I am developing a linear model with 13 variables, including the target variable (online purchase revenue for items). So, I first built model1 with regular variable and then build model2 after normalizing of the data. I have copied the coefficients for two models here :
Model1(Without Normalized Data)
Coefficients:
(Intercept) xid xcartadd
6.386e+01 4.301e03 1.229e+02
xcartuniqadd xcartaddtotalrs xcartremove
1.239e+02 7.788e02 1.424e+02
xcardtremovetotal xcardtremovetotalrs xproductviews
5.588e+02 3.445e02 1.369e+01
xuniqprodview xprodviewinrs xsizeselecteduniview
1.530e+01 5.401e04 1.299e+02
xsizeselectedtotalviews xsizeselectedtotalviewsrs
6.280e+01 2.453e02
Model 2(With Normalized data)
Coefficients:
(Intercept) xid
3.900e+02 4.301e03
xcartadd_n xcartuniqadd_n
2.623e+03 2.069e+03
xcartaddtotalrs_n xcartremove_n
1.785e+03 1.721e+02
xcardtremovetotal_n xcardtremovetotalrs_n
4.474e+02 5.360e+01
xproductviews_n xuniqprodview_n
7.979e+03 7.378e+03
xprodviewinrs_n xsizeselecteduniview_n
4.757e+02 1.218e+03
xsizeselectedtotalviews_n xsizeselectedtotalviewsrs_n
1.044e+03 5.374e+02
and my questions are :

Is it appropriate to take only normalized data into model or non normalized data?

Is it appropriate to take combination of normalized data as well as non normalized data?

How can I choose most appropriate predictor variable from them for model?
Best Answer
The difference between using normalized and nonnormalized data is one of interpretation. If you use the original data, the coefficients apply to changes of one unit on the original scale. If you use the normalized data, they apply to changes of one unit on the new scale (usually, one standard deviation).
This is an issue on which there is no universal agreement among statisticians. My own tendency is to use unstandardized data. However, the two models really mean the same thing.