Question

What are the conditions required to apply the multiple regression test?
how to apply it using ANOVA table?

Answer 1

The conditions are the following:

1. Uncorrelatedness of errors

2. The errors should be gaussian and homoscedastic (i.e have same variance for each response)

3. The linearity assumption in parameter should be more or less valid (though this is not a mathematical requirement, but fitting linear regression to actually non linear setup gives bizzare result)

[The above are the basic requirements, but one also does other data cleaning jobs like checking for outliers, etc.]

The ANOVA table can be used in an ANOVA model for testing significance of factors. Suppose we want to test whether a certain factor A, really makes any significant contribution, i.e

This is done by reading off the sum of squares due to factor A (); it's degrees of freedom ,  as well as the error SS () and error degrees of freedom ().

We then construct,

And reject the null hypothesis if T is greater than the corresponding F quantile.