There is a moderate positive linear correlation between variables $x$ and $y$. The regression line for $y$ on $x$ is $y=2x+1$, and it was determined from a table of values where $x$ is such that
$3\le x\le 12$.

Explain why it is not valid to use the regression line to estimate the value of $x$ when $y=20$.

Find the line of regression of $y$ on $x$ from the following table.

Hence, estimate the value of $y$ when $x=6$.

The following results were obtained with respect to two variables $x$ and $y$:

$\sum x=15,\sum y=25,\sum xy=83,\sum x^2=55,\sum y^2=135\text{ and }n=5$

Find the regression coefficient $b_{xy}$

Find the equation of the regression line of $y$ on $x$, if the observations $\left(x,y\right)$ are as follows:

$(1,4), (2,8), (3,2), (4,12), (5,10), (6,14), (7,16), (8,6), (9,18)$.

Also, find the estimated value of $y$ when $x=14$.

Find the regression coefficients $b_{yx}, b_{xy}$ and correlation coefficient $\text{'}r\text{'}$ for the following data:

$(2,8), (6,8), (4,5), (7,6), (5,2)$

The following results were obtained with respect to two variables $x$ and $y$:

$\sum x=15,\sum y=25,\sum xy=83,\sum x^2=55,\sum y^2=135\text{ and }n=5$

Find the regression equation of $x$ on $y$.

From the given data

and coefficient correlation $\frac{2}{3}$. Find regression line of $x$ on $y$.

Find the line of regression of $y$ on $x$ for the following data :

Find the equation of the regression line of $y$ on $x$, if the observations $(x_i,y_i)$ are :

$\left(1,4\right), \left(2,8\right), \left(3,2\right), \left(4,12\right), \left(5,10\right), \left(6,14\right), \left(7,16\right), \left(8,6\right), \left(9,18\right).$

Also draw the regression line of $y$ on $x$.