Lack-of-fit and lack-of-fit tests

What is lack-of-fit?

A regression model exhibits lack-of-fit when it fails to adequately describe the functional relationship between the experimental factors and the response variable. Lack-of-fit can occur if important terms from the model such as interactions or quadratic terms are not included. It can also occur if several, unusually large residuals result from fitting the model.

Lack-of-fit test in Minitab

Minitab displays the lack-of-fit test when your data contain replicates (multiple observations with identical x-values). Replicates represent "pure error" because only random variation can cause differences between the observed response values.

To determine whether the model accurately fits the data, compare the p-value (P-value) to your significant level. Usually, a significance level (also called alpha or α) of 0.05 works well. An α of 0.05 means that your chance of concluding that the model does not fit the data when it really does is only 5%.

P-value < α : The model does not fit the data: If the p-value is less than or equal to α, you conclude that the model does not accurately fit the data. To get a better model, you may need to add terms or transform your data.
P-value > α : There is no evidence that the model does not fit the data: If the p-value is larger than α, you cannot conclude that the model does not fit the data well.