Question

The mean and standard deviation of the two variables x and y are given as `barx = 6, bary = 8, σ_x = 4, σ_y = 12`. The correlation coefficient is given as r = `2/3` Find the regression line of x on y.

Answer 1

Given: 

`barx = 6, bary = 8, σ_x = 4, σ_y = 12, r = 2/3`

The regression line of x on y is given by:

`(x − barx) = b_(xy) (y − bary),    ...[∵ b_xy = (rσ_x)/(σ_y)]`

⇒ `(x − barx) = (rσ_x)/(σ_y) (y − bary)`

On putting values, 𝑥 − 6 = `2/3 xx 4/12 (y − 8)`

`x − 6 = 2/9 (y − 8)    ...(b_(xy) = 2/3 × 4/12 = 2/3 xx 1/3 = 2/9 ) `

⇒ 9(x − 6) = 2(y − 8)

⇒ 9x − 54 = 2y − 16

⇒ 9x − 2y − 38 = 0