Question

The following table shows the Mean, the Standard Deviation and the coefficient of correlation of two variables x and y.

Series	x	y
Mean	8	6
Standard deviation	12	4
Coefficient of correlation	0.6

Calculate:

1. the regression coefficient b_xy and b_yx
2. the probable value of y when x = 20

Answer 1

Given `barx` = 8,

`bary` = 6

σ_x = 12,

σ_y = 4

 and r = 0.6

a. b_xy = `r σ_x/σ_y = 0.6 xx 12/4` = 1.8

and b_yx = `r σ_y/σ_x = 0.6 xx 4/12` = 0.2

b. Regression line of y on x is

`y - bary = b_(yx)(x - barx)`

`\implies` y – 6 = 0.2(x – 8)

`\implies` y = 0.2x – 1.6 + 6

`\implies` y = 0.2x + 4.4      ...(1)

When x = 20,

y = 0.2 × 20 + 4.4

= 4 + 4.4

= 8.4