In my test there was a false/true question:
Your estimated model for predicting house prices has a large positive weight on 'square feet living'. This implies that if we remove the feature 'square feet living' and refit the model, the new predictive performance will be worse than before.
In fact, if we change the units of this feature into sq meters, we could get a much lower positive weight. Meaning that the weight does not say anything about the importance of the feature.
However, in the ridge and lasso regression, the smaller the weight is, the less important is the feature. As far as I understand it, it implies only to ridge and lasso but not to a-non-regularized-regression (and therefore the answer is "false" to the question). Is it right?