Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

State whether the following statement is True or False:

b_xy is the slope of regression line of y on x

For the following bivariate data obtain the equations of two regression lines:

From the data of 20 pairs of observations on X and Y, following results are obtained.

`barx` = 199, `bary` = 94,

`sum(x_i - barx)^2` = 1200, `sum(y_i - bary)^2` = 300,

`sum(x_i - bar x)(y_i - bar y)` = –250

Find:

1. The line of regression of Y on X.
2. The line of regression of X on Y.
3. Correlation coefficient between X and Y.

If `bar"X"` = 40, `bar"Y"` = 6, σ_x = 10, σ_y = 1.5 and r = 0.9 for the two sets of data X and Y, then the regression line of X on Y will be:

The two lines of regressions are x + 2y – 5 = 0 and 2x + 3y – 8 = 0 and the variance of x is 12. Find the variance of y and the coefficient of correlation.

Identify the regression equations of x on y and y on x from the following equations, 2x + 3y = 6 and 5x + 7y − 12 = 0

For a bivariate data `barx = 10`, `bary = 12`, V(X) = 9, σ_y = 4 and r = 0.6
Estimate y when x = 5

Solution: Line of regression of Y on X is

`"Y" - bary = square ("X" - barx)`

∴ Y − 12 = `r.(σ_y)/(σ_x)("X" - 10)`

∴ Y − 12 = `0.6 xx 4/square ("X" - 10)`

∴ When x = 5

Y − 12 = `square(5 - 10)`

∴ Y − 12 = −4

∴ Y = `square`

Find the equation of the line of regression of Y on X for the following data:

n = 8, `sum(x_i - barx).(y_i - bary) = 120, barx = 20, bary = 36, sigma_x = 2, sigma_y = 3`