This paper presents that the joint F-test in the linear regression analysis is equivalent to a distance function in the metric space. This formulation using mathematical topology provides us with a much clearer view of the joint F-test. The relationship between the individual t-test and the joint F-test turns out to be the one between the distance functions of one dimensional and higher dimensional spaces. It then becomes intuitively clear that the joint confidence region is not equal to the direct product of each confidence interval. The paper also analyzes a case where there is no correlation between any two independent variables. It follows that in this case the joint test is always significant if each coefficient involved in the joint test is individually significant, and if the sample size is sufficiently large relative to the total number of independent variables.
|ジャーナル||Sociological Theory and Methods|
|出版物ステータス||出版済み - 12 1 1997|
All Science Journal Classification (ASJC) codes
- Social Sciences (miscellaneous)
- Sociology and Political Science