The fundamental assumptions of regression analysis seem to be in terra incognita by all too many researchers in agricultural meteorology. Abuses are abundant in the literature. Through the presentation of three examples, this work demonstrates how to identify and correctly analyze three commonly found problems. The first problem comes from comparing simultaneous radiometer recordings from different radiometers. The problem is that the data are serially correlated. One solution to this type of problem is to use an autoregression. The second problem comes from an assessment of energy balance closure. The problem is that the independent data are measured and subject to random errors. The solution is to use measurement error methodology. The third problem comes from long-term precipitable water records. The problem is that the variability of the dependent variable is not constant over its range. The solution is to use a weighted regression analysis. These three examples represent common problems with solutions that demonstrate considerable improvements in analysis results. Generally interpolation and prediction are improved; moreover the underlying statistical assumptions are more tenable. Therefore when the assumptions of ordinary regression are not sound, the relevant alternative methodology should be used instead.