When a straight line is the wrong model
Ordinary regression assumes two things people rarely check: the response can take any value, and its spread is the same everywhere. Two very common kinds of factory data break both.
Counts. "How many defects this shift?" is a count. Fit a straight line and it will happily predict minus one defect, and it will treat a shift with 2 faults and a shift with 40 as equally noisy — they are not. Poisson regression uses a log link, so predictions stay positive and the effect is read as a rate: a rate ratio of 1.30 means each unit of X multiplies the expected count by 1.30, that is +30%. That is also how the shop floor actually talks about it.
The trap inside Poisson. It assumes the variance equals the mean. Real defect data almost never does — machines, shifts and batches add extra variation. When that happens the standard errors come out too small, p-values shrink, and effects that do not exist look significant. SenSight measures the dispersion, and if it exceeds the threshold it widens the standard errors (quasi-Poisson) and says so above the table. A dispersion of 1.0 would be a perfect fit; 3.9 means the counts are almost four times more variable than Poisson expects.
Curves. Tool wear, yield against temperature, dissolution, drying — these bend. Curve Fit tries the common industrial shapes and ranks them against the straight line using AIC, which already penalises extra parameters. So a curve only wins when the shape is genuinely there, not because it has more knobs. If the straight line wins, that is a real answer too: nothing is bending.
Counts. "How many defects this shift?" is a count. Fit a straight line and it will happily predict minus one defect, and it will treat a shift with 2 faults and a shift with 40 as equally noisy — they are not. Poisson regression uses a log link, so predictions stay positive and the effect is read as a rate: a rate ratio of 1.30 means each unit of X multiplies the expected count by 1.30, that is +30%. That is also how the shop floor actually talks about it.
The trap inside Poisson. It assumes the variance equals the mean. Real defect data almost never does — machines, shifts and batches add extra variation. When that happens the standard errors come out too small, p-values shrink, and effects that do not exist look significant. SenSight measures the dispersion, and if it exceeds the threshold it widens the standard errors (quasi-Poisson) and says so above the table. A dispersion of 1.0 would be a perfect fit; 3.9 means the counts are almost four times more variable than Poisson expects.
Curves. Tool wear, yield against temperature, dissolution, drying — these bend. Curve Fit tries the common industrial shapes and ranks them against the straight line using AIC, which already penalises extra parameters. So a curve only wins when the shape is genuinely there, not because it has more knobs. If the straight line wins, that is a real answer too: nothing is bending.
Try it in the app
Try: open Counts (Poisson) with a defect-count column and read the rate ratio rather than the coefficient. Then open Curve Fit on a pair that you suspect flattens out, and compare the AIC of the curve with the line.