Given price and demand for a cluster of attributes, how can I solve for a single attribute differential?
For example,
Hotel rooms with Standard Layout and King Bed have an average rate of $150 and 600,000 Room Night Stays for the past year.
Hotel rooms with Standard Layout and Queen Bed have an average rate of $130 and 300,000 Room Night Stays for the past year.
Hotel rooms with Suite Layout, King Bed and have an average rate of $160 and 400,000 Room Night Stays for the past year.
An additional layer of View type may be added to the room description. For the purpose of this exercise, how can I determine the driving attribute and its value? Say,
Room rate in USD = Intercept +$a_1*Layout+a_2*BedType+a_3*View+...+a_n*AttributeClass_n$
where,
Intercept = $100
Layout = $ \left\{ \begin{array}{ll} Standard & x \\ Suite & y \\ \end{array} \right. $
BedType = $ \left\{ \begin{array}{ll} King Bed & p \\ Queen Bed & q \\ \end{array} \right. $
View = $ \left\{ \begin{array}{ll} View & c \\ TwoView & d \\ no View & e \\ \end{array} \right. $
It is true that $a_1...a_n$ can be used as weights. It is true that a set of constraints may be used such that,
$Suite + King < y + p$
Please help with this problem by example and/ or references.
Thank you very much for your help.