Question

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

You gave four different model-based conclusions that contradict each other, so I can’t pick a company without more information. Which company pays more at 22 hours depends on which regression model you trust. To choose correctly, do one of the following:

1. If you can, compute the predicted weekly pay for each company at 22 hours from each model (linear, quadratic, exponential). Compare the two companies’ predicted amounts for the same model type.
2. Decide which model type is most appropriate for pay vs. hours (usually pay is proportional to hours, so a linear model is the most sensible choice unless there is a reason pay per hour changes with hours). Then use the predictions from that model type to pick the company.
3. Use model-fit statistics (R², residual plots, standard error) to pick the best-fitting model for each company, then compare the best-fit predictions at 22 hours.
4. If models disagree but have similar fit, compare the magnitudes of the differences and consider practical factors (risk of extrapolation, variability, benefits).

If you want, paste the predicted pay values at 22 hours from each model (or the raw data or R² values) and I’ll compare them and give a definitive recommendation.