Does feature scaling need to be done separately for independent variables?

Question

I am currently doing a Udemy course, and the lecturer for the SVR class said that feature scaling has to be applied separately for X and y, as their standard deviation and mean are different. The following is the screenshot of the code and the dataset. X is level and y is salary. code for feature scaling

dataset for SVR class

For the data-preprocessing class, the lecturer used different dataset, and the dataset consisted of more than 1 independent variable. However, he did not feature scale them independently, as shown in the code. I am confused with this part, because all the independent variables have different standard deviation and mean as well. So why do we not feature scale them separately? The following is the code and dataset code

dataset for pre-processing class

Btw this code is by Kirill Eremenko

Answer 1

Feature Scaling basically helps to normalize the data within a particular range. Normally several common class types contain the feature scaling function so that they make feature scaling automatically. However, the SVR class is not a commonly used class type so we should perform feature scaling.

Scaling inputs helps to avoid the situation, when one or several features dominate others in magnitude, as a result, the model hardly picks up the contribution of the smaller scale variables, even if they are strong.

The idea behind StandardScaler is that it will transform your data such that its distribution will have a mean value of 0 and standard deviation of 1. In the case of multivariate data, this is done feature-wise (in other words independently for each column of the data). Given the distribution of the data, each value in the dataset will have the mean value subtracted and then divided by the standard deviation of the whole dataset (or feature in the multivariate case).

If we don't do scaling separately the distribution/magnitude of the dependent variable might be impacted. It is often common practice to normalize dependent and independent features separately.