Creating a regression model with a dependent variable, categorical variables and standardized independent variables I have created a regression model that is centered around my dependent variable R.
I have a set of categorical variables and their interactions (days of week and shift [DAY/ NIGHT])
I have a set of independent variables that i have standardized so that their effect can be compared. Y
Q1: I would like to know if this is correct or if i should have standardized my dependent variable also?
Q2: when interpreting the coefficients for my independent variables is the coef an increase in R for 1 standard deviation of Y from 0? or from the mean of Y?
p.shape
xx=pd.get_dummies(data=p[['y1', 'y2', 'y3', 'Day','Shift', 'Terminal']]
                  ,columns=['Day','Shift','Terminal']).drop(columns=['Day_Monday','Shift_Day','Terminal_L'])
xx['Intercept']=1
y = p['R']

from statsmodels.formula.api import ols
from statsmodels.regression.linear_model import OLS
# ols('R~Day_Friday+Day_Tuesday+Day_Wednesday+Day_Thursday+Day_Saturday+Day_Sunday+1',
#     data=pd.get_dummies(data=p,columns=['Day'])).fit().summary()
# xx.columns
xx.columns
xx['Shift_Nightx'+'Terminal_Tx']=xx['Shift_Night']*xx['Terminal_T']


for c in ['Day_Friday', 'Day_Saturday', 'Day_Sunday', 'Day_Thursday','Day_Tuesday', 'Day_Wednesday']:
    xx['Shift_Nightx'+c]=xx['Shift_Night']*xx[c]
for c in ['Day_Friday', 'Day_Saturday', 'Day_Sunday', 'Day_Thursday','Day_Tuesday', 'Day_Wednesday']:
    xx['Terminal_Tx'+c]=xx['Terminal_T']*xx[c]
for c in ['Day_Friday', 'Day_Saturday', 'Day_Sunday', 'Day_Thursday','Day_Tuesday', 'Day_Wednesday']:
    xx['Shift_Nightx'+'Terminal_Tx'+c]=xx['Shift_Night']*xx['Terminal_T']*xx[c]
 
    
OLS(y,xx).fit().summary()
```



Q1: I would like to know if this is correct or if i should have standardized my dependent variable also?

No, you don't need to standardize your dependent variable. Standardizing your independent variables will be enough - as you say, it will allow you to compare the magnitude of your regression coefficients.

Q2: when interpreting the coefficients for my independent variables is the coef an increase in R for 1 standard deviation of Y from 0? or from the mean of Y?

Both. You have standardized your independent variables $y_1$, $y_2$, and $y_3$ i.e. for each of them, you have subtracted the mean and divided by the standard deviation. This means that your standardized variables will have mean 0, so 1 standard deviation from 0 and 1 standard deviation from the mean are equivalent statements in this case.
