Question

Use linear regression to find afunction that fits the followingpoints.(-5,14), (1,-16)

Answer 1

Given:

(-5,14), (1,-16)

The linear regression formula is

`y=mx+b`

Substitute x=1 and y=-16 in the formula, we get

`-16=m(1)+b`

`-16=m+b`

Subtracting m from both sides of the equation, we get

`-16-m=m+b-m`

`-16-m=b`

We get

`b=-16-m`

Substitute x=-5 and y=14 in the formula, we get

`14=m(-5)+b`

`14=-5m+b`

Substitute b=-16-m in this equation to find the value of m.

`14=-5m-16-m`

`14=-6m-16`

Adding 16 to both sides of the equation, we get

`14+16=-6m-16+16_{}`

`30=-6m`

Dividing both sides by (-6), we get

`(30)/(-6)=-(6m)/(-6)`
`m=-5`

Substitue m=-5 in b=-16-m to find the value of b.

`b=-16-(-5)`

`b=-16+5`
`b=-11`

Substitute b= -11 and m= -5 in the line equation, we get

`y=-5x-11`

Hence linear regression is

`y=-5x-11`