What to do when a linear regression gives negative estimates which are not possible I am using linear regression to estimate values that in reality are always non-negative. The predictor variables are also non-negative. For instance, regressing the number of years of education and age to predict salary. All variables in this case are always non-negative.
Due to the negative intercept, my model (determined with OLS) results in some negative predictions (when the value of the predictor variable is low with respect to the range of all values).
This topic has already been covered here, and I am also aware that forcing the intercept at 0 is discouraged, so it seems that I have to accept this model as the one I have to use. However, my question here is about the accepted norms and rules when evaluating such model.
Are there any particular rules here? Specifically:


*

*If I get a negative estimate can I just round it to 0?

*If the observed value is 100, and the predicted value is -300, and I know that the minimum possible value is 0, is the error 400 or 100? For instance, when calculating the ME and RMSE.


If it is relevant to the discussion: I have used both simple linear regression and multiple linear regression. Both result in several negative values.

Edit:
Here is the example of the samples with the fit:

The coefficients of the linear regression are 0.0010(x) and -540 (intercept).
Here is what happens when I use log for the X:

Is linear regression suitable here?
 A: You haven't given context, but you have linked to a post that offers one solution.  I will assume that that solution is not applicable here.
Then another solution is to not use linear regression (simple or multiple) since they do not solve the problem you have. 
First, though, let's use your of income as a function of age and education. Here, negative predicted values are reasonable because you are probably not interested in the income of newborn babies.  However, there, taking log(income) is also reasonable, unless some people in your data set have no income. 
But suppose that's not it. Then you can use a regression method that respects bounds on the dependent variable. One such is beta regression, which requires a DV that is between 0 and 1 - so you could scale your DV to be between 0 and 1 and then use beta regression.
But I would really urge you to add your actual variables to the question. 
A: Your definition of x may not include, as a previous poster said, all situations. In fact, you can have a negative income. If you spend more than you make, then that is a net negative.
Explicitly defining age and/or education is just as important. Some folks have trust funds and are earning money at birth, and some are on welfare and are a net negative income at 100 years. It is also true that a person with 10 years of school, like a doctor for instance, commits felony or fraud on a grand scale and has a net negative income, losing everything, maybe charged with paying restitution on top of that, and becoming a ward of the state in prison.
In short, details matter. Clearly define the details and you will have no negative intercept.
