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 (i.e., by mathematical proof or by showing a numerical example)

Answer 1

Yes, Our statement is true of any linear regression model be checked for model adequacy then we used the statistical testing for lack of fit.

Test for lack of fit of a regression model This test for lack of fit of a regression model is based on the assumptions of normality, independence and constant variance which are satisfied. Only the first order or straight line character of the relationship is in doubt . For example, the data in the following scatter plot where the indication is there that straight line fit is not very satisfactory.

The test procedure determines if there is systematic curvature is present. The test requires replicate observations on y for at least one level of x and they should be true replications and not just the duplicate readings or measurement of y.The true replications consists of running i n separate experiments at x = x_i and observe y . It is not just running a single experiment at x = x_i and measuring y, n_i times in which the information only on the variability of the method of measuring y is obtained. These replicated observations are used to obtain a model-independent estimate of σ².

Model Adequacy Checking:-The fitting of linear regression model, estimation of parameters testing of hypothesis properties of the estimator are based on following major assumptions:

1. The relationship between the study variable and explanatory variables is linear, at least approximately.
2. The error term has zero mean.
3. The error term has constant variance.
4. The errors are uncorrelated.
5. The errors are normally distributed.