# Is converting a numerical target to binary helpful?

I'm trying to solve an ML problem where the target variable is numeric, let's say the pollution level in a city. But the client is not interested in predicting the actual amount of pollutants, they are just interested in knowing whether the pollution level is high or low based on an agreed upon threshold. (High if the PM2.5 level is above 200, Low otherwise).

Should I treat it as a regression problem and take the numeric PM2.5 levels as target or as a classification problem where I make another feature of high/low pollution level based on the threshold and use that binary variable as a target? What are the advantages and disadvantages of both and What impact it can have on accuracy, if any?

## 1 Answer

When you convert a variable from numerical to binary, what happens is that you lose information about the magnitude of the variable and summarise it into a >=X variable.

It has advantages and disadvantages depending on the use you will give to your model:

If your model has to determine the exact amount of "how high" is your pollution, then is not a good idea to convert it because you are loosing crucial information, but if the city major declares a curfew if the pollution is bigger than x, then a binary output is not only good idea but necessary for the decision you are achieving with it.

When you convert the variable to binary, the hypothetical model you are achieving has different kind of information that the model with numerical variables:

• You will not be comparing exact values (measuring RMSE), you will be measuring membership to a set (measuring AUC).
• If your client wants to measure wheter you trespassed or not a threshold, you should explain to him what is achievable with that model and ask him it that meets the requirements of his job.