Question

Find the line of best fit for the following data, treating x as the dependent variable (Regression equation x on y): 

X	14	12	13	14	16	10	13	12
Y	14	23	17	24	18	25	23	24

Hence, estimate the value of x when y = 16.

Answer 1

X	Y	`x = "X" - bar"X"`	`y = "Y" - bar"Y"`	`"x"^2`	`"y"^2`	"xy"
14	14	14 - 13 = 1	14 - 21 = -7	1	49	-7
12	23	12 - 13 = -1	23 - 21 = 2	1	4	-2
13	17	13 - 13 = 0	17 - 21 = -4	0	16	0
14	24	14 - 13 = 0	24 - 21 = 3	1	9	3
16	18	16 - 13 = 3	18 - 21 = -3	9	9	-9
10	25	10 - 13 = -3	25 - 21 = 4	9	16	-12
13	23	13 - 13 = 0	23 - 21 = 2	0	4	0
12	24	12 -13 = -1	24 - 21 = 3	1	9	-3
∑X = 104	∑Y = 168			∑x2 = 22	∑y2 = 116	∑xy = -30

`bar"X" = 104/8 = 13 ,  bar"Y" = 168/8 = 21`

`"b"_"xy" = (sum"xy")/(sum"y"^2) = (-30)/116 = -0.259`

Regression equation of x on y is

`"x" - bar"X" = "b"_"xy"("y" - bar"Y")`

`"x" - 13 = (-30)/116("y" - 21)`

58x - 754 = -15y + 315

58x + 15y = 1069

Put y = 16,

58x + 15(16) = 1069

58x + 240 = 1069

58x = 829

x = 14.29