There are two series of index numbers : $P$ for price index and $S$ for stock of a commodity. The mean and standard deviation of $P$ are $100 \mathrm{and} 8 \mathrm{and} \mathrm{of} S \mathrm{are} 103 \mathrm{and} 4$ respectively. The correlation coefficient between the two series is $0.4.$ With these data, obtain the regression lines of $P$ on $S$ and $S$ on $P$.

The line of regression of marks in statistics ($X$) on marks in accountancy ($Y$) for a class of $50$ students is $3Y-5X+180=0.$

Average score in accountancy is $44$ and variance of marks in statistics is $\frac{9}{16}$th of variance of marks in accountancy. Find the average score in statistics and also the coefficient of correlation between marks in statistics and accountancy.

From the equations of the two regression lines, $4x+3y+7=0 \mathrm{and} 3x+4y+8=0,$ find the means of $x$ and $y$.

From the equations of the two regression lines, $4x+3y+7=0 \mathrm{and} 3x+4y+8=0,$ find the regression coefficients.

From the equations of the two Regression lines, $4x+3y+7=0 \mathrm{and} 3x+4y+8=0,$ find the coefficient of Correlation.

Two random variables have Regression lines $3x+2y-26=0 \mathrm{and} 6x+y-31=0.$ Calculate the mean values of $x$ and $y$.

Two random variables have Regression lines $3x+2y-26=0 \mathrm{and} 6x+y-31=0.$ Calculate the coefficient of Correlation.

Two random variables have Regression lines $3x+2y-26=0 \mathrm{and} 6x+y-31=0.$ Calculate the standard deviation of $y$, given variance of $x$ is $25.$