Estimating Relative Value from Price and Rating Data

Summary

The document proposes estimating whether a hotel is good value by comparing its price and rating with those of other hotels. Its suggested method is to collect observations, plot price against rating, and fit a linear regression. An offering priced below the fitted line is treated as a better deal relative to the observed relationship; one priced above it appears expensive for its rating.

The example contrasts two hotels, but the answer says a third observation is needed for its proposed comparison. More broadly, the approach depends on having a suitable set of comparable hotels and assumes a roughly linear relationship between price and rating. Ratings are subjective, and the note gives no guidance on data quality, uncertainty, or how to weigh price against rating. It illustrates a simple benchmarking idea rather than a validated valuation model, and its application to trading or quantitative research is indirect.

Key ideas

• Compare price and rating across a group of similar offerings.
• Use a regression line to represent the typical price-rating relationship.
• Treat observations below the line as relatively better value under this method.
• The conclusion depends on subjective ratings, comparable data, and the assumed linear relationship.

Tags

# How to value pricing and ratings? How to quantify best value?


# How to value pricing and ratings? How to quantify best value?












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!

## Answer by John Doe (score 0)

https://quant.stackexchange.com/a/25143

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.