R语言统计分析实战：数据建模与案例解析

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"该资源是关于R语言在统计分析中的应用，主要面向数据分析初学者，包含实际案例和代码，旨在帮助学习者理解数据建模的基本概念。书籍由Gareth James、Daniela Witten、Trevor Hastie和Robert Tibshirani等知名专家合著，是 Springer Texts in Statistics 系列的一部分，提供了使用R语言进行统计学习的全面介绍。" 在统计分析领域，R语言因其强大的数据处理、图形制作和统计计算能力而备受青睐。本资源详细探讨了R语言在数据建模中的应用，是学习数据分析基础知识的理想选择。以下是该资源可能涵盖的一些关键知识点： 1. **R语言基础**：R语言的基本语法、数据类型、向量、矩阵、列表和数据框的操作，以及如何读取和写入数据文件。 2. **统计基础**：描述性统计、概率论基础、假设检验、置信区间和显著性水平的概念，这些都是数据分析的基石。 3. **数据预处理**：包括数据清洗、缺失值处理、异常值检测和转换，这是建模前必不可少的步骤。 4. **回归分析**：线性回归、逻辑回归、多项式回归等，这些模型用于预测连续或分类变量。 5. **聚类分析**：K-means聚类、层次聚类等，用于发现数据中的自然群体。 6. **判别分析**：如主成分分析（PCA）、因子分析等，用于降低数据的维度并识别变量之间的关系。 7. **决策树与随机森林**：这些算法在分类和回归问题中广泛应用，随机森林则通过集成学习提高预测性能。 8. **支持向量机（SVM）**：一种高效且灵活的分类和回归方法，能处理高维数据。 9. **机器学习算法**：如神经网络、Boosting、Bagging等，以及它们在R中的实现，如caret包。 10. **模型评估与选择**：交叉验证、AUC、ROC曲线、R-squared等指标的使用，以及模型比较和选择的方法。 11. **可视化**：R中的ggplot2库用于创建专业图表，有助于理解数据和展示结果。 12. **大数据处理**：使用data.table或dplyr等包进行大规模数据操作，以及使用SparkR进行分布式计算。 13. **实战案例**：书中包含的案例分析将理论知识与实际问题相结合，使学习者能够将理论应用于实际场景。通过这本书，读者不仅可以掌握R语言的基本用法，还能深入了解统计建模的原理和应用。此外，书中的代码示例提供了实践操作的机会，对于初学者来说，这是一条快速进入数据分析世界的捷径。

2 1. Introduction

Age

Wage

Ye a r

Wage

20 40 60 80

50 100 200 300

2003 2006 2009

12345

Education Level

Wage

FIGURE 1.1. Wage data, which contains income survey information for males

from the central Atlantic region of the United States. Left: wage as a function of

age. On average, wage increases with age until about 60 years of age, at which

point it begins to decline. Center: wage as a function of year.Thereisaslow

but steady increase of approximately $10,000 in the average wage between 2003

and 2009. Right: Boxplots displaying wage as a function of education,with1

indicating the lowest level (no high school diploma) and 5 the highest level (an

advanced graduate degree). On average, wage increases with the level of education.

Givenanemployee’sage, we can use this curve to predict his wage. However,

it is also clear from Figure 1.1 that there is a signiﬁcant amount of vari-

ability associated with this average value, and so

age alone is unlikely to

provide an accurate prediction of a particular man’s

wage.

We also have information regarding each employee’s education level and

the

year in which the wage was earned. The center and right-hand panels of

Figure 1.1, which display

wage as a function of both year and education,in-

dicate that both of these factors are associated with

wage. Wages increase

by approximately $10,000, in a roughly linear (or straight-line) fashion,

between 2003 and 2009, though this rise is very slight relative to the vari-

ability in the data. Wages are also typically greater for individuals with

higher education levels: men with the lowest education level (1) tend to

have substantially lower wages than those with the highest education level

(5). Clearly, the most accurate prediction of a given man’s

wage will be

obtained by combining his

age,hiseducation,andtheyear. In Chapter 3,

we discuss linear regression, which can be used to predict

wage from this

data set. Ideally, we should predict

wage in a way that accounts for the

non-linear relationship between

wage and age. In Chapter 7, we discuss a

class of approaches for addressing this problem.

Stock Market Data

The Wage data involves predicting a continuous or quantitative output value.

This is often referred to as a regression problem. However, in certain cases

we may instead wish to predict a non-numerical value—that is, a categorical

1. Introduction 3

Yesterday

Today’s Direction

Percentage change in S&P

Two Days Previous

Percentage change in S&P

Down Up

Today’s Direction

Down Up

Today’s Direction

Down Up

−4 −2 0 2 4 6

Three Days Previous

Percentage change in S&P

FIGURE 1.2. Left: Boxplots of the previous day’s percentage change in the S&P

index for the days for which the market increased or decreased, obtained from the

Smarket data. Center and Right: Same as left panel, but the percentage changes

for 2 and 3 days previous are shown.

or qualitative output. For example, in Chapter 4 we examine a stock mar-

ket data set that contains the daily movements in the Standard & Poor’s

500 (S&P) stock index over a 5-year period between 2001 and 2005. We

refer to this as the

Smarket data. The goal is to predict whether the index

will increase or decrease on a given day using the past 5 days’ percentage

changes in the index. Here the statistical learning problem does not in-

volve predicting a numerical value. Instead it involves predicting whether

a given day’s stock market performance will fall into the

Up bucket or the

Down bucket. This is known as a classiﬁcation problem. A model that could

accurately predict the direction in which the market will move would be

very useful!

The left-hand panel of Figure 1.2 displays two boxplots of the previous

day’s percentage changes in the stock index: one for the 648 days for which

the market increased on the subsequent day, and one for the 602 days for

which the market decreased. The two plots look almost identical, suggest-

ing that there is no simple strategy for using yesterday’s movement in the

S&P to predict today’s returns. The remaining panels, which display box-

plots for the percentage changes 2 and 3 days previous to today, similarly

indicate little association between past and present returns. Of course, this

lack of pattern is to be expected: in the presence of strong correlations be-

tween successive days’ returns, one could adopt a simple trading strategy

to generate proﬁts from the market. Nevertheless, in Chapter 4, we explore

these data using several diﬀerent statistical learning methods. Interestingly,

there are hints of some weak trends in the data that suggest that, at least

for this 5-year period, it is possible to correctly predict the direction of

movement in the market approximately 60% of the time (Figure 1.3).

4 1. Introduction

Down Up

0.46 0.48 0.50 0.52

Today’s Direction

Predicted Probability

FIGURE 1.3. We ﬁt a quadratic discriminant analysis model to the subset

of the Smarket data corresponding to the 2001–2004 time period, and predicted

the probability of a stock market decrease using the 2005 data. On average, the

predicted probability of decrease is higher for the days in which the market does

decrease. Based on these results, we are able to correctly predict the direction of

movement in the market 60% of the time.

Gene Expression Data

The previous two applications illustrate data sets with both input and

output variables. However, another important class of problems involves

situations in which we only observe input variables, with no corresponding

output. For example, in a marketing setting, we might have demographic

information for a number of current or potential customers. We may wish to

understand which types of customers are similar to each other by grouping

individuals according to their observed characteristics. This is known as a

clustering problem. Unlike in the previous examples, here we are not trying

to predict an output variable.

We devote Chapter 10 to a discussion of statistical learning methods

for problems in which no natural output variable is available. We consider

the

NCI60 data set, which consists of 6,830 gene expression measurements

for each of 64 cancer cell lines. Instead of predicting a particular output

variable, we are interested in determining whether there are groups, or

clusters, among the cell lines based on their gene expression measurements.

This is a diﬃcult question to address, in part because there are thousands

of gene expression measurements per cell line, making it hard to visualize

the data.

The left-hand panel of Figure 1.4 addresses this problem by represent-

ing each of the 64 cell lines using just two numbers, Z

and Z

.These

are the ﬁrst two principal components of the data, which summarize the

6, 830 expression measurements for each cell line down to two numbers or

dimensions. While it is likely that this dimension reduction has resulted in

1. Introduction 5

−40 −20 0 20 40 60

−60 −40 −20 0 20

−40 −20 0 20 40 60

FIGURE 1.4. Left: Representation of the NCI60 gene expression data set in

a two-dimensional space, Z

and Z

. Each point corresponds to one of the 64

cell lines. There appear to be four groups of cell lines, which we have represented

using diﬀerent colors. Right: Same as left panel except that we have represented

each of the 14 diﬀerent types of cancer using a diﬀerent colored symbol. Cell lines

corresponding to the same cancer type tend to be nearby in the two-dimensional

space.

some loss of information, it is now possible to visually examine the data for

evidence of clustering. Deciding on the number of clusters is often a diﬃ-

cult problem. But the left-hand panel of Figure 1.4 suggests at least four

groups of cell lines, which we have represented using separate colors. We

can now examine the cell lines within each cluster for similarities in their

types of cancer, in order to better understand the relationship between

gene expression levels and cancer.

In this particular data set, it turns out that the cell lines correspond

to 14 diﬀerent types of cancer. (However, this information was not used

to create the left-hand panel of Figure 1.4.) The right-hand panel of Fig-

ure 1.4 is identical to the left-hand panel, except that the 14 cancer types

are shown using distinct colored symbols. There is clear evidence that cell

lines with the same cancer type tend to be located near each other in this

two-dimensional representation. In addition, even though the cancer infor-

mation was not used to produce the left-hand panel, the clustering obtained

does bear some resemblance to some of the actual cancer types observed

in the right-hand panel. This provides some independent veriﬁcation of the

accuracy of our clustering analysis.

A Brief History of Statistical Learning

Though the term statistical learning is fairly new, many of the concepts

that underlie the ﬁeld were developed long ago. At the beginning of the

nineteenth century, Legendre and Gauss published papers on the method

6 1. Introduction

of least squares, which implemented the earliest form of what is now known

as linear regression. The approach was ﬁrst successfully applied to problems

in astronomy. Linear regression is used for predicting quantitative values,

such as an individual’s salary. In order to predict qualitative values, such as

whether a patient survives or dies, or whether the stock market increases

or decreases, Fisher proposed linear discriminant analysis in 1936. In the

1940s, various authors put forth an alternative approach, logistic regression.

In the early 1970s, Nelder and Wedderburn coined the term generalized

linear models for an entire class of statistical learning methods that include

both linear and logistic regression as special cases.

By the end of the 1970s, many more techniques for learning from data

were available. However, they were almost exclusively linear methods, be-

cause ﬁtting non-linear relationships was computationally infeasible at the

time. By the 1980s, computing technology had ﬁnally improved suﬃciently

that non-linear methods were no longer computationally prohibitive. In mid

1980s Breiman, Friedman, Olshen and Stone introduced classiﬁcation and

regression trees, and were among the ﬁrst to demonstrate the power of a

detailed practical implementation of a method, including cross-validation

for model selection. Hastie and Tibshirani coined the term generalized addi-

tive models in 1986 for a class of non-linear extensions to generalized linear

models, and also provided a practical software implementation.

Since that time, inspired by the advent of machine learning and other

disciplines, statistical learning has emerged as a new subﬁeld in statistics,

focused on supervised and unsupervised modeling and prediction. In recent

years, progress in statistical learning has been marked by the increasing

availability of powerful and relatively user-friendly software, such as the

popular and freely available

R system. This has the potential to continue

the transformation of the ﬁeld from a set of techniques used and developed

by statisticians and computer scientists to an essential toolkit for a much

broader community.

This Book

The Elements of Statistical Learning (ESL) by Hastie, Tibshirani, and

Friedman was ﬁrst published in 2001. Since that time, it has become an

important reference on the fundamentals of statistical machine learning.

Its success derives from its comprehensive and detailed treatment of many

important topics in statistical learning, as well as the fact that (relative to

many upper-level statistics textbooks) it is accessible to a wide audience.

However, the greatest factor behind the success of ESL has been its topical

nature. At the time of its publication, interest in the ﬁeld of statistical

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