Question

Find the line of best fit for the following set of data:

x y
2 -2.9
3.5 -2
-1.4 -4.8
4.2 -1.5
0 -4
-2.8 -6
1.5 -3.5

y = 0.613x – 4.141

y = -0.613x – 4.141

y = -0.613x + 4.141

y = -4.141x + 0.613

Answer 1

Compute the least-squares slope and intercept.

n = 7
sum x = 7
sum y = -24.7
sum xy = -0.83
sum x^2 = 45.94

Slope:
m = [n·Σ(xy) − (Σx)(Σy)] / [n·Σ(x^2) − (Σx)^2]
= [7(−0.83) − 7(−24.7)] / [7(45.94) − 7^2]
= 167.09 / 272.58 ≈ 0.613

Intercept:
b = (Σy − m·Σx) / n = (−24.7 − 0.613·7)/7 ≈ −4.141

So the best-fit line is y = 0.613x − 4.141.