Properties of Regression Coefficients

The two regression lines are $9x+3y=46$ and $3x+12y=19$. Identify which one of these is the regression line of $y$ on $x$ and which one is that of $x$ on $y$.

The regression lines of $y$ on $x$ and $x$ on $y$ respectively given as $y=x+5$ and $16x=9y+95$. Then ${\sigma }_y=4$, the find the value of $\overline{x}, \overline{y}, {\sigma }_x$ and $r_{xy}$. Also, find the estimate of $x$ when $y=12$ and justify your answer.

State the differences between correlation and regression from their definitions.

State the differences between correlation and regression

From the equation of two regression lines, $4x+3y+7=0$ and $3x+4y+8=0$, find the coefficient of correlation.

Find the standard deviation of $Y$ given that $V\left(X\right)$ is $16$, $b_{XY} = 0.8$, $r_{XY}=0.5$.

If the regression coefficients are $b_{yx}=-0·2354$ and $b_{xy}=-0·4257$, then find the correlation coefficient.(Answer upto three decimals).

If the regression coefficient of $X$ on $Y$ is $8$ and the regression coefficient of $Y$ on $X$ is $2$, then find the correlation coefficient.

Find the regression coefficient of $y$ on $x$ for the following data : $\Sigma x=80, \Sigma y=105, \Sigma x^2=800, \Sigma y^2=2000, \Sigma xy=1200 \mathrm{and} \mathrm{n}=10$. (answer up to two decimal places).

If the two coefficients of regression are $-0.4$ and $-1.4$, find the coefficient of correlation.(answer up to $3$ decimal places).

From the given data

The coefficient of correlation is $\frac{2}{3}$. Find the regression coefficients $b_{yx}$ and $b_{xy}$ respectively.

Find the coefficient of correlation from the following regression lines $x-2y+3=0$, $4x-5y+1=0$.(Answer up to four decimal places).

If the regression coefficients are $b_{yx}=-0·3235$ and $b_{xy}=-0·4583$, then find the correlation coefficient.

The following results were obtained with respect to two variables $x$ and $y$, $\Sigma x=30, \Sigma y=42, \Sigma xy=199, \Sigma x^2=184, \Sigma y^2=318, n=6$. Find the regression coefficients for $y$ on $x$ and $x$ on $y$ respectively. (Answer upto four decimal places).

Find the standard deviation of $Y$ given that $V\left(X\right)$ is $36$, $b_{XY} = 0.8$, $r_{XY}=0.5$.

If the regression coefficient of $X$ on $Y$ is $16$ and the regression coefficient of $Y$ on $X$ is $4$, then find the correlation coefficient.

Find the regression coefficient of $y$ on $x$ for the following data : $\Sigma x=60, \Sigma y=105, \Sigma x^2=800, \Sigma y^2=2000, \Sigma xy=1200 \mathrm{and} \mathrm{n}=10$. (answer up to four decimal places).

If the two coefficients of regression are $-0.6$ and $-1.4$, find the coefficient of correlation.(answer up to $3$ decimal places).

Find the regression coefficient of $X$ on $Y$ if the correlation coefficient is $\frac{1}{6}$ and regression coefficient of $Y$ on $X$ is $\frac{1}{9}$.

If the regression coefficient of $X$ on $Y$ is $-\frac{1}{9}$ and the regression coefficient of $Y$ on $X$ is $-\frac{1}{4}$, then find the correlation coefficient.