Can we fit a regression model when the dependent variable is poorly correlated with the independent variables? I have a requirement, I need to predict Y from 2 X_variables, I plotted two scattered plots ie Y vs X1, Y vs X2, As you can see the below pics, the plots are sparced. There is poor correlation between Y and X_variables, I also plotted a correlation plot, which also shows a poor correlation between X_variables and Y. I'm asked to predict Y from X1 and X2, can I fit any regression model which will work for this dataset? Is it possible to fit a regression model for the below data? If yes, then how and which regression model? Should I make any data transformations? If yes then which transformations I need to apply. I attached scattered plots, correlation plot and distribution plots below. I also tried polynomial regression, It didn't work well. I scaled data with StandardScaler and MinMax scaler, they didn't work either. There are negative values in X2 so I couldn't apply log transformation. Please refer below Images. If you need more information I can add it.




On the question: Should I make any data transformations? Yes, take a subsample and apply an analysis of transformation routine (research, for example, the Box-Cox method here).
As to whether you should use poor explanatory variables to improve your predictions, my answer is it depends on whether say variables are understandably fundamental to the nature of the dependent variable and there is a good explanation as to the current poor correlation. If not, just work with the dependent variable possibly in a transformed state (and then reverse the transform albeit interpretation issues may arise). Speaking somewhat generally, this likely will, with time, produce a lower average error measure.
I hope this helps.
