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It is the law for merchandises to specify…

It is the law for merchandises to specify…. Food products Medicine TV sets. Mathematics. Precise mathematics versus Uncertain mathematics The loophole of the normal distribution. 相关关系的概念 correlation. 很多现象之间存在着一定的联系 人的身高与体重 血压与年龄 家庭的消费支出、结构与收入. 关系 relationship. 严格的确定性关系：函数关系

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It is the law for merchandises to specify…

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  1. It is the law for merchandises to specify… • Food products • Medicine • TV sets

  2. Mathematics Precise mathematics versus Uncertain mathematics The loophole of the normal distribution

  3. 相关关系的概念correlation • 很多现象之间存在着一定的联系 • 人的身高与体重 • 血压与年龄 • 家庭的消费支出、结构与收入

  4. 关系 relationship • 严格的确定性关系：函数关系 A = πr2, a = F/m 销售收入 = 产品数量 * 价格 • 非确定性关系：非严格的、不确定的依存关系 --- 相关关系

  5. 关系Relationship • 现象之间确实存在数量上的客观内在关系。表现在一个现象发生数量上的变化，要影响另一个现象也相应地发生数量上的变化 • 劳动生产率的提高会影响成本的降低 • Disclaimer: grow rate of a tree and of a child. • 现象之间数量依存关系不是确定的，具有一定的随机性。表现在给定自变量一个数值，因变量会有若干个数值和它对应。并且因变量总是遵循一定规律围绕这些数值的平均数上下波动。

  6. Correlation and regression • In regression we intend to describe the dependence of a variable Y on an independent variable X. • In correlation, we are concerned whether two variables are interdependent, or covary (vary together). A typical assumption is that the two variables are both effects of a common cause.

  7. Correlation and regression • 相关分析研究的都是随机变量，并且不分自变量与因变量 • 回归分析研究的变量要定出自变量与因变量， 并且自变量是确定的普通变量，因变量是随机变量

  8. Correlation and regression

  9. 相关分析与回归分析的作用 • 通过对数量关系的研究分析，深入认识现象之间的相互依存关系 • 有回归分析求出的关系式，称为回归模型，通过回归模型进行预测和预报并能补充缺少的资料。Extrapolation

  10. Karl Pearson correlation coefficient

  11. 协方差定义covariance • Cov(X, Y) = E(X-EX)(Y-EY) • Correlation coefficient

  12. The property of covariance Non correlation: Cov(X, Y) =0 X and Y have not correlation EXY = EXEY D(X +Y) = DX + DY

  13. Independence and Covariance If X and Y are independence, then they are non-correlated. Cov(X, Y) = 0 If X and Y are independence, then EXY = EXEY D(X+Y) = DX + DY

  14. 相关系数的性质The properties of correlation coefficient • -1 ≤r ≤1 • 当 r = 0 时, y 的变化与x 无关， 即为零相关 • 当 | r | = 1时，y的变化完全由 x 的变化所引起，称为完全相关： 函数关系 • 正相关、负相关 (positively or negatively correlated)

  15. 相关系数 • 当 | r | ≥ 0.7 称为高度相关 • 当 | r | ≤ 0.3 称为低度相关 • 当 0.3 < | r | < 0.7 称为中度相关

  16. 相关关系示意图

  17. 某机械公司购进一新型设备，为了分配合适的工人操纵设备，进行该设备的工人劳动生产率与工龄之间的相关分析。某机械公司购进一新型设备，为了分配合适的工人操纵设备，进行该设备的工人劳动生产率与工龄之间的相关分析。 工人工龄与劳动生产率表

  18. r as an indicator of correlation? • Disclaimer: When n = 2, r is always 1 !

  19. 相关系数的检验Hypothesis test for significance of correlation • 零假设 • 备择假设 • 检验统计量：服从自由度为 n-2 的 t 分布 • 查表确定临界值 • 落入拒绝域或接受域

  20. 由工龄与生产率（分钟/件）的相关系数，检验总体是否相关 （α =0.05）？

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