Question

Can any linear regression model be checked for model adequacy by statistical testing for lack of fit or goodness of fit? Why or why not? Please provide your answer with detailed justification

Answer 1

In general, a model fits the data well if the differences between the observed values and the model's predicted values are small and unbiased. Before you look at the statistical measures for goodness-of-fit, you should check the residual plots.Lack of Fit tells us whether a regression model is a poor model of the data. ... If unusually large residuals or errors appear when fitting the model, we know we have lack-of-fit.

To avoid from poor model of the data we need to statistical testing for goodness of fit.