Compute Karl Pearson's Coefficient of Correlation between sales and expenditures of a firm for six months.

Sales (in lakh of ₹)	$18$	$20$	$27$	$20$	$21$	$29$
Expenditure (in lakh of ₹)	$23$	$27$	$28$	$28$	$29$	$30$

 

Find correlation coefficient:

Find the coefficient of correlation from the following data: 

Prove that though covariance is independent of the choice of origin it depends upon the scale. If $u=ax+b, v=cy+d,$ show that $\mathrm{cov} \left(u\mathit{,}\mathit{ }v\right)=a\mathit{.}c.\mathrm{cov} \left(x\mathit{,}\mathit{ }\mathrm{y}\right)$.

Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.

$\begin{array}{|cccccccccc|}\hline x& 9& 8& 7& 6& 5& 4& 3& 2& 1\\ y& 15& 16& 14& 13& 11& 12& 10& 8& 9\\ \hline\end{array}$

Calculate the covariance of the following bivariate data :

Calculate the Spearman’s rank correlation coefficient between price and supply from the following data.

$\begin{array}{|ccccccccc|}\hline \text{ Price }& 4& 6& 8& 10& 12& 14& 16& 18\\ \text{ Supply }& 10& 15& 20& 25& 30& 35& 40& 45\\ \hline\end{array}$

Calculate the covariance of observations $(3, 5), \left(6, 7\right), (9, 9), (12, 11) (15,13), (18, 15), (21, 17), (24, 19)$, using assumed means $A=13$ and $B =12$.

Calculate the coefficient of correlation for the following data using ranks.

$\begin{array}{|lllllll|}\hline \text{ Mark in Tamil }& 29& 24& 25& 27& 30& 31\\ \text{ Mark in English }& 29& 19& 30& 33& 37& 36\\ \hline\end{array}$

 Calculate the Karl Pearson’s correlation coefficient between the marks (out of 10) in statistics and mathematics of 6 students.

$\begin{array}{|lcccccc|}\hline \text{ Student }& 1& 2& 3& 4& 5& 6\\ \text{ Statistics }& 7& 4& 6& 9& 3& 8\\ \text{ Mathematics }& 8& 5& 4& 8& 3& 6\\ \hline\end{array}$