Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 05

Year : DEC 2014

$$x+6y=6 $$

$\therefore 6y=6-x \\ \therefore y=\dfrac 66+\dfrac {(-1)}6x\\ \therefore y=\dfrac {-1}6x+1 ------ (1) \\ 3x+2y=10 \\ \therefore 2y=10-3x \\ y=\dfrac {10}2-\dfrac {3x}2\\ \therefore y=\dfrac {-3x}2 + 5 ---- (2)\\ Let, \space b_1=\dfrac {-1}6 \space \space \& \space \space b_2 =\dfrac {-3}2\\ since \space \space |b_1| \lt |b_2| : b_{yx}=b_1=\dfrac {-1}6 \space \space \& \space \space b_{xy}=\dfrac 1{b_2}=\dfrac {-2}3 ----(3)$

Hence, equation (1) is regression equation of y on x type and

equation (2) is regression equation of x on y type.

from (1) and (2)

$\dfrac {-1}6x+1=\dfrac {-3}2x+5 \\ \therefore \dfrac 32x-\dfrac 16x=5-1 \\ \therefore 86x=4\\ \therefore x=\dfrac {6\times 4}8 \\ x=3 $

substitute $x=3$ in (1)

$$\therefore y=(-1/6)(3)+1=0.5$$