If time is the only term in the final model, then all batches share the same intercept and slope, so Minitab displays a single regression equation. Otherwise, Minitab displays a separate equation for each batch.

If the batch factor is included in the final model, but the batch by time interaction is not included, then all batches have different intercepts but the same slope.

If both the batch term and the batch by time interaction term are included in the final model, then all batches have different intercepts and different slopes.

For the pill data, both Month and the Month by Batch interaction are significant. Thus the regression equations for each batch have different intercepts and slopes. Batch 3 has the steepest slope, -0.1630, which indicates that, each month, the concentration of medication (Drug%) for Batch 3 decreases 0.163 percentage points. Batch 4 has the smallest intercept, 99.769, which indicates that Batch 4 had the lowest concentration at time zero.