Question

What is the equation of the line of best fit for the following data? Round slope and y-intercept of the line to three decimal places X 2 5 7 12 16 Y 9 10 5 3 2

Answer 1

Answer: y ≈ -0.212x + 7.784

Explanation:

I think...

first of all:

Calculate the means of the x-values (
`X`) and y-values (
`Y`):

`X` = (2 + 5 + 7 + 12 + 16) / 5 = 8.4

`Y` = (9 + 10 + 5 + 3 + 2) / 5 = 5.8

X -
`X`: -6.4, -3.4, -1.4, 3.6, 7.6

Y -
`Y`: 3.2, 4.2, -0.8, -2.8, -3.8

Σ[(X -
`X`)(Y -
`Y`)] = (-6.4 x 3.2) + (-3.4 x 4.2) + (-1.4 x -0.8) + (3.6 x -2.8) + (7.6 x -3.8) = -40.64

Σ[(X -
`X`)^2] = (-6.4)^2 + (-3.4)^2 + (-1.4)^2 + (3.6)^2 + (7.6)^2 = 191.2

m = Σ[(X -
`X`)(Y -
`X`)] / Σ[(X -
`X`)^2] = -40.64 / 191.2 ≈ -0.212

b =
`Y` - m x
`X` = 5.8 - (-0.212 x 8.4) ≈ 7.784

y ≈ -0.212x + 7.784