Estimation of a Linear Regression Model from Aggregate Means

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  • 層別に縮約された平均系列データに対する線形回帰モデルのあてはめ
  • ソウ ベツ ニ シュクヤクサレタ ヘイキン ケイレツ データ ニ タイスル センケイ カイキ モデル ノ アテハメ

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This paper discusses a linear regression model for the aggregate means which result from some partitions of the independent variable. These are called stratified data. The data at hand indicate the aggregate means of independent variable and the number of data in intervals, as well as the means and the variances (or standard deviations) of the dependent variable calculated by strata or intervals. The regression coefficients estimated by this data are approximately equal to the regression coefficients obtained from the data prior to aggregation. However, the coefficient of determination is clearly different. The differences of these regression coefficients are verified, and a method for estimating the original coefficient of determination is proposed by using the aggregate means and the variance of each stratum. The efficiency of the proposed method is illustrated through some numerical experiments.

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