A note on least squares sensitivity in single-index model estimation and the benefits of response transformations

Ordinary Least Squares (OLS) is recognised as being useful in the context of multiple linear regression but can also be effective under the more general framework of the single-index model. In cases where it is ineffective, transformations to the response can improve performance while still allowing for interpretation on the original scale. In this paper we introduce an influence diagnostic for OLS that can be used to assess its effectiveness in the general setting and which can also be used following response transformations. These findings are further emphasized and verified via some simulation studies.