這篇研究我們想提供一個變化係數迴歸模型(varying coefficient regression model)上對係數函數的檢定方法，以決定係數函數是否可以以更簡單的形式去描述之，因此我們建立了變化係數回歸模型的變異數分析表(analysis of variance table)。這個構想起源於Huang及Chen在2008年的論文，此篇論文描述如何建構局部多項式回歸(local polynomial regression)之變異數分析表，且文中有提到變化係數迴歸模型是可建構出變異數分解(anova decomposition)，只不過沒有提供相關的檢定方式，因此我們覺得可以繼續把變化係數迴歸模型的變異數分析表給建構出來並做出一些檢定。我們證明有關變化係數模型(varying coefficient model)的變異數分解的數學理論後，提供了三種變異數分析表來檢定變化係數迴歸模型的單一係數函數是否為零(zero)、常數(constant)以及線性(linearity)。

而為了明瞭我們提出的假設檢定方法的可行性，於是我們針對簡單變化係數模型(simple varying coefficient model)，使用模擬(simulation)數據來探討我們提出方法的拒絕率(rejection rate)，並與Fan及Huang在2005年的方法做比較。實際資料分析(real data analysis)採用台灣房價的資料，以這三個檢定來探討變化係數與反應變數之間的關係。最後我們會提供變化係數迴歸模型這三個檢定的R的程式，為了考慮使用者的便利性，參考線性模型(linear model)的寫法以及字串的處理來建構，這邊會用到平常統計用不到的內建程式來建立變異數分析表的程式。除此之外，我們也會提供估計出來的係數函數來方便分析者使用。

Analysis of Variance (ANOVA) for varying coefficient models was investigated in Huang and Chen (2008). In this thesis, we extend their work to construct ANOVA tables and hypothesis tests to examine whether a coefficient function is zero, nonzero constant, and linearity. Based on local polynomial regression, we show that the ANOVA test statistics have asymptotically F-distributions. We compare our ANOVA tests with the GLR tests (Fan and Huang (2005)) by simulations. The numerical results show that the power of the tests are comparable, while the empirical type-I errors are generally smaller than 0.05 for the ANOVA tests, and bigger than 0.05 for the GLR tests. Finally, the proposed tests are used to analyze housing price data in Songshan and Xinyi districts in Taipei city, which leads to some interesting interpretations. The R-code of the proposed ANOVA tests are provided for convenience of applications.

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[9] 內政部不動產交易時價查詢服務網 http://lvr.land.moi.gov.tw/N11/login.action