Let R²_unrestricted and R²_restricted be 0.4366 and 0.4149 respectively. The difference between the unrestricted and the restricted model is that you have imposed two restrictions. There are 420 observations. The F-statistic in this case is A)4.61 B)8.01 C)10.34 D)7.71

Question

Quizplus · Accepted Answer

To calculate the F-statistic, we first need to find the sum of squared residuals (SSR) for both models. Let SSR_unrestricted and SSR_restricted be the sum of squared residuals for the unrestricted and restricted models, respectively.

Then, we can use the formula for the F-statistic:

F = ((SSR_restricted - SSR_unrestricted) / q) / (SSR_unrestricted / (n - k))

where q is the number of restrictions (in this case, q = 2), n is the sample size (420), and k is the number of parameters estimated in the unrestricted model (13).

From the information given in the question, we have:

SSR_unrestricted = (1 - 0.4366) * 420 = 235.812
SSR_restricted = (1 - 0.4149) * 420 = 243.912

Plugging these values into the formula, we get:

F = ((243.912 - 235.812) / 2) / (235.812 / (420 - 13))
  ≈ 8.01

Therefore, the answer is B.

Let R2unrestricted and R2restricted Be 0

Let R²_unrestricted and R²_restricted Be 0