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I'm trying to define which hotel offers the best value.

Let's say we have two hotels - A and B.

For A, you pay $10 a night and the rating for the hotel is 9.8.

For B, you pay $8 a night and the rating for the hotel is 9.6.

So for A, you pay $2 more and get one with a higher rating of 0.2. But is it the better value?

How would you solve this?

Thanks!

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closed as off-topic by assylias, Bob Jansen Mar 30 '16 at 8:14

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    $\begingroup$ I'm voting to close this question as off-topic because it is not about quantitative finance. $\endgroup$ – assylias Mar 30 '16 at 7:31
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In order to answer this question you need a 3rd point and then proceed in this way, although it is quite empirical as it is all based on subjective rating assumption. Plot hotel A and B price and rating in a graph, search for a 3rd hotel C whose cost is between 8 and 10 and plot that too. Draw the line AC. If point B is above AC then you might think that hotel B's price is above average for that ratings, and viceversa.

Basic concept underlying here: You would have to do a linear regression of all the hotel data, the more your hotel is under that line, the better the deal.

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  • $\begingroup$ So like this: Maybe I can plot an X-Y graph of price and rating data by hotel. Then create a trend line which shows what the "fair value" would be based on the data. Any data that is above the line is probably more expensive and anything below is less expensive and thus better value. So this tells us what is fair and not fair value but we can't get "best" value. Reasonable? $\endgroup$ – law2255 Mar 30 '16 at 16:44
  • $\begingroup$ Nope, you can also find the "best" value. Proceed in this way. Draw the segment line (perpendicular to the x axis) that link a point and the trend line. The point that maximize the length of that segment is the best deal you are looking for. $\endgroup$ – John Doe Mar 30 '16 at 18:35

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