Interpreting coefficients of scaled features

In the MLS course 1 week 2, we talked about feature scaling.

After scaling all the features, how do I interpret the coefficients of the variables? Eg, a variable called square_ft ranges from 1000-50000 and we scaled it between 0.4 and 1. The coefficient of new scaled feature is 0.00983.

How do I make sense of this coefficient? What does 0.00983 mean?

Hello @Uma_Savili,

See which of the below hits your question:

  1. you can scale the learned weight back to the original scale, because after scaling back, you can say the coefficient has the unit of dollar/sqft, if you are predicting for the price. this should give you some ideas of how to do it.

  2. However, I would not recommend you to interpret it as a real dollar-per-sqft measurement, even though it carries only the unit of dollar/sqft. Carrying the unit is different from carrying that meaning.

  3. It does not necessarily carry the meaning because a feature’s coefficient takes into account (A) the correlation between that feature and the label and (B) the correlations between that feature and each of the other features.

  4. When (B) gets into play, your coefficient for square_ft can change dramatically as the number of your features increase or decrease, which means that you cannot rely on the coefficient value to carry a consistent meaning independent of other factors. Consider the case that when you have 5 features, the coefficient for square_ft (after scaling back) is 200dollar/sqft, but you are motivated to add 3 new very informative features into the model, and after re-training the model, the coefficient will also adapt itself to its feature’s corelation with the 3 new features and, for example, become 50 dollar/sqft. This can and will happen and it makes you unable to rely on the coefficient for its meaning.

  5. The only chance that a feature’s coefficient won’t be affected by other features is when the feature is uncorrelated with all other features. This is extremely rare if not impossible.

  6. Lastly, one thing for certain is, if the coefficient is zero or is very close to zero, then you can interpret that feature as unimportant and just drop it. As for how close is close enough, you may drop it first, re-evaluate your model, and if the evaluation result is as good as before dropping it, then it would be close enough.

Raymond

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