Translating scaled features results to original values

The discussion on feature scaling made a lot of sense for determining the best weights and lowest cost function value. Once you have scaled the features values (Square-feet; bedrooms; age; etc.) and determined the weights for the scaled feature values that provide the best fit, how do you then take new feature data (outside of the training data set) and determine the y-hat value for a particular instance?

y = w*[scaled data values] + b, while the real world provides us with real world values of square feet, bedrooms, etc.

If you normalized the features by subtracting the mean and dividing by sigma, then trained to get the weights, then the process to prepare the features for the new prediction is to subtracting the same mean and divide by the same sigma.

Got it – essentially apply the same method you did to the training data. In a scenario where I was working with a client who wants to sell a house that is A sq. feet, has B bedrooms, and is C years old I would scale the “real world” inputs, determine the estimated value of the house, and then report back to the client that their A, B, C feature house is worth $Y. Is that correct?

When you normalize the training set, you use the mean and sigma values to get a new set of scaled examples.

To make predictions, you apply that same scaling before you compute the prediction.