Question

Let R unrestricted and R restricted be 0.4366 and 0.4149 respectively. The difference between the 9) unrestricted and the restricted model is that you have imposed two restrictions. There are 420 observations. The F-statistic in this case is:_______ A) 10.34 B) 4.61 C) 7.71 D) 8.01

Answer 1

Complete Question

Let R unrestricted and R restricted be 0.4366 and 0.4149 respectively. The difference between the 9) unrestricted and the restricted model is that you have imposed two restrictions. There are 420 observations. The F-statistic in this case is:_______

A) 10.34

B) 4.61

C) 7.71

D) 8.01

Answer:

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The  $R^2_{unrestricted } = 0.4366$

     The  $R^2_{restricted } = 0.4149$

       The  number of observation is  n=  420

Generally the number of independent variables is  k($R^2_{unrestricted } , \ n \ \ and \ R^2_{restricted }$)  =  3

Then the number of  restriction is  (i.e $R^2_{unrestricted } \ and \ R^2_{restricted }$) is  q =  2

  Generally the F-statistics is mathematically represented as

                $F = \frac{\frac{R^2_{unrestricted } - R^2_{restricted}}{q} }{ \frac{(1- R^2_{unrestricted }) }{n-k-1} }$

substituting values

                $F = \frac{\frac{0.4366 -0.4149}{2} }{ \frac{(1-0.4366) }{420-3-1} }$      

                 $F = 8.01$