Business Context

FreshCart, a grocery delivery app, needs a simple forecasting approach for next week's order volume for one city. The analytics team tested two lightweight methods on the last 8 weeks of holdout data: a 3-week moving average and a linear trend forecast.

Problem Statement

Determine which forecasting technique is more effective using standard forecast error metrics, and quantify whether the difference in average absolute error is meaningful enough to guide a business choice.

Given Data

Historical actual demand and model forecasts for the same 8 weeks are shown below.

Assume these 8 weeks are representative of recent demand behavior and that forecast errors across weeks are independent enough for a simple comparison.

Requirements

1. Compute the forecast error for each method in each week.
2. Calculate MAE and RMSE for both methods.
3. Identify which method performs better overall.
4. Compute the mean absolute error difference across weeks: $d_i = |e_{MA,i}| - |e_{LT,i}|$.
5. Construct a 95% confidence interval for the mean difference in absolute error.
6. Recommend which method FreshCart should use for short-term forecasting.

Assumptions

• Lower MAE and RMSE indicate better forecasts.
• The 8 weekly paired errors are treated as a small sample for inference on the mean error difference.
• No major promotion or supply shock occurred during the evaluation window.