Problem 1:
Scientific modeling is a scientific activity, the aim
of which is to make a particular part or feature of the world easier to
understand, define, quantify, visualize or simulate by referencing it to
existing and usually commonly accepted knowledge. It requires selecting
and identifying relevant aspects of a situation in the real world and
then using different types of models for different aims, such as
conceptual models to better understand, operational models to
operationalize, mathematical models to quantify, and graphical models to
visualize the subject.
Problem 2:
Problem 3:
Do a research for interesting, unexpected, and useful
relationships in a dataset. These findings may be interesting mainly
because either they are unusual patterns or because they are very common
in the sense of being considered key characteristics of the phenomena.
Problem 4:
Problem 5:
Exploratory data analysis includes a series of
techniques that have as the main goal to provide useful summaries of a
dataset that highlight some characteristics of the data that the users
may find useful.
Problem 6:
TRUE
Problem 7:
Data summaries try to provide overviews of key
properties of the data. More specifically, they try to describe
important properties of the distribution of the values across the
observations in a dataset.
Problem 8:
package dplyr
Problem 9:
(a)
library(DMwR2)
library(dplyr)
data(algae)
algae## # A tibble: 200 × 18
## season size speed mxPH mnO2 Cl NO3 NH4 oPO4 PO4 Chla a1
## <fct> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 winter small medium 8 9.8 60.8 6.24 578 105 170 50 0
## 2 spring small medium 8.35 8 57.8 1.29 370 429. 559. 1.3 1.4
## 3 autumn small medium 8.1 11.4 40.0 5.33 347. 126. 187. 15.6 3.3
## 4 spring small medium 8.07 4.8 77.4 2.30 98.2 61.2 139. 1.4 3.1
## 5 autumn small medium 8.06 9 55.4 10.4 234. 58.2 97.6 10.5 9.2
## 6 winter small high 8.25 13.1 65.8 9.25 430 18.2 56.7 28.4 15.1
## 7 summer small high 8.15 10.3 73.2 1.54 110 61.2 112. 3.2 2.4
## 8 autumn small high 8.05 10.6 59.1 4.99 206. 44.7 77.4 6.9 18.2
## 9 winter small medium 8.7 3.4 22.0 0.886 103. 36.3 71 5.54 25.4
## 10 winter small high 7.93 9.9 8 1.39 5.8 27.2 46.6 0.8 17
## # ℹ 190 more rows
## # ℹ 6 more variables: a2 <dbl>, a3 <dbl>, a4 <dbl>, a5 <dbl>, a6 <dbl>,
## # a7 <dbl> data(iris)
iris## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
## 7 4.6 3.4 1.4 0.3 setosa
## 8 5.0 3.4 1.5 0.2 setosa
## 9 4.4 2.9 1.4 0.2 setosa
## 10 4.9 3.1 1.5 0.1 setosa
## 11 5.4 3.7 1.5 0.2 setosa
## 12 4.8 3.4 1.6 0.2 setosa
## 13 4.8 3.0 1.4 0.1 setosa
## 14 4.3 3.0 1.1 0.1 setosa
## 15 5.8 4.0 1.2 0.2 setosa
## 16 5.7 4.4 1.5 0.4 setosa
## 17 5.4 3.9 1.3 0.4 setosa
## 18 5.1 3.5 1.4 0.3 setosa
## 19 5.7 3.8 1.7 0.3 setosa
## 20 5.1 3.8 1.5 0.3 setosa
## 21 5.4 3.4 1.7 0.2 setosa
## 22 5.1 3.7 1.5 0.4 setosa
## 23 4.6 3.6 1.0 0.2 setosa
## 24 5.1 3.3 1.7 0.5 setosa
## 25 4.8 3.4 1.9 0.2 setosa
## 26 5.0 3.0 1.6 0.2 setosa
## 27 5.0 3.4 1.6 0.4 setosa
## 28 5.2 3.5 1.5 0.2 setosa
## 29 5.2 3.4 1.4 0.2 setosa
## 30 4.7 3.2 1.6 0.2 setosa
## 31 4.8 3.1 1.6 0.2 setosa
## 32 5.4 3.4 1.5 0.4 setosa
## 33 5.2 4.1 1.5 0.1 setosa
## 34 5.5 4.2 1.4 0.2 setosa
## 35 4.9 3.1 1.5 0.2 setosa
## 36 5.0 3.2 1.2 0.2 setosa
## 37 5.5 3.5 1.3 0.2 setosa
## 38 4.9 3.6 1.4 0.1 setosa
## 39 4.4 3.0 1.3 0.2 setosa
## 40 5.1 3.4 1.5 0.2 setosa
## 41 5.0 3.5 1.3 0.3 setosa
## 42 4.5 2.3 1.3 0.3 setosa
## 43 4.4 3.2 1.3 0.2 setosa
## 44 5.0 3.5 1.6 0.6 setosa
## 45 5.1 3.8 1.9 0.4 setosa
## 46 4.8 3.0 1.4 0.3 setosa
## 47 5.1 3.8 1.6 0.2 setosa
## 48 4.6 3.2 1.4 0.2 setosa
## 49 5.3 3.7 1.5 0.2 setosa
## 50 5.0 3.3 1.4 0.2 setosa
## 51 7.0 3.2 4.7 1.4 versicolor
## 52 6.4 3.2 4.5 1.5 versicolor
## 53 6.9 3.1 4.9 1.5 versicolor
## 54 5.5 2.3 4.0 1.3 versicolor
## 55 6.5 2.8 4.6 1.5 versicolor
## 56 5.7 2.8 4.5 1.3 versicolor
## 57 6.3 3.3 4.7 1.6 versicolor
## 58 4.9 2.4 3.3 1.0 versicolor
## 59 6.6 2.9 4.6 1.3 versicolor
## 60 5.2 2.7 3.9 1.4 versicolor
## 61 5.0 2.0 3.5 1.0 versicolor
## 62 5.9 3.0 4.2 1.5 versicolor
## 63 6.0 2.2 4.0 1.0 versicolor
## 64 6.1 2.9 4.7 1.4 versicolor
## 65 5.6 2.9 3.6 1.3 versicolor
## 66 6.7 3.1 4.4 1.4 versicolor
## 67 5.6 3.0 4.5 1.5 versicolor
## 68 5.8 2.7 4.1 1.0 versicolor
## 69 6.2 2.2 4.5 1.5 versicolor
## 70 5.6 2.5 3.9 1.1 versicolor
## 71 5.9 3.2 4.8 1.8 versicolor
## 72 6.1 2.8 4.0 1.3 versicolor
## 73 6.3 2.5 4.9 1.5 versicolor
## 74 6.1 2.8 4.7 1.2 versicolor
## 75 6.4 2.9 4.3 1.3 versicolor
## 76 6.6 3.0 4.4 1.4 versicolor
## 77 6.8 2.8 4.8 1.4 versicolor
## 78 6.7 3.0 5.0 1.7 versicolor
## 79 6.0 2.9 4.5 1.5 versicolor
## 80 5.7 2.6 3.5 1.0 versicolor
## 81 5.5 2.4 3.8 1.1 versicolor
## 82 5.5 2.4 3.7 1.0 versicolor
## 83 5.8 2.7 3.9 1.2 versicolor
## 84 6.0 2.7 5.1 1.6 versicolor
## 85 5.4 3.0 4.5 1.5 versicolor
## 86 6.0 3.4 4.5 1.6 versicolor
## 87 6.7 3.1 4.7 1.5 versicolor
## 88 6.3 2.3 4.4 1.3 versicolor
## 89 5.6 3.0 4.1 1.3 versicolor
## 90 5.5 2.5 4.0 1.3 versicolor
## 91 5.5 2.6 4.4 1.2 versicolor
## 92 6.1 3.0 4.6 1.4 versicolor
## 93 5.8 2.6 4.0 1.2 versicolor
## 94 5.0 2.3 3.3 1.0 versicolor
## 95 5.6 2.7 4.2 1.3 versicolor
## 96 5.7 3.0 4.2 1.2 versicolor
## 97 5.7 2.9 4.2 1.3 versicolor
## 98 6.2 2.9 4.3 1.3 versicolor
## 99 5.1 2.5 3.0 1.1 versicolor
## 100 5.7 2.8 4.1 1.3 versicolor
## 101 6.3 3.3 6.0 2.5 virginica
## 102 5.8 2.7 5.1 1.9 virginica
## 103 7.1 3.0 5.9 2.1 virginica
## 104 6.3 2.9 5.6 1.8 virginica
## 105 6.5 3.0 5.8 2.2 virginica
## 106 7.6 3.0 6.6 2.1 virginica
## 107 4.9 2.5 4.5 1.7 virginica
## 108 7.3 2.9 6.3 1.8 virginica
## 109 6.7 2.5 5.8 1.8 virginica
## 110 7.2 3.6 6.1 2.5 virginica
## 111 6.5 3.2 5.1 2.0 virginica
## 112 6.4 2.7 5.3 1.9 virginica
## 113 6.8 3.0 5.5 2.1 virginica
## 114 5.7 2.5 5.0 2.0 virginica
## 115 5.8 2.8 5.1 2.4 virginica
## 116 6.4 3.2 5.3 2.3 virginica
## 117 6.5 3.0 5.5 1.8 virginica
## 118 7.7 3.8 6.7 2.2 virginica
## 119 7.7 2.6 6.9 2.3 virginica
## 120 6.0 2.2 5.0 1.5 virginica
## 121 6.9 3.2 5.7 2.3 virginica
## 122 5.6 2.8 4.9 2.0 virginica
## 123 7.7 2.8 6.7 2.0 virginica
## 124 6.3 2.7 4.9 1.8 virginica
## 125 6.7 3.3 5.7 2.1 virginica
## 126 7.2 3.2 6.0 1.8 virginica
## 127 6.2 2.8 4.8 1.8 virginica
## 128 6.1 3.0 4.9 1.8 virginica
## 129 6.4 2.8 5.6 2.1 virginica
## 130 7.2 3.0 5.8 1.6 virginica
## 131 7.4 2.8 6.1 1.9 virginica
## 132 7.9 3.8 6.4 2.0 virginica
## 133 6.4 2.8 5.6 2.2 virginica
## 134 6.3 2.8 5.1 1.5 virginica
## 135 6.1 2.6 5.6 1.4 virginica
## 136 7.7 3.0 6.1 2.3 virginica
## 137 6.3 3.4 5.6 2.4 virginica
## 138 6.4 3.1 5.5 1.8 virginica
## 139 6.0 3.0 4.8 1.8 virginica
## 140 6.9 3.1 5.4 2.1 virginica
## 141 6.7 3.1 5.6 2.4 virginica
## 142 6.9 3.1 5.1 2.3 virginica
## 143 5.8 2.7 5.1 1.9 virginica
## 144 6.8 3.2 5.9 2.3 virginica
## 145 6.7 3.3 5.7 2.5 virginica
## 146 6.7 3.0 5.2 2.3 virginica
## 147 6.3 2.5 5.0 1.9 virginica
## 148 6.5 3.0 5.2 2.0 virginica
## 149 6.2 3.4 5.4 2.3 virginica
## 150 5.9 3.0 5.1 1.8 virginica summary(algae)## season size speed mxPH mnO2
## autumn:40 large :45 high :84 Min. :5.600 Min. : 1.500
## spring:53 medium:84 low :33 1st Qu.:7.700 1st Qu.: 7.725
## summer:45 small :71 medium:83 Median :8.060 Median : 9.800
## winter:62 Mean :8.012 Mean : 9.118
## 3rd Qu.:8.400 3rd Qu.:10.800
## Max. :9.700 Max. :13.400
## NA's :1 NA's :2
## Cl NO3 NH4 oPO4
## Min. : 0.222 Min. : 0.050 Min. : 5.00 Min. : 1.00
## 1st Qu.: 10.981 1st Qu.: 1.296 1st Qu.: 38.33 1st Qu.: 15.70
## Median : 32.730 Median : 2.675 Median : 103.17 Median : 40.15
## Mean : 43.636 Mean : 3.282 Mean : 501.30 Mean : 73.59
## 3rd Qu.: 57.824 3rd Qu.: 4.446 3rd Qu.: 226.95 3rd Qu.: 99.33
## Max. :391.500 Max. :45.650 Max. :24064.00 Max. :564.60
## NA's :10 NA's :2 NA's :2 NA's :2
## PO4 Chla a1 a2
## Min. : 1.00 Min. : 0.200 Min. : 0.00 Min. : 0.000
## 1st Qu.: 41.38 1st Qu.: 2.000 1st Qu.: 1.50 1st Qu.: 0.000
## Median :103.29 Median : 5.475 Median : 6.95 Median : 3.000
## Mean :137.88 Mean : 13.971 Mean :16.92 Mean : 7.458
## 3rd Qu.:213.75 3rd Qu.: 18.308 3rd Qu.:24.80 3rd Qu.:11.375
## Max. :771.60 Max. :110.456 Max. :89.80 Max. :72.600
## NA's :2 NA's :12
## a3 a4 a5 a6
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 1.550 Median : 0.000 Median : 1.900 Median : 0.000
## Mean : 4.309 Mean : 1.992 Mean : 5.064 Mean : 5.964
## 3rd Qu.: 4.925 3rd Qu.: 2.400 3rd Qu.: 7.500 3rd Qu.: 6.925
## Max. :42.800 Max. :44.600 Max. :44.400 Max. :77.600
##
## a7
## Min. : 0.000
## 1st Qu.: 0.000
## Median : 1.000
## Mean : 2.495
## 3rd Qu.: 2.400
## Max. :31.600
## summary(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
##
Problem 10:
The summarise() function can be used to apply any
function that produces a scalar value to any column of a data frame
table.
Problem 11:
We can apply a set of functions to all columns of a
data set table using functions summarise_each() and funs().
Problem 12:
It can be used to form sub-groups of a dataset using
all combinations of the values of one or more normal variables.
Problem 13:
summarise()
Problem 14:
Mode <- function(x, na.rm = FALSE){
if(na.rm) x <- x[!is.na(x)]
ux <- unique(x)
return(ux[which.max(tabulate(match(x, ux)))])
}
Mode(iris$Sepal.Length, na.rm = TRUE)## [1] 5Mode(iris$Petal.Length)## [1] 1.4
Problem 15:
Function centralValue() in our book package can be
used to obtain the more adequate statistic of centrality of a given
sample of values. It will return the median in the case of numeric
variables and the mode for nominal variables.
Problem 16:
(a) IQR is the difference between the 3rd and 1st
quartiles. It is the interval that contains 50% of the most central
values of a continuous variable.
(b) The x-quartile is the value
below which there are x % of the observed values.
(c) A large
value of the IQR means that these central values are spread over a large
range.
(d) A small value represents a very packed set of values.
Problem 17:
the range
Problem 18:
a.
aggregate(iris$Sepal.Length, list(Species=iris$Species), quantile)## Species x.0% x.25% x.50% x.75% x.100%
## 1 setosa 4.300 4.800 5.000 5.200 5.800
## 2 versicolor 4.900 5.600 5.900 6.300 7.000
## 3 virginica 4.900 6.225 6.500 6.900 7.900
Problem 19:
Mode <- function(x, na.rm = FALSE){
if(na.rm) x <- x[!is.na(x)]
ux <- unique(x)
return(ux[which.max(tabulate(match(x, ux)))])
}
Mode(iris$Species, na.rm = TRUE)## [1] setosa
## Levels: setosa versicolor virginica
Problem 20:
(a) R pipes are a way to chain multiple operations
together in a concise and expressive way.
(b) They are represented
by the %>% operator.
(c) It takes the output of the expression
on its left and passes it as the first argument to the function on its
right.
Problem 21:
The second argument of the aggregate() function is a
list that can include as many factors as you want to form the sub-group
of the data.
Problem 22:
The second argument was answered in the previous
question. For each sub-group the function supplied in the third argument
is applied to the values of the variables specified in the first
argument.
Problem 23:
You can use the as.numeric() function.
Problem 24:
(a) If we want to check how many unknown values
exist in a database, we can proceed as follows.
(b)
data(algae, package = "DMwR2")
nasRow <- apply(algae, 1, function(r) sum(is.na(r)))
cat("The Algae database contains ", sum(nasRow), " NA values.\n")## The Algae database contains 33 NA values.
Problem 25:
(a) The method is the boxplot rule.
(b) This
rules states that a value in a sample of a continuous variable is
considered an outlier if it is outside of the interval [Q1 - 1.5 * IQR,
Q3 + 1.5 * IQR], where Q1, Q3 are the first, and third quartile, and IQR
= Q3 - Q1 the interquartile range.
Problem 26:
The result is a summary of basic descriptive
statistics of the dataset.
Problem 27:
(a) It is used for a global summary of a dataset.
(b) Hmisc
Problem 28:
As a verb, it means to analyze (a sentence) into its
parts and describe their syntactic roles.
As a noun, it means an
act of or the result obtained by parsing a string or a text.