Question

Obtain the equation of the regression line Y on X for the given bivariate data using Method of Least Squares: X: 3 5 8 12 18 Y: 6 8 13 25 38 Also estimate y for x = 20.​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n is

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Now we have to find ratio

Let ratio be k:1

Hence

m

1

=k,m

2

=1

x

1

=1,y

1

=−5

x

2

=−4,y

2

=5

Also

x=x,y=0

Using section formula

y=

m

1

+m

2

m

1

y

2

+m

2

y

1

0=

k+1

k×5+1×(−5)

⇒0=

k+1

5k−5

⇒5k−5=0

⇒5k=5

∴k=1

Now, for x

x=

m

1

+m

2

m

1

x

2

+m

2

x

2

=

k+1

k×(−4)+1×1

=

1+1

1×(−4)+1

=

2

−4+1

=

2

−3

Hence the coordinate of point is P(x,0)=P(

2

−3

,0)