PLEASE CHECK MY WORK OF DERIVING PARTIAL F STATISTIC(in term of R^2 instead of RSS)

Hi, In this question I try to express the partial F statistics in terms of R^2, and here is my work. Could you please check it for me? If it is incorrect, please give me some suggestions. Thank you.

\fDate Ho: Reduced model with P parameters HA full model with K Parameters KER - RSSF 2 Since Rreduced = 1- RSSK TSS notice that TSS remains the save R full = 1 - RSSF as y did not change. TSS constaal TSS - RSSR = Rreduced RSSR= TSS ( 1 - Radeced ) TSS - RSST - Rfall for RSSF= TSS (1-R full ) 2 = PSS ( 1 - R-reduced ) - TSE (172 - full ) n - k X FiSS (1-72 - full ) RZfull - R reduced h - k K - P = R z Full - P." reduced/ (n-k/ K P/ (1-R full ) R 2 full - Rreduced X (1-R Sull/ - R full - Riedeled I-R KOKLY