Question

Let R^2 unrestricted and R^2 restricted be 0.4366 and 0.4149 respectively. The difference between the unrestricted and the restricted model is that you have imposed two restrictions.The number of regressors in the unrestricted model is 3. There are 420 observations. The F-statistic (under the assumption of homoskedasticity) in this case is:A) 4.61B) 8.01 C) 10.34 D) 7.71

Answer 1

Answer:

Option (B) is correct.

Explanation:

Given that,

$R^{2}[tex/] unrestricted = 0.4366[tex]R^{2}[tex/] restricted = 0.4149Regressors in the unrestricted model = 3No. of observations, n = 420No. of independent variables, k = 3Degree of freedom i.e no. of restrictions, q = 2F-Statistic:[tex]=\frac{(\frac{R^{2} _{UR}-R^{2} _{R}}{q})}{\frac{1-R^{2} _{UR}}{(n-k-1)}}$

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

$=\frac{0.01085}{0.5634} \times 416$

= 8.01