In this paper, the cross-validation methods namely the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$C_{p}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>C</mi> <mi>p</mi> </msub> </math> </EquationSource> </InlineEquation>, PRESS and GCV are presented under the multiple linear regression model when multicollinearity exists and additional information imposes restrictions among the parameters that should hold in exact terms. The selection...</equationsource></equationsource></inlineequation>