Question

Given that the observations are: (9, -4), (10, -3), (11, -1), (12, 0), (13, 1), (14, 3), (15, 5), (16, 8). Find the two lines of regression and estimate the value of y when x = 13·5.

Answer 1

x	9	10	11	12	13	14	15	16	`sumx= 100`
y	-4	-3	-1	0	1	3	5	8	`sum y = 9`
`x^2`	81	100	121	144	169	196	225	256	`sum x^2 = 1292`
`y^2`	16	9	1	0	1	9	25	64	`sum y^2 = 125`
xy	-36	-30	-11	0	13	42	75	128	`sum xy = -77  + 258 = 181`

`barx = (sumx)/n = 12.5`

`bar y = (sum y)/n = 9/8`

`b_"yx" (sumxy - 1/n sum x sum y)/(sum x^2 -  1/n (sumx)^2)` = `(181 - 1/8 xx 100 xx 9)/(1292 - 1/8 (100)^2)`

`= (181 xx 8 - 900)/(1292 xx - 10000)`

` = (1448 - 900)/336 = 548/336 = 1.631`

`b_"xy" = (sum xy - 1/n sum x sum y)/(sum y^2 - (sumy)^2/n) = (181 - 1/8 xx 100 xx 9)/(125 - 81/8)`

`= 548/919 = 0.596`

Equation of line of y on x is y - 1.125 = 1.63 (x - 12.5)

y - 1.631x = -20.388 + 1.125

y - 1.631x = -19.263

Equation of line x on y is x - 12.5 = 0.596 (y - 1.125)

`x - 0.596y = - 0.6705 + 12.5`

= 11.830

y at x = 13.5

y = -19.263 + 1.631 x 13.5

= 2.7555