and the errors are vectors from that projected point to the data point and are perpendicular to the hyperplane. The goal of factor analysis is to find a hyperplane which is a "best fit" to the data in some sense, so it doesn't matter how the factor vectors which define this hyperplane are chosen, as long as they are independent and lie in the hyperplane. We are free to specify them as both orthogonal and normal (formula_98) with no loss of generality. After a suitable set of factors are found, they may also be arbitrarily rotated within the hyperplane, so that any rotation of the factor vectors will define the same hyperplane, and also be a solution. As a result, in the above example, in which the fitting hyperplane is two dimensional, if we do not know beforehand that the two types of intelligence are uncorrelated, then we cannot interpret the two factors as the two different types of intelligence. Even if they are uncorrelated, we cannot tell which factor corresponds to verbal intelligence and which corresponds to mathematical intelligence, or whether the factors are linear combinations of both, without an outside argument.