共變異數與 Pearson 相關係數

Statistical Thinking in Python (Part 1)

Justin Bois

Teaching Professor at the California Institute of Technology

2008 年美國搖擺州選舉結果

ch2-4_v2.003.png

¹ 資料取自 Data.gov (https://www.data.gov/)

2008 年美國搖擺州選舉結果

ch2-4_v2.004.png

¹ 資料取自 Data.gov (https://www.data.gov/)

2008 年美國搖擺州選舉結果

ch2-4_v2.005.png

¹ 資料取自 Data.gov (https://www.data.gov/)

繪製散佈圖

_ = plt.plot(total_votes/1000, dem_share,
             marker='.', linestyle='none')
_ = plt.xlabel('total votes (thousands)')
_ = plt.ylabel('percent of vote for Obama')

共變異數

衡量兩個量如何同時變動

共變異數的計算

ch2-4_v2.011.png

¹ 資料取自 Data.gov (https://www.data.gov/)

共變異數的計算

ch2-4_v2.012.png

¹ 資料取自 Data.gov (https://www.data.gov/)

共變異數的計算

ch2-4_v2.013.png

¹ 資料取自 Data.gov (https://www.data.gov/)

共變異數的計算

ch2-4_v2.014.png

$$covariance = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})$$

¹ 資料取自 Data.gov (https://www.data.gov/)

Pearson 相關係數

$$\rho = \text{Pearson correlation} = \frac{\text{covariance}}{(\text{std of x}) (\text{std of y})}$$

$$= \frac{\text{variability due to codependence}}{\text{independant variability}}$$

Pearson 相關係數範例

ch2-4_v2.020.png

一起來練習吧！

Statistical Thinking in Python (Part 1)