Question

Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit the coordinate grid at (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6). Which equation best approximates the line of best fit of the darts?

y = 0.6x + 0.6
y = 0.1x + 0.8
y = 0.8x + 0.1
y = 0.5x + 0.6

Answer 1

Compute the least-squares line. For the six points x̄ = 1/6 ≈ 0.167, ȳ = 2/3 ≈ 0.667. Using the slope formula b = Σ(x−x̄)(y−ȳ)/Σ(x−x̄)^2 gives b ≈ 0.633 and intercept a = ȳ − b x̄ ≈ 0.561. So the best-fit line is about y = 0.63x + 0.56, and the closest choice is

y = 0.6x + 0.6.