TL;DR
Key findings: star cost per delivery day and satisfaction threshold
Each additional delivery day is associated with -0.0881 stars change in review score (highly significant (p < 0.001)), controlling for order status. The model explains 38.6% of review score variance (R² = 0.3856). Average delivery time is 14.8 days; average review score is 4.06 stars. 61.2% of orders exceeded the 10-day late threshold.
Delivery Time Distribution
Histogram of delivery days across all matched orders
Delivery times across 49 matched orders range from under 1 day to 38.1 days. The median delivery is 12.1 days and the mean is 14.8 days, indicating a right-skewed distribution with a long tail of slow deliveries. The 90th percentile delivery time is 31.2 days — 10% of orders take longer than this. Long-tail deliveries are disproportionately likely to generate low review scores.
Average Review Score by Delivery Bin
Mean review score for four delivery time bins: 0-5, 5-10, 10-20, and 20+ days
Average review scores are grouped into delivery windows to reveal non-linear satisfaction patterns. The fastest delivery window (0-5 Days) averages 4.833 stars, while the slowest window (20+ Days) averages 2.923 stars — a drop of 1.91 stars across the full delivery time range. This binned view complements the regression by showing whether the score decline is gradual or concentrated in a specific window.
OLS Regression Coefficients
Regression coefficients with 95% confidence intervals for delivery days and order status
Each bar shows a regression coefficient — how much review score changes per unit increase in that predictor, holding others constant. The delivery_days coefficient is -0.0881 stars per day (statistically significant). Bars extending into negative territory indicate factors that reduce review scores. The error bars show 95% confidence intervals: coefficients whose CI does not cross zero are statistically significant.
Late Delivery Rate vs 1-Star Rate
Percentage of orders exceeding 10 days to delivery, grouped by order status
Late delivery is defined as delivery exceeding 10 days. Overall, 61.2% of matched orders are late by this definition. The order status with the highest late rate is 'Delivered' at 61.2%. Order statuses with consistently high late rates are strong candidates for operational improvements that would directly improve customer satisfaction scores.
Residuals vs. Fitted Values
OLS diagnostic: residuals plotted against fitted values to check model assumptions
This residuals vs fitted plot checks the OLS linearity and homoscedasticity assumptions. Residuals should be randomly scattered around zero with no systematic pattern or fan shape. Mean residual is 0 (expected near zero) and the maximum absolute residual is 3.26. A curved pattern would indicate a non-linear delivery effect not captured by the model; a widening fan would suggest that dissatisfaction becomes harder to predict for shorter or longer deliveries.
Regression Model Summary
Full OLS regression table: all coefficients with standard errors, t-statistics, and p-values
| Term | P Value | Estimate | Statistic | Std Error |
|---|---|---|---|---|
| (Intercept) | 2.042e-23 | 5.362 | 18.71 | 0.2866 |
| Delivery Days | 1.935e-06 | -0.0881 | -5.431 | 0.0162 |
The regression table shows all coefficients, standard errors, t-statistics, and p-values. Overall model fit: R² = 0.3856, Adjusted R² = 0.3725, model p-value = 1.935e-06. 2 of 2 terms (including intercept) are significant at p < 0.05. The delivery_days row is the primary estimate: a negative value confirms that slower delivery is associated with lower review scores.