Step Deviation Method to Calculate R

Q.

If Var $\left(x\right)=8.25$ , Var $\left(y\right)=33.96$ and Covariance $(x,y)=10.2$ , then the correlation coefficient is

1. $0.89$

2. $–0.98$

3. $0.61$

4. $–0.16$

Q.

The regression of savings $\left(s\right)$ of a family on income $y$may be expressed as $s=a+\left(\frac{y}{m}\right)$, where $a$ and $m$ are constants. In a random sample of $100$ families, the variance of savings is one-quarter of the variance of incomes and the correlation is found to be $0.4$ the value of $m$ is

1. $2$

2. $5$

3. $8$

4. None of these

Q.

For the given data, the calculation corresponding to all value of pairs $(x,y)$ is following $\sum {(x-\overline{x})}^2=36,\sum {(y-\overline{y})}^2=25,\sum (x-\overline{x})\sum (y-\overline{y})=20$. Then the Karl Pearson’s correlation coefficient is

1. $0.2$

2. $0.5$

3. $0.66$

4. $0.33$