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$n=25,\sum x=125,\sum x^2=650, \sum y=100,\sum y^2=460,\sum xy=508$. It was observed that two pair of values of $(x,y)$ were copied as $ (6,14)$ and $(8,6) $ instead of $(8,12),(6,8).$ The correct correlation coefficient is 

statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

  1. $0.667$

  2. $0.87$

  3. $-0.25$

  4. $0.356$

Show answer
Correct Option: A
Explanation:

Corrected $\sum x=125-6-8+8+6=125$

Corrected $\sum y=100-14-6+12+8=100$
Corrected $\sum x^2=650-(6)^2-(8)^2+(6)^2+(8)^2=650$
Corrected $\sum y^2=460-(14)^2-(6)^2+(12)^2+(8)^2=436$
Corrected $\sum xy=508-6\times 18-8\times 6+8\times 12+6\times 8=520$
The formula for Pearson product moment correlation is
$r=\dfrac{n\sum xy-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}$

    $=\dfrac{25\times 520-125\times 100}{\sqrt{[25\times 650-(125)^2][25\times 436-(100)^2]}}$

   $=\dfrac{13000-12500}{\sqrt{[16250-15625][10900-10000]}}$

   $=\dfrac{500}{\sqrt{[625][900]}}$

   $=\dfrac{500}{(25)(30)}$

   $=\dfrac{2}{3}$

   $=0.667$

The coefficient of correlation when coefficients of regression are $0.2$ and $1.8$ is

statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

  1. $0.36$

  2. $0.2$

  3. $0.6$

  4. $0.9$

Show answer
Correct Option: C
Explanation:

$Given\quad { b } _{ xy }=0.2\\ { b } _{ yx }=0.8\\ r=\sqrt { { b } _{ xy }\times { b } _{ yx } } \\ r=\sqrt { 0.36 } \\ r=0.6$

Where r is coefficient of correlation.

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

Show answer
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. $0.5\lt r \lt0.699$

Show answer
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. $-10\ and \ 10$

Show answer
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. $r=-1$

Show answer
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. $\dfrac{\sum xy}{\sigma _x \sigma _y}$

Show answer
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

Show answer
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.