Dears

Being from IT , I have some queries on the Math behind :

I am working in python where most models are under Generalised Linear model category ...

I am doing a Linear Regression (and its other forms like Lasso - ultimate aim is to find feature importances)

My Y is a continuous variable. My Xs are all standardized (meaning : x-xmean/xstd.dev)

Interpretation of Log-Linear Beta Coefficients under the following cases :

My data is server data and some IVs are like: X1 = % of time spent in executing user programs , X2 = % of time spent executing Kernel jobs, etc. and there are other numeric IVs as well (upto 1300 IVs)

Please assume:

1. all my IVs / Xs are standardized

2. my target Y (resource usage) is natural log so that I can get the percentage change in Y due to X (also to remove the skewness of Y)

so ln(Y) = b1X1 + b2X2 + .....

My doubts:

a. How can I interpret % change in Y given Xs are standardized ?

b. How can I interpret % change in Y given Xs are already a % ?

I have read previous posts and I understand that the Coefficients b1 and b2 have to be read as :[ exponential(b1) -1 ] *100

Please check my understanding below for above 2 queries:

a. % change in Y for 1 standard deviation change in X1 (say std.dev is 3.5) is [ exp(b1) -1 ] *100 / 3.5

or should I do :

% change in Y for 1 standard deviation change in X1 (say std.dev is 3.5) is [ exp{ b1 / std.dev(X1) } -1 ] *100 / 3.5

b. I am confused for this part - whether I should interpret as a percentage-point or just leaves them as percentages..

Regards

Sherin