Riemann surface
matlab
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多元统计分析的基本概念：涵盖多元统计分析的基础知识，如多元正态分布、多元线性回归等。
多元数据的描述和推断：研究多元数据的描述性统计量，包括平均向量、协方差矩阵等，以及基于多元正态分布的推断方法。
多元线性回归分析：介绍多元线性回归分析的方法和应用，包括模型设定、参数估计和假设检验。
判别分析和聚类分析：探索判别分析和聚类分析的理论和方法，如线性判别分析、K-means聚类等。
主成分分析和因子分析：研究主成分分析和因子分析的理论和方法，如主成分的提取、因子旋转和因子得分的计算。
多维尺度分析和对应分析：介绍多维尺度分析和对应分析的理论和方法，如经典的多维尺度分析、对应分析的应用等。
多元方差分析：探讨多元方差分析的理论和方法，如模型设定、参数估计和假设检验。
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EXERCISE 1.1 Is the upper extreme always an outlier?
EXERCISE 1.2 Is it possible for the mean or the median to lie outside of the fourths or even outside of the outside bars?
EXERCISE 1.3 Assume that the data are normally distributed $N(0,1)$. What percentage of the data do you expect to lie outside the outside bars?
EXERCISE 1.4 What percentage of the data do you expect to lie outside the outside bars if we assume that the data are normally distributed $N\left(0, \sigma^2\right)$ with unknown variance $\sigma^2$ ?
EXERCISE 1.5 How would the five-number summary of the 15 largest U.S. cities differ from that of the 50 largest U.S. cities? How would the five-number summary of 15 observations of $N(0,1)$-distributed data differ from that of 50 observations from the same distribution?
EXERCISE 1.6 Is it possible that all five numbers of the five-number summary could be equal? If so, under what conditions?
EXERCISE 1.7 Suppose we have 50 observations of $X \sim N(0,1)$ and another 50 observations of $Y \sim N(2,1)$. What would the 100 Flury faces look like if you had defined as face elements the face line and the darkness of hair? Do you expect any similar faces? How many faces do you think should look like observations of $Y$ even though they are $X$ observations?
EXERCISE 1.8 Draw a histogram for the mileage variable of the car data (Table B.3). Do the same for the three groups (U.S., Japan, Europe). Do you obtain a similar conclusion as in the parallel boxplot on Figure 1.3 for these data?
EXERCISE 1.9 Use some bandwidth selection criterion to calculate the optimally chosen bandwidth $h$ for the diagonal variable of the bank notes. Would it be better to have one bandwidth for the two groups?
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