Can probability distributions be used as an alternative for regression models? 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
Etc.
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?
Thanks!

You can, but not without consequences.

*

*Linear regression is a pretty flexible model in terms of your ability to define the functional relationship between the features and the dependent variable. If you use multivariate distribution, you are limited by what kind of relationships between variables are possible under the distribution.

*For fitting the distribution you need to make more assumptions, for example, if you choose multivariate normal distribution you assume that all the variables follow normal distribution vs only $Y$ (conditionally) as in linear regression.

*For fitting the distribution you may need much more data. Think of discrete distribution: in conditional distribution case (regression) you need only enough data to observe relations of the other variables with $Y$, with the joint distribution you need data for all the combinations of all the levels of all the variables.

It is easier to focus only on the conditional distribution and conditional expectation, as we do with linear regression.
