If I have variables x1,x2,x3,and x4 that have correlation coefficients $-0.9, -0.5, 0.5,$ and $0.9$ to another variable y, what is the effect of choosing different combinations of them in a multivariate regression. Should I not use the negative ones ($-0.9$ and $-0.5$), or should I only use the most strongly correlated (ie $-0.9$ and $0.9$)?
2026-03-30 21:12:28.1774905148
Which variables to use in regression
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The correlations with $y$ are not enough information for answering the question. Any linear model that includes one of the $\pm 0.9$ variables has $R^2$ of at least $0.81$. Without knowing the intercorrelations of the $x$ variables it's not possible to say anything more.