This study investigates the use of functions of a vector X as auxiliary variables in the regression estimation of the population mean with survey data. Functions of the vector X are estimated by estimating the unknown parameters of the transformation. Under certain assumptions, the error in the estimated parameters is order n('- 1/2), where n is the sample size. The effect of estimating the auxiliary variables is investigated under the assumption that the finite population is a random sample of an infinite population. Asymptotic properties of regression estimators of the finite population mean constructed with estimated auxiliary variables are developed;The U.S. Department of Agriculture (USDA) uses satellite (LANDSAT) data to improve crop acreage estimates. LANDSAT data consist of a vector X of four radiation values in four wavelength bands of the electromagnetic spectrum. Based on these data, the USDA has developed a classification function for use as an auxiliary variable. In this study, other transformations of LANDSAT data are considered. The estimated posterior probability that a point with a satellite value of X is from crop j is developed as one auxiliary variable. Based on the estimated probability, a "classification rule" is constructed as another auxiliary variable;Data collected in northern Missouri by USDA are used in the study of alternative auxiliary variables. Two regressions are computed to evaluate the auxiliary variables. The first regression uses the individual pixels as observations, where a pixel is the unit of observation for the satellite data. In the second regression, both the dependent variable and the independent variable are constructed by summing pixel values over all the pixels in a segment, where the segment is the primary sampling unit in the survey. The estimated posterior probability transformation performs considerably better than the classification functions in the pixel regressions, but the posterior probability is only marginally superior to the classification function in the segment regressions;An estimator of the variance of the regression estimator based on an estimated auxiliary variable can be constructed using asymptotic theory. A form of the jackknife estimator of variance is compared with the estimator based on asymptotic theory. For a sample of 45 segments, it is estimated that the estimator based on the asymptotic formula underestimates the variance by 10 to 20 percent.