2 a Find the best fit line for 1 3 2 4 3 7 to three decimal

2. (a) Find the best fit line for (1, 3), (2, 4), (3, 7) to three decimal places. (b) Find the SSE of the best-fit line you obtained in part (a) to three decimal places. Show all calculations!

Solution

Q(3)

(a) given three points are (1 3) (2 4) (3 7)

=> C=the number of piont =3

=> X=sum of all x value=1+2+3=6

=> Y=sumof all y value=3+4+7=14

=> X^2=sum of square of x value=1^2+2^2+3^2=14

=> XY=sum of product of x and y=1*3+2*4+3*7=3+8+21=32

=>Xm=mean X=X/C=6/3=2

=> Ym=mean Y=Y/C=14/3=4.6667

slope of line=(XY-X*Ym)/(X^2-X*Xm)=(32-6*4.667)/(14-6*2)=1.999=2.00

equation of line

y=2*X+0.6667

(b)

y\'=2x+0.667

predicted y value

Y-Y\'

residual

sum of squares error (SSE)=0.3333^2+(-0.3333)^2+0.3333^2=0.33326

X	Y	y\'=2x+0.667 predicted y value	Y-Y\' residual
1	3	2*1+0.6667=2.6667	3-2.6667=0.3333
2	4	2*2+0.6667=4.6667	4-4.6667=-0.3333
3	7	2*3+0.6667=6.6667	7-6.6667=0.3333