Find the regression equation of $y$ on $x$ for the results obtained below :

$\sum _{}^{}x=30, \sum _{}^{}y=42, \sum _{}^{}xy=199, \sum _{}^{}{x}^2=184, \sum _{}^{}{y}^2=318, n=6$.

The results obtained with respect to two variables $x$ and $y$ are

$\sum _{}^{}x=30, \sum _{}^{}y=42, \sum _{}^{}xy=199, \sum _{}^{}{x}^2=184, \sum _{}^{}{y}^2=318, n=6$.

Find the likely value of $y$ when $x=10.$ (up to three places of decimal)

Out of the two regression lines, find the line of regression of $y$ on $x$:

$3x+12y=8, 9x+3y=46$

Find the coefficient of correlation from the regression lines $x-2y+3=0$ and $4x-5y+1=0$.

Find the coefficient of correlation from the given regression lines. (Up to three places of decimal).

$3x+4y-7=0, 4x+y-5=0$

The following table shows the mean and standard deviation of the marks of Mathematics and Physics scored by the students of a school:

The correlation coefficient between the given marks is $0.86.$ Estimate the likely marks in Physics if the marks in Mathematics are $92.$