迴歸分析：環境變異因子對區域均溫的探討

Abstract

為探討影響台灣本島各地溫度的各種環境因素，我們選定的樣本為2012年11月27日下午六點的大氣溫度，再考慮以下六種可能影響溫度的變數有相對溼度、懸浮粒子濃度、一氧化碳濃度、氮氧化物濃度、風速以及雨量。以敘述統計做為參考，觀察散佈圖的趨勢，使讀者對資料有初步認知。開始檢視變數是否有自我相關後，產生初步模型。為挑選重要變數，使用五大方法：向後消去法、前進選擇法、逐步選取法、調整R2擷取法、CP選擇法，比較各方法的選取差異及共同點後，採用了相對溼度、懸浮粒子濃度及雨量作為篩選結果，進而建立最佳模式，變數中發現當相對濕度及雨量增加則氣溫會降低，懸浮粒子則反之。最後，觀察殘差分析中的誤差項是否符合基本假設後，再檢視資料中異常點或影響點的影響程度，經由分析過程發現，異常點並不存在，為了提升我們解釋能力，所以我們刪除了一點影響點為屏東縣恆春鄉，反映出此為最佳模式。

Abstract

We investigate several environmental factors which possibly affect the temperatures around the island of Taiwan. Six variables which might caused to Taiwan’s temperature are considered in this project : relative humidity, concentration of suspended particulates, concentration of carbon monoxide, concentration of nitrogen oxides, wind speed, and rainfall. The data set was collected at 6:00 pm, November 27th, 2012 which is available at Environmental Protection Department’s webpage. We fit a multiple linear regression using SAS statistical package. We use five model selection procedures to select important variables which affect the temperatures. There are backward elimination, forward selection, stepwise regression, adjusted R2 Selection, and CP Selection. Relative humidity, concentration of suspended particulates, and rainfall are the most important independent variables in our final model. Our results show when relative humidity and rainfall increase, temperatures would reduce, and when concentration of suspended particulates decline, temperatures would rise. Finally, we also work on diagnostic checking to check if there is any outlier or influential point. We remove two influential points Hengchun Township, Pingtung County in order to improve prediction power and to reflect the best model.