Feature Normalization/Scaling: Prediction Step
I have learned what the correct answer is: you have to transform your prediction location in precisely the same way you do for the columns of matrix $X$: first, subtract the means element-wise from each component of the prediction location $x$. Second, divide element-wise by the standard deviation. Third, prepend a $1$ to allow for the bias. Finally, perform the dot product with your $\theta$ vector. Since the $\theta$ vector was calculated on transformed data, it's meant to operate on transformed data. It will contain units and scaling appropriate to produce an answer in engineering units. Reference: see Week 2, FAQ, Question 8 in Andrew Ng's Machine Learning course on Coursera. (Login is probably necessary.)