title: Regions of Significance in Multiple Regression Analysis.
abstract: There has been frequent confusion about the meaning of the various possible tests of significance in multiple regression, and this has led to discussions of "apparent contradictions" in regression. This paper considers the case of two predictor variables, and figures are obtained which show the regions of significance of joint regression coefficients, regression coefficients considered separately, and the multiple correlation. The intersection of these regions of significance and non-significance illustrates how the various "apparent contra- dictions" and anomalies may occur.
authors.forename: Y
authors.initials: Y
authors.lastname: Takane
authors.forename: E M
authors.initials: EM
authors.lastname: Cramer