We are trying to estimate the value of an NBA player based on its in-field statistics (shot percentage, rebounds...).In the literature, analysis identifying the determinants of their salaries are typical, but we are aiming to estimate the players' economic values.
Which techniques can we use?
Fabio -
This sounds like multiple regression where you would have your dependent variable, y, on one side of the regression equation, and the 'independent' variables on the other, with the estimated residual term. In order to get this, and estimate the regression coefficients, you must have a sample of cases where you have data for the dependent, and all independent variables. That means you would not only have to decide on a definition of a "players' economic value," you would have to have observed/measured/collected that data item on a number of cases, i.e., a sample. Then one could use weighted least squares regression (with the weights determined by the data), or whatever regression technique you find appropriate to predict "players' economic value" from the 'independent' variables.
If you do not have a reasonable sample of such data, but were just asking about deciding on some kind of score for a "player's economic value," based on a number of other variables, then I still say that a reasonable way to do this is to obtain such a sample. Otherwise, you may make a guess at this relationship, but until you define these variables and collect data for them, you don't have a quantitative way to estimate regression coefficents or to estimate the variance of the prediction error and prediction intervals.
Perhaps I misunderstood your question, but this is the way you predict for a dependent variable, and have a "formula" for such a prediction.
This is not to detract from the importance of subject matter knowledge to decide what independent variables might be used. Also, some results could be spurious. It is a combination of subject matter knowledge/expertise, and "fit" of a regression model to the data which matters. You could use "graphical residual analysis" (found on the internet and elsewhere) to check on fit, but to avoid overfitting to the particular sample data, it is good to save some data not used for model selection, including not used for estimating the regression coefficients, and see how well you can predict for those data. A more formal check would be "cross-validation." I never practiced really formal "statistical learning," but you might want to look into it here.
Best wishes - Jim
PS - It seems kind of strange when referring to a player, not as a person, but in terms of his/her "economic value," but I understand what you mean.
PSS - "Prediction" does not mean a forecast. It just means that you are trying to do an analogy of an "estimate," but for a random variable, y. That is, you are using regression, so there is an estimated residual.
First you have to adopt a reasonable model:
- salary depends on a)...b)... c)..
Then you must suppose a functional form for it:
- create the regression formula
Then you just run an OLS on a good amount of data and find the coefficients.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics