Question

Find the regression coefficients b_yx, b_xy and correlation coefficient ‘r’ for the following data:

(2, 8), (6, 8), (4, 5), (7, 6), (5, 2)

Answer 1

x	x2	y	y2	xy
2	4	8	64	16
6	36	8	64	48
4	16	5	25	20
7	49	6	36	42
5	25	2	4	10
Σx = 24	Σx2 = 130	Σy = 29	Σy2 = 193	Σxy = 136

`b_(yx) = (sumxy - 1/n sumx sumy)/(sumx^2 - 1/n (sumx)^2)`

= `(136 - 1/5 (24)(29))/(130 - 1/5 (24)^2)`

= `((136 xx 5 - 696)/5)/((130 xx 5 - 576)/5)`

= `(680 - 696)/(650 - 576)`

= `(-16)/74`

= – 0.22

`b_(xy) = (sumxy - 1/n sumx sumy)/(sumy^2 - 1/n (sumy)^2)`

= `(136 - 1/5 (24)(29))/(193 - 1/5 (29)^2)`

= `(136 xx 5 - 696)/(193 xx 5 - 841)`

= `(680 - 696)/(965 - 841)`

= `(-16)/124`

= – 0.13

`r = +- sqrt(b_(yx) b_(xy))`

= `+- sqrt((-0.22)(-0.13))`

= `+- sqrt(0.0286)`

= ± 0.17

Since, r has same sign as regression coefficients

∴ r(x, y) = – 0.17

∴ b_yx = – 0.22, b_xy = – 0.13

And r = – 0.17