Question

Rose drew a regression line for this paired data set.

Her line passed through (1, 2) and (3, 5) .

What is the equation of Rose's regression line?

Answer 1

yˆ=1.5x+0.5

Explanation:

took the test and got it correct

Answer 2

A.
`y=1.5x+0.5`

Explanation:

We are given that,

The linear regression passes through the points (1,2) and (3,5).

As, the slope of a linear line is given by,
`(y_(2)-y_(1))/(x_(2)-x_(1))`.

We get, the slope of the linear regression is,

Slope =
`(y_(2)-y_(1))/(x_(2)-x_(1))`.

i.e. Slope =
`(5-2)/(3-1)`.

i.e. Slope =
`(3)/(2)`.

i.e. Slope = 1.5

As, the linear line is given by 'y=mx+b', where m is the slope and b is the y-intercept.

Substituting the slope and point (1,2) in the general form, we have,

`y=mx+b` implies
`2=1.5* 1+b` implies
`b=2-1.5` i.e. b= 0.5

Hence, the equation for the regression line is
`y=1.5x+0.5`