Question

Company A: A 2-column table with 5 rows. The first column is labeled hours with entries 5, 12, 20, 29, 42. The second column is labeled earnings (dollar sign) with entries 340, 404, 460, 530, 630. Company B: A 2-column table with 5 rows. The first column is labeled hours with entries 4, 9, 20, 32, 39. The second column is labeled earnings (dollar sign) with entries 125, 234, 450, 668, 828.
If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? Explain your answer.

Company A: Using linear regression models from both data sets, she determines that it pays about $14 more.
Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more.
Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.

Answer 1

Company B.

Reasoning (use values nearest 22 hours rather than whole-sample global fits):

- Company A: use the two nearby points 20 h → $460 and 29 h → $530.
Slope ≈ (530 − 460)/(29 − 20) = 70/9 ≈ $7.78 per hour.
Predicted at 22 h: 460 + 2·7.78 ≈ $476.

- Company B: use the two nearby points 20 h → $450 and 32 h → $668.
Slope ≈ (668 − 450)/(32 − 20) = 218/12 ≈ $18.17 per hour.
Predicted at 22 h: 450 + 2·18.17 ≈ $486.

So at 22 hours Company B would pay about $486 vs Company A about $476 — roughly $10 more for Company B.

Note: different regression choices (global linear, quadratic, exponential) can give different answers. Because 22 is very close to the 20-hour data point in each set, local interpolation between nearby points is a sensible, robust approach here and points to Company B.