An error analysis is presented for the remote reference magnetotelluric method. The variances in the elements of the remote reference impedance tensor, Z^R, are calculated, and general expressions are found for the variances in an arbitrary function of Z^R. The variances in the apparent resistivities, the phases of the elements of Z^R, and the skewness are derived for a fixed coordinate frame. The variance in the rotation angle of the coordinate frame required to maximize the sum of the squares of the off-diagonal tensor elements is calculated, and expressions are presented for the variance in the apparent resistivities and phase angles in the rotated frames. The distribution of errors and the estimation of confidence limits are discussed. Expressions are given for the signal and noise power spectra of the electric, magnetic, and remote reference fields. Throughout the calculations, emphasis is placed on the physical assumptions made, and possible circumstances under which the assumptions may be violated are discussed. The calculations are illustrated with magnetotelluric data obtained near Hollister, California