#### gargi.adhikari

##### Active Member

@David Harper CFA FRM had indicated in a thread that -" The

**general form of the F-statistic**is F[numerator df, denominator df] =

**(ESS/df)/(RSS/df) "**

**F -Statistic**is also expressed as = {Sum Of Squares BETWEEN / df-BETWEEN } / { Sum Of Squares WITHIN / df-WITHIN } => This expression of the F-Statistic I conceptually and intuitively understand.

However, there are some other Variations for the

**F -Statistic**Formula

**F -Statistic = { ( SSR-Restricted - SSR-UNRestricted ) / No of Restrictions } / (**which again I understand the conceptually and intuitively.

**SSR-UNRestricted ) /(N-k-1)**

**Also,**

**F -Statistic = { (R-****UNRestricted ^2 -****R-Restricted ^ 2 ) /q } / ( 1-****R-****UNRestricted ^2 ) /****(N-k-1)**

**How does (****SSR-Restricted - SSR-UNRestricted ) translate to****(R-****UNRestricted ^2 -****R-Restricted ^ 2 ) given that in general, R^2 = { 1 - SSR/ (SSR + SSExplained)**