# Are there any way to handle the derived response variable?

I have a response variable problem, there is a response variable "Y", but what I want to do is make

$$\#(y_i>\hat{y_i})/n \rightarrow 0.5$$ (If I have n entities)

and simultaneously, $$\hat{y_i} \rightarrow y_i$$

So, there are two objectives that I want to achieve.

The first method comes to mind is using linear regression(OLS), but results don't look good, it doesn't fit my first objective (It is biased because of highly correlated attributes).

I know it may sound weird, but is there any way can achieve my objectives without transforming my explained variables? With exist R packages?