I have built a linear model (LM) based on detrended and scaled Y1 and Y2 time series. The original Y1 and Y2 values varies between 0 and 100, and 0 and 500 respectively. The detrended-scale time series (X1 and X2) values varies between -2 and 3. The linear model is statistically significant for my purpose.

I am now applying LM to estimate values of Y2 based on new Y1. Let’s call these y2 and y1. I have detrended y1, and the y2 estimates look reasonable.

Question: since the units of Y1 and Y2 are unimportant after detrend/scaling, how can I interpret the estimated y2 values? For instance, if estimate y2 = 0.6, what does that mean in terms of the original Y2?