NBA球員得分之迴歸分析：以Steve Nash為例

Abstract

在一場籃球比賽中，球員的比賽結果往往是大家的焦點所在。但是在很多情況下，出手次數、命中率、籃板、失誤、抄截、助攻，都會影響球員的表現。我們擷取美國職業籃球聯賽中現役湖人隊後衛奈許在2007-2009單場表現數據來觀察出手次數、命中率、籃板、失誤、抄截、助攻，對於得分的影響。 在此報告中，主要探討在各項反應變數裡，何者對解釋變數(得分)具有較大的解釋能力。先對各項反應變數做適合度檢定，來判斷是否與解釋變數(得分)有線性迴歸關係。在確定之間具有線性迴歸關係後，再對模型來進行選取，針對模型選取，本篇報告對此使用了三種選取方法，第一為前進選取法(Forward method),第二為後退選取法(Backward method)，第三是逐步迴歸法(Stepwise method)，而本報告也藉由使用其他選取法尋找變數，並且與前三種選取方法來綜合比較來選取解釋變數，也就是出手次數和命中率，以求得最佳的迴歸模型。 在得到迴歸模型後，我們也針對模型使用殘差檢定來檢測樣本是否服從常態分配、變異數是否為常數及迴歸模型是否為最佳的線性迴歸模型。 而最後的結論我們得到，當不考慮其他變數，出手次數越多、命中率越高，則得分也會越高。

Abstract In a basketball game, what people focus on is usually the result. However, what can affect players’ performance includes steals, errors, rebounds, assists and field goals. We take Steve Nash, one of the Lakers’ guards, as an analytical basis to understand the effects of steals, errors, rebounds, assists and field goals upon scores. The data range from 2007 to 2009. This report focuses on all response variables and tries to find which one has more expansion in explanatory variables (scores). At first, we conducted fitness tests to recognize if a response variable has any relationship with explanatory variables. And then, after we collected and calculated the data, we were sure that they have relationships of linear regression. Then, we used three methods (forward method, backward method and stepwise method) to test the model. In addition to the three methods, we used other methods to make a comparison. Finally, we found that the greatest explanatory variables are field goal attempts and percentage. The field goal attempts and percentage contribute to the best model of regression. After getting the model, we used the residual analysis to test if it has the relationship of normal distribution, if the variance is contact, and if the model of regression is the best model linear regression. We came to the conclusion that when the other conditions are fixed, more field goal attempts and higher field goal percentage lead to more scores.