Which of the following are true?

When using regression to predict house prices...

i) we cannot perfectly predict the price of the house even if we know the true betas, because of idiosyncratic shock

ii) the prediction interval can be arbitrarily narrow with a large sample of retrospective data

iii) the explanatory variables must be attributes which affect the value of the house

iv) extrapolations will always be accurate if we have lots of explanatory variables

v) the prediction interval for the actual value of the house will be wider than the confidence interval for the mean

vi) we can perfectly predict the price of an individual house if we know the true betas

Vii) the prediction interval for the actual value of the house will be narrower than the confidence interval for the mena