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Correct Option: C
Explanation:

Two independent variables have coefficient of correlation $0$, So they are always uncorrelated.

Positive coefficient means they both move in same direction, so if $X$ decreases then $Y$ also decreases.
So, both the statements are correct.
Hence, C is correct.