【第2章课后习题参考答案】
Chapter 2 Exercise
1.
(a) better - a more flexible approach will fit the data closer and with the
large sample size a better fit than an inflexible approach would be obtained

(b) worse - a flexible method would overfit the small number of observations

(c) better - with more degrees of freedom, a flexible model would obtain a
better fit

(d) worse - flexible methods fit to the noise in the error terms and increase variance

2.
(a) regression. inference. quantitative output of CEO salary based on CEO
firm's features.
n - 500 firms in the US
p - profit, number of employees, industry

(b) classification. prediction. predicting new product's success or failure.
n - 20 similar products previously launched
p - price charged, marketing budget, comp. price, ten other variables

(c) regression. prediction. quantitative output of % change
n - 52 weeks of 2012 weekly data
p - % change in US market, % change in British market, % change in German market

3.
(a) See 3a.jpg.

(b)
all 5 lines >= 0

i. (squared) bias - decreases monotonically because increases in flexibility
yield a closer fit

ii. variance - increases monotonically because increases in flexibility yield
overfit

iii. training error - decreases monotonically because increases in flexibility
yield a closer fit

iv. test error - concave up curve because increase in flexibility yields a closer
fit before it overfits

v. Bayes (irreducible) error - defines the lower limit, the test error is bounded
below by the irreducible error due to variance in the error (epsilon) in the output
values (0 <= value). When the training error is lower than the irreducible error,
overfitting has taken place.
The Bayes error rate is defined for classification problems and is determined by
the ratio of data points which lie at the 'wrong' side of the decision boundary,
(0 <= value < 1).

4.
(a) i. stock market price direction, prediction, response: up, down,
input: yesterday's price movement % change, two previous day price movement %
change, etc.

ii. illness classification, inference, response: ill, healthy, input: resting
heart rate, resting breath rate, mile run time

iii. car part replacement, prediction, response: needs to be replace, good,
input: age of part, mileage used for, current amperage

(b) i. CEO salary. inference. predictors: age, industry experience, industry,
years of education. response: salary.

ii. car part replacement. inference. response: life of car part. predictors: age
of part, mileage used for, current amperage.

iii. illness classification, prediction, response: age of death,
input: current age, gender, resting heart rate, resting breath rate, mile run
time.

(c) i. cancer type clustering. diagnose cancer types more accurately.

ii. Netflix movie recommendations. recommend movies based on users who have
watched and rated similar movies.

iii. marketing survey. clustering of demographics for a product(s) to see which
clusters of consumers buy which products.

5.
The advantages for a very flexible approach for regression or classification
are obtaining a better fit for non-linear models, decreasing bias.

The disadvantages for a very flexible approach for regression or classification
are requires estimating a greater number of parameters, follow the noise too
closely (overfit), increasing variance.

A more flexible approach would be preferred to a less flexible approach when we
are interested in prediction and not the interpretability of the results.

A less flexible approach would be preferred to a more flexible approach when we
are interested in inference and the interpretability of the results.

6.
A parametric approach reduces the problem of estimating f down to one of
estimating a set of parameters because it assumes a form for f.

A non-parametric approach does not assume a functional form for f and so
requires a very large number of observations to accurately estimate f.

The advantages of a parametric approach to regression or classification are the
simplifying of modeling f to a few parameters and not as many observations are
required compared to a non-parametric approach.

The disadvantages of a parametric approach to regression or classification
are a potential to inaccurately estimate f if the form of f assumed is wrong or
to overfit the observations if more flexible models are used.

7.
(a)    Obs.   X1   X2   X3  Distance(0, 0, 0)   Y
---------------------------------------------
1      0    3    0   3                   Red
2      2    0    0   2                   Red
3      0    1    3   sqrt(10) ~ 3.2      Red
4      0    1    2   sqrt(5) ~ 2.2       Green
5      -1   0    1   sqrt(2) ~ 1.4       Green
6      1    1    1   sqrt(3) ~ 1.7       Red

(b) Green. Observation #5 is the closest neighbor for K = 1.

(c) Red. Observations #2, 5, 6 are the closest neighbors for K = 3. 2 is Red,
5 is Green, and 6 is Red.

(d) Small. A small K would be flexible for a non-linear decision boundary,
whereas a large K would try to fit a more linear boundary because it takes more
points into consideration.

# 8. (a)
college = read.csv("../data/College.csv")
# 8. (b)
fix(college)
rownames(college) = college[,1]
college = college[,-1]
fix(college)
# 8. (c)
# i.
summary(college)
# ii.
pairs(college[,1:10])
# iii.
plot(college$Private, college$Outstate)
# iv.
Elite = rep("No", nrow(college))
Elite[college$Top10perc>50] = "Yes"
Elite = as.factor(Elite)
college = data.frame(college, Elite)
summary(college$Elite)
plot(college$Elite, college$Outstate)
# v.
par(mfrow=c(2,2))
hist(college$Apps)
hist(college$perc.alumni, col=2)
hist(college$S.F.Ratio, col=3, breaks=10)
hist(college$Expend, breaks=100)
# vi.
par(mfrow=c(1,1))
plot(college$Outstate, college$Grad.Rate)
# High tuition correlates to high graduation rate.
plot(college$Accept / college$Apps, college$S.F.Ratio)
# Colleges with low acceptance rate tend to have low S:F ratio.
plot(college$Top10perc, college$Grad.Rate)
# Colleges with the most students from top 10% perc don't necessarily have
# the highest graduation rate. Also, rate > 100 is erroneous!

# 9.
Auto = read.csv("../data/Auto.csv", header=T, na.strings="?")
Auto = na.omit(Auto)
dim(Auto)
summary(Auto)

#9.(a)
# quantitative: mpg, cylinders, displacement, horsepower, weight,
# acceleration, year
# qualitative: name, origin

#9.(b)
# apply the range function to the first seven columns of Auto
sapply(Auto[, 1:7], range)
#       mpg cylinders displacement horsepower weight acceleration year
# [1,]  9.0         3           68         46   1613          8.0   70
# [2,] 46.6         8          455        230   5140         24.8   82

# 9.(c)
sapply(Auto[, 1:7], mean)
#         mpg    cylinders displacement   horsepower       weight acceleration
#   23.445918     5.471939   194.411990   104.469388  2977.584184    15.541327
#        year
#   75.979592

sapply(Auto[, 1:7], sd)
#         mpg    cylinders displacement   horsepower       weight acceleration
#    7.805007     1.705783   104.644004    38.491160   849.402560     2.758864
#        year
#    3.683737

#9.(d)
newAuto = Auto[-(10:85),]
dim(newAuto) == dim(Auto) - c(76,0)
newAuto[9,] == Auto[9,]
newAuto[10,] == Auto[86,]

sapply(newAuto[, 1:7], range)
#       mpg cylinders displacement horsepower weight acceleration year
# [1,] 11.0         3           68         46   1649          8.5   70
# [2,] 46.6         8          455        230   4997         24.8   82
sapply(newAuto[, 1:7], mean)
#         mpg    cylinders displacement   horsepower       weight acceleration
#   24.404430     5.373418   187.240506   100.721519  2935.971519    15.726899
#        year
#   77.145570
sapply(newAuto[, 1:7], sd)
#         mpg    cylinders displacement   horsepower       weight acceleration
#    7.867283     1.654179    99.678367    35.708853   811.300208     2.693721
#        year
#    3.106217

# 9.(e)
pairs(Auto)
plot(Auto$mpg, Auto$weight)
# Heavier weight correlates with lower mpg.
plot(Auto$mpg, Auto$cylinders)
# More cylinders, less mpg.
plot(Auto$mpg, Auto$year)
# Cars become more efficient over time.

#9.(f)
pairs(Auto)
# See descriptions of plots in (e).
# All of the predictors show some correlation with mpg. The name predictor has
# too little observations per name though, so using this as a predictor is
# likely to result in overfitting the data and will not generalize well.

# 10.
# 10.(a)
library(MASS)
?Boston
dim(Boston)
# 506 rows, 14 columns
# 14 features, 506 housing values in Boston suburbs

#10.(b)
pairs(Boston)
# X correlates with: a, b, c
# crim: age, dis, rad, tax, ptratio
# zn: indus, nox, age, lstat
# indus: age, dis
# nox: age, dis
# dis: lstat
# lstat: medv

#10.(c)
plot(Boston$age, Boston$crim)
# Older homes, more crime
plot(Boston$dis, Boston$crim)
# Closer to work-area, more crime
plot(Boston$rad, Boston$crim)
# Higher index of accessibility to radial highways, more crime
plot(Boston$tax, Boston$crim)
# Higher tax rate, more crime
plot(Boston$ptratio, Boston$crim)
# Higher pupil:teacher ratio, more crime

# 10.(d)
par(mfrow=c(1,3))
hist(Boston$crim[Boston$crim>1], breaks=25)
# most cities have low crime rates, but there is a long tail: 18 suburbs appear
# to have a crime rate > 20, reaching to above 80
hist(Boston$tax, breaks=25)
# there is a large divide between suburbs with low tax rates and a peak at 660-680
hist(Boston$ptratio, breaks=25)
# a skew towards high ratios, but no particularly high ratios

# 10.(e)
dim(subset(Boston, chas == 1))
# 35 suburbs

# 10.(f)
median(Boston$ptratio)
# 19.05

# 10.(g)
> t(subset(Boston, medv == min(Boston$medv)))
#              399      406
# crim     38.3518  67.9208 above 3rd quartile
# zn        0.0000   0.0000 at min
# indus    18.1000  18.1000 at 3rd quartile
# chas      0.0000   0.0000 not bounded by river
# nox       0.6930   0.6930 above 3rd quartile
# rm        5.4530   5.6830 below 1st quartile
# age     100.0000 100.0000 at max
# dis       1.4896   1.4254 below 1st quartile
# rad      24.0000  24.0000 at max
# tax     666.0000 666.0000 at 3rd quartile
# ptratio  20.2000  20.2000 at 3rd quartile
# black   396.9000 384.9700 at max; above 1st quartile
# lstat    30.5900  22.9800 above 3rd quartile
# medv      5.0000   5.0000 at min
summary(Boston)
# Not the best place to live, but certainly not the worst.

# 10.(h)
dim(subset(Boston, rm > 7))
# 64
dim(subset(Boston, rm > 8))
# 13
summary(subset(Boston, rm > 8))
summary(Boston)
# relatively lower crime (comparing range), lower lstat (comparing range)

【资源来源】
代码、数据：
https://github.com/asadoughi/stat-learning/archive/refs/heads/master.zip
https://www.statlearning.com/resources-first-edition

课后答案：
https://blog.princehonest.com/stat-learning/

网上视频：
https://www.dataschool.io/15-hours-of-expert-machine-learning-videos/

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