Suppose you have 3 variables: height, weight and salary. Can you first attempt to fit a 3 dimensional probability distribution to this data - then, if someone gives you a height and weight measurement, could you use the probability distribution to estimate the probability of observing a range of salaries for a fixed value of weight and height?
This would in effect produce a conditional probability distribution for this specific combination and you can take the expected value of this distribution to predict the most likely salary?
Here was my thought: once the 3 dimensional distribution was fit to this data, for a height = 180 cm and weight = 100 kg:
Probabilith (Salary = $10,000 | height = 180 cm, weight = 100 kg) = 0.2
Probabilith (Salary = $10,500 | height = 180 cm, weight = 100 kg) = 0.1
Probabilith (Salary = $9,000 | height = 180 cm, weight = 100 kg) = 0.01
Evaluating many such values of salary combinations, you can derive a posterior distribution. There would be no need for beta regression coefficients in this approach.
Is this correct?
Or this is a flawed idea and is it better to just fit a regression model to this problem?