Best value model

ectoraige

I'm trying to work out an approach for maximising the cost vs. value for a set of objects.

I have 35 objects which were evaluated and given points out of a possible 100, the highest score being the most desirable. The actual values awarded range from 44.45 to 80.8, with a mean of 59.25 and a median of 58.95

Each object also has a cost, ranging from 400 to 5000.

What methods are there for determining the best cost to value? Broadly speaking the cheapest item also has the lowest value, and the most expensive has the highest.

I'm thinking that the expected graph for the values to cost would be linear, so I need to determine which objects deviate the most from this.

I'm sure there's pretty standard solutions but I don't know what they might be called so google is failing me here, any pointers are appreciated.

Yakuza

Have you tried a linear regression yet?
Assuming there is a linear regression between cost and value (cost = a + b * value, a linear regression would find values for a and b that minimise differences between actual and expected values) Excel can do this fairly handily.

If you wanted to test that a linear regression was appropriate, you could follow use a goodness of fit test (some form of [LATEX]\chi^2[/LATEX] test, based on summing the squares of differences between observed and expected values divided by the expected value) to check this.