2022-12-06T14:29:45Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000165752021-08-30T02:53:48ZRecommended Regression Models Using Slope Direction as a Continuous Explanatory Variable斜面方位を説明変数とする回帰モデルについて荒瀬, 輝夫岡野, 哲郎熊谷, 真由子内田, 泰三斜面方位Slope direction三角関数Trigonometric function3次曲線Cubic curve極値Extremal value精度PrecisionSlope direction is an important environmental factor in various field studies, but it is difficult to employ as an explanatory variable in regression analysis because of its periodicity. In the present study, actual data was used to assess the goodness of fit of three different regression models using slope direction as an explanatory variable. Results show that a non-linear regression of y = a sin(θ + b) can be transformed into a linear multiple regression with sin θ and cos θ. A multiple regression, with sin θ and cos θ, should be applied when the two slope directions bearing a maximum or minimum are assumed to be exactly opposite to each other. Conversely, a cubic-curve regression should be applied when the two slope directions are not assumed to be opposite. Presumed errors of estimation were almost equal in the multiple and cubic-curve regressions. Furthermore, p-values were almost equal for both the multiple and cubic-curve regressions when there was little variation in the data, but the p-value for the cubic-curve regression dramatically increased as the variation in the data increased.Article環境科学年報34:6-9(2012)research report信州大学環境科学研究会2012-03-31application/pdf環境科学年報34690915-7492AN1054947Xhttps://soar-ir.repo.nii.ac.jp/record/16575/files/34-02_Arase.pdfjpn