4. Testing Hypothesis about Multiple Coefficients

Question 1

When do we use F tests?

Answer 1

When we want to test hypotheses about groups of coefficients

Question 2

What are exclusion restrictions?

Answer 2

Where our null hypotheses is that there is no relationship between certain x variables and y

Question 3

What is the alternative hypothesis to the exclusion restrictions?

Answer 3

There is a relationship between at least one of the x variables and y

Question 4

What does a large F value indicate?

Answer 4

That the explanatory power of the restricted model is poor compared to the unrestricted model, implying Ho is false

Question 5

What are the two sets of degrees of freedom

Answer 5

• Numerator= q- number of restrictions imposed under Ho

* Donominator= n-k-1- the degrees of freedom in the unrestricted model

Question 6

When do we reject Ho?

Answer 6

When F is greater than the critical value

Question 7

What does the critical value depend on?

Answer 7

• the significance level
• q the number of restrictions imposed under Ho
• n-k-1 the degrees of freedom from the unrestricted model

Question 8

What is true if the t test is low for certain variables but the F test is high for them combined?

Answer 8

There is high multicollinearity between those variables

Question 9

When is an F test superior to a set of individual t tests?

Answer 9

When the groups of regressors are co-linear