Question

Melinda works at a cafe. Each day that she works, she records x, the total dollar amount of her customers’ bills and then y, her total daily wages. The table shows her data for 2 weeks.

A 2-column table with 11 rows. The first column is labeled x with entries 50, 100, 75, 80, 90, 140, 150, 95, 125, 160, 165. The second column is labeled y with entries 36, 43, 38, 40, 42, 50, 60, 43, 46, 50, 55. A graph shows the horizontal axis numbered 40 to 160 and the vertical axis numbered 10 to 60. A line increases from 0 to 160.
According to the line of best fit, what is the minimum amount, to the nearest dollar, Melinda will earn for each day of work, even if she serves no customers?

$18
$26
$36
$40

Answer 1

Find the least-squares line y = a + bx.

Using the data:
- slope b = [Σ(xy) − (Σx)(Σy)/n] / [Σ(x^2) − (Σx)^2/n] ≈ 0.177
- intercept a = ȳ − b x̄ ≈ 45.727 − 0.177(111.818) ≈ 25.94

Rounded to the nearest dollar, the minimum she’ll earn (y‑intercept) is $26.