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

Regression equation of X on Y is_________

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`

Out of the two regression lines x + 2y – 5 = 0 and 2x + 3y = 8, find the line of regression of y on x.

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`

If for a bivariate data b_yx = – 1.2 and b_xy = – 0.3 then find r.

The data obtained on X, the length of time in weeks that a promotional project has been in progress at a small business, and Y, the percentage increase in weekly sales over the period just prior to the beginning of the campaign.

Find the equation of the regression line to predict the percentage increase in sales if the campaign has been in progress for 1.5 weeks.

Compute the product moment coefficient of correlation for the following data: 
n = 100, `bar x` = 62, `bary` = 53, `sigma_x` = 10, `sigma_y` = 12

`Sigma (x_i - bar x) (y_i - bary) = 8000`

If Σ_x1 = 56 Σ_y1 = 56, Σ`x_1^2` = 478,
Σ`y_1^2` = 476, Σ_x1y1 = 469 and n = 7, Find
(a) the regression equation of y on x.
(b) y, if x = 12.