電影票房之迴歸分析：以『西遊記之大鬧天宮』為例

Abstract

在生活中，看電影是很普遍的一種休閒活動之餘，在報紙裡有時候會討論到一部電影的票房成績，因此我們想知道是什麼樣的因素會影響到票房。在此報告裡，我們藉由一部電影『西遊記之大鬧天宮』為例，探討一部電影的總票房與平均票價、放映場次、觀影人次和上座率，四個解釋變數與應變數之間的關聯。 在這個報告裡，主要目的是找出所有解釋變數中，對於總票房這個應變數最有解釋能力的模型。首先，我們先對各個變數做散佈圖及相關係數表，以判讀自變數是否與應變數有線性的關係。在確立線性關係後，利用三種選取法，分別為前進選擇法(Forward Selection) 、後退選取法(Backward Method) 與逐步迴歸法(Stepwise Method)，篩選解釋變數。由於三種方法選取的最後模型皆為相同，因此直接採用此模型為最後模型。 模型確立完畢後，要回歸原本的假設前題，因此模型必須要通過殘差的三個檢定(常態性、變異數齊一性、獨立性)，最後才可能為最佳模型。 在不考慮其他因素下，最後的結果為當平均票價下降、觀影人次增加與上座率的上升，都會使總票房越高。

In our life, go to see a movie is a common leisure activity. We sometimes read newspaper could see the report about the movie's box office, so we want to know what kind of factors impacts on the box office. On this report, we took "The Monkey King" for example, to discuss the relation of explanatory variable (average fare, screen, visitors, attendance rate) and dependent variable. On this report, we wanted to find the best explanatory capability of the explanatory variable to influence the box office. First, we did the scatter plot and correlation coefficient to recognize whether the explanatory variable and dependent variable are linearity or not. After we confirmed their linearity, then we used three methods(forward method, backward method and stepwise method) to sift out the explanatory variable. Due to the same of the final model, so we adopted that to be the final model. After confirmed the model, we back to our hypothesis, so the model had to pass through the residual analysis (normally, homoscedasticity, independently), then we could probably find the best model. We did not consider other factors, the conclusion is that when the average fare decrease or the visitors and attendance rate increase may tend to the box office getting higher.