In a study of solar wind control of high-latitude current patterns as induced from Godhavn magnetometer observations, we apply multiple linear regression methods. The regular component of the solar wind can be distinguished by considering daily averages of the solar wind parameters. A set of daily Godhavn perturbation quantities is constructed from the three hourly magnetic elements H, D, and Z. These are defined so that they reflect essential ionospheric current patterns, for example, the westward electrojet. For instance, in analogy with the electrojet activity indices, AL, AU, and AE, we define for a single station similar, although more simple, perturbation quantities. The available satellite data enable us to study continuously the solar wind-magnetosphere coupling (SMC) correlations for the period 1967 to 1987. To take the seasonal and yearly change in the height-integrated ionospheric conductivity into account, we divide the regression analysis into 3-month sets. We emphasize the use of robust estimation methods and apply Huber type regression. The large number of 3-month regression sets allow us to perform a detailed analysis of, for example, the temporal variation in the SMC correlations. The principal solar wind parameters are identified by constructing the regression a model recursively by adding the independent variables one by one. We demonstrate that the Godhavn quantities associated with the westward electrojet depend most significantly on the solar wind speed V, the southward interplanetary magnetic field (IMF) component Bs and the azimuthal IMF component By. Adding the solar wind density &rgr; does not improve the regression solution. The poor predictability of the Godhavn quantities associated with the eastward electrojet may indicate a major misunderstanding of the sources controlling it. The perturbation range quantities in the horizontal component H, the declination D, and the vertical component Z are determined solely by V and Bs. The influence of By is even less than that of &rgr;. In contrast, the daily mean quantities in H and D are dominated by the azimuthal component By. Two principal physical quantities describing the solar wind-magnetosphere interaction are the merging electric field Em and Akasofu's energy transfer function ϵ. Generally, we find that by using two or three elementary solar wind parameters as independent variables, it is possible to substantially improve the regression solution obtained by means of the composite parameter Em or ϵ.¿ 1996 American Geophysical Union