▁data ▁▁▁ ▁Problem ▁statement ▁ ▁We ▁can ▁use ▁the ▁least ▁square ▁mechanism ▁to ▁figure ▁out ▁the ▁equation ▁of ▁a ▁two ▁body ▁orbit ▁in ▁polar ▁base ▁co - ordinates . ▁The ▁equation ▁typically ▁used ▁is ▁ ▁where ▁ ▁is ▁the ▁radius ▁of ▁how ▁far ▁the ▁object ▁is ▁from ▁one ▁of ▁the ▁bodies . ▁In ▁the ▁equation ▁the ▁parameters ▁ ▁and ▁ ▁are ▁used ▁to ▁determine ▁the ▁path ▁of ▁the ▁orbit . ▁We ▁have ▁measured ▁the ▁following ▁data . ▁▁▁ ▁We ▁need ▁to ▁find ▁the ▁least - squ ares ▁approximation ▁of ▁ ▁and ▁ ▁for ▁the ▁given ▁data . ▁▁ ▁Solution ▁ ▁First ▁we ▁need ▁to ▁represent ▁e ▁and ▁p ▁in ▁a ▁linear ▁form . ▁So ▁we ▁are ▁going ▁to ▁rewrite ▁the ▁equation ▁ ▁as ▁. ▁Now ▁we ▁can ▁use ▁this ▁form ▁to ▁represent ▁our ▁observ ational ▁data ▁as : ▁▁ ▁where ▁ ▁is ▁ ▁and ▁ ▁is ▁ ▁and ▁ ▁is ▁constructed ▁by ▁the ▁first ▁column ▁being ▁the ▁coefficient ▁of ▁ ▁and ▁the ▁second ▁column ▁being ▁the ▁coefficient ▁of ▁ ▁and ▁ ▁is ▁the ▁values ▁for ▁the ▁respective ▁ ▁so ▁▁▁ ▁and ▁▁ ▁On ▁solving ▁we ▁get ▁▁ ▁so ▁ ▁and ▁'' ▁ ▁See ▁also ▁▁ ▁Bay esian ▁least ▁squares ▁ ▁F ama – Mac B eth ▁regression ▁ ▁Non - linear ▁least ▁squares ▁ ▁N umer ical ▁methods ▁for ▁linear ▁least ▁squares ▁ ▁Non linear ▁system ▁identification ▁ ▁References ▁ ▁Further ▁reading ▁▁ ▁Category : Param et ric ▁statistics ▁Category : Le ast ▁squares <0x0A> </s> ▁" Inv ict us " ▁is ▁a