Question

A data set consists of the following data points:

(2, 12), (3, 7), (5, 4)

The slope of the best-fit line is -2.5. Find the y-intercept of this line.

A. 16
B. 13
C. 15
D. 14

Answer 1

i think it is D. 14

Answer 2

no its 16

Answer 3

@Tallan This is not an easy problem with an exact answer using an equation.
It can be done by several approaches.
The best is to calculate the regression line and obtain the correct answer of
y=-2.5x+16

Answer 4

Assuming you are not expected to find the regression line, there are still other ways. Did your teacher show any particular way to do that?

Answer 5

One way is to find the centroid of the three points, and pass the line with the given slope through it.
The centroid is ((2+3+5)/3,(12+7+4)//3) = (10/3, 23/3)
Substitute into the regression line:
23/3=-2.5(10/3)+b
Solving gives b=16

Another way is to substitute each of the points to find b for each point, the average of which is 16.2.

So all methods point to the correct answer of 16.

@Tallan
Please realize that the important part of the exercise is to learn HOW to find the answer, not just the answer itself.