Question

Rob is investigating the effects of font size on the number of words that fit on a page. He changes the font size on an essay and records the number of words on one page of the essay. The table shows his data.

A 2-row table with 10 columns. The first row is labeled font size with entries 14, 12, 16, 10, 12, 14, 16, 18, 24, 22. The second row is labeled word count with entries 352, 461, 340, 407, 435, 381, 280, 201, 138, 114.


Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?

y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723

Answer 1

Compute the least-squares line. For the data x̄ = 15.8 and ȳ = 310.9, the slope b = Σ(x−x̄)(y−ȳ)/Σ(x−x̄)^2 ≈ −4680.2/179.6 ≈ −26.05 and the intercept a = ȳ − b x̄ ≈ 310.9 − (−26.05)(15.8) ≈ 722.5.

So the best-fit line (approximately) is y ≈ −26x + 723.