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In regression analysis a traditional approach, the so-called constrained coefficient approach, is usually used for model selection. We propose a new approach, named as constrained coefficient-component approach, instead. The constrained coefficient-component approach is developed based on a basic model which contains all of the explanatory variables that may be available and will be meaningful for practical applications. The procedure for the constrained coefficient-component approach is as follows. Firstly, we define a vector of coefficient-components by using an orthogonal transformation of the vector of regression coefficients in the basic model. Then, we construct a number of contending models by constraining some coefficient-components to be zeros. Further, the best model among all the contending models is selected by using Akaike information criterion, AIC. The constrained coefficient-component approach has many advantages, e.g., (1) the total number of the contending models can be reduced so that the process of model selection becomes really easy; (2) by using the newly-proposed approach we can obtain more stable estimation for parameters and a model that has better performance measuring by AIC. The constrained coefficient-component approach is applied to analyzing the influence of temperature on productivity of rice production in Hokkaido as an example.

A procedure of analysis of variance (ANOVA) using AIC (Akaike information criterion) statistics is introduced and applied to the analysis of the data on personal digital assistant (PDA). Several basic concepts of AIC statistics are reviewed in Section 2. In Section 3, a procedure of ANOVA based on F-test and a procedure of ANOVA using AIC statistics are shown, and then a numerical simulation is given in order to compare these two procedures. In Section 4 the procedure of ANOVA using AIC statistics is applied to the analysis of the data which is obtained from an experiment on a PDA. The main advantages of the procedure of ANOVA using AIC statistics are as follows, (1) It can give a unique result for testing statistical hypotheses. (2) It is easier to be programmed. (3) The results of this procedure are independent of the significance level that is difficult to be determined objectively. The results of the simulation show that the procedure of ANOVA using AIC statistics can lead a better performance than that using F-test. The results of the PDA data analysis are very useful for the pointing device design.