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Is SSRr greather than SSRur? why? When to use F-test? When to use t-test? Some regressors...

Is SSRr greather than SSRur? why?

When to use F-test? When to use t-test?

Some regressors may be insignificant individually, but they are jointly significant. What is the possible reason?

In order for t-test, F-test and CI to be valid, which assumptions have to be satisfied?

Math   Statistics-And-Probability   
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Answer #1

(1) SSRr is greater than SSRur because the SSR for restricted model is always greater than the residual sum of squares in unrestricted model.

(2) F test is used when we deal with categorical variable and t test is used when we deal with binary variables.

(3) The possible reason for some regressors to be insignificant individually, but they are jointly significant is the collinearity, i.e. when the variables are highly correlated with each other, then the model become insufficient to decide which variable is insignificant.

(4) Assumptions which are required be satisfied are independent sampling, no biasing and simple random sampling.

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