Calculation of Correlation Coefficient

Q.

The relationship between the correlation coefficient $r$ and the regression coefficient $b_{xy}$, and $b_{yx}$is

1. $r=\frac{1}{2}(b_{xy}+b_{yx})$

2. $r=\sqrt{b_{xy}.b_{yx}}$

3. $r={(b_{xy}{b}_{yx})}^2$

4. $r=b_{xy}+b_{yx}$

Q.

If the correlation between $x$ and $y$ is $r$, then between $y$ and $x$ correlation will be:

1. $-r$

2. $\frac{1}{r}$

3. $r$

4. $1-r$

Q.

From a random sample space, $5$ students have been selected. Their marks in Maths and Statistics are given below. The rank correlation coefficient is

Roll number	1	2	3	4	5
Marks in maths	85	60	73	40	90
marks in statistics	93	75	65	50	80

1. $0.8$

2. $0.6$

3. $0.5$

4. $-0.8$

Q.

If the variances of two variables $x$ and $y$ are respectively $9$ and $16$ and their covariance is $8$, then their coefficient of correlation is

1. $\frac{2}{3}$

2. $\frac{8}{3\sqrt{2}}$

3. $\frac{9}{8\sqrt{2}}$

4. $\frac{2}{9}$

Q.

Karl Pearsons coefficient of rank correlation between the ranks obtained by ten students in Mathematics and Chemistry in a class test as given below is: Rank in Mathematics $12345678910$. Rank in Chemistry $31051294876$

1. $0.224$

2. $0.204$

3. $0.240$

4. None of these

Q. Find correlation coefficient $f(x,y)$, where
$cov(x,y)=-2.25$,
$var\left(x\right)=6.25$,
and $var\left(y\right)=20.25$