Loads at which '10 amp' fuses fail
predicted proportion,
Use this diagram to explain that a linear model predicts proportions outside [0, 1] for extreme values of the explanatory variable.
Drag the vertical red line to see the predicted proportion of fuses that fail at different currents. For currents under 9.1 amps, the least squares linear model predicts a negative proportion, whereas when the current is over 10.8 amps, the predicted proportion is greater than 1.
Select Nonlinear model from the pop-up menu and repeat, noting that a nonlinear model is needed to ensure that the predictions are always between 0 and 1.
Some manufactured products are designed to fail under load as a safety precaution. For example, in cars many parts are designed to collapse or break off in accidents. It is important that these items fail within a fairly tight range of loads.
A company manufactures fuses that are designed to blow when a current of 10 amps flows through them. Batches of one hundred fuses were tested at currents of 9 amps, 9.5 amps, ..., 11.5 amps and failures were noted. The bar charts show the data that were collected.