I had a large data set but extracted three factors from the original data set through factor analysis. I then used the extracted factors as my independent variables to develop a regression model for predicting the dependent variable. After obtaining the regression model, I'm now in the dark on the following. How will I know the values of the new variables given that the original values were provided?
As an illustration, suppose the original regression model is $y=3+2x1+4x2+7x3$ and for prediction $x1=3$, $x2=4$ and $x3=9$. Now suppose after extraction we get a regression model of the form $y=3+4R1+2R2$. How will I figure out the values of $R1$ and $R2$ when I need to predict? Is there a solid relationship between original variables and extracted variables?