Computer Science Concatenating Constructing & Modifying Lists Question

Organize the key contents in the textbook and make notes.

An Introduction to R
Notes on R: A Programming Environment for Data Analysis and Graphics
Version 4.3.1 (2023-06-16)
W. N. Venables, D. M. Smith
and the R Core Team
This manual is for R, version 4.3.1 (2023-06-16).
Copyright c 1990 W. N. Venables
Copyright c 1992 W. N. Venables & D. M. Smith
Copyright c 1997 R. Gentleman & R. Ihaka
Copyright c 1997, 1998 M. Maechler
Copyright c 1999–2023 R Core Team
Permission is granted to make and distribute verbatim copies of this manual provided
the copyright notice and this permission notice are preserved on all copies.
Permission is granted to copy and distribute modified versions of this manual under
the conditions for verbatim copying, provided that the entire resulting derived work
is distributed under the terms of a permission notice identical to this one.
Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this
permission notice may be stated in a translation approved by the R Core Team.
i
Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1
Introduction and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 The R environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Related software and documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 R and statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 R and the window system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Using R interactively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.6 An introductory session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.7 Getting help with functions and features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.8 R commands, case sensitivity, etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.9 Recall and correction of previous commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.10 Executing commands from or diverting output to a file . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.11 Data permanency and removing objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2
Simple manipulations; numbers and vectors . . . . . . . . . . . . . . . . . 7
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3
Objects, their modes and attributes . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1
3.2
3.3
3.4
4
Intrinsic attributes: mode and length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Changing the length of an object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Getting and setting attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
The class of an object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Ordered and unordered factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1
4.2
4.3
5
Vectors and assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Vector arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Generating regular sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Logical vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Missing values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Character vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Index vectors; selecting and modifying subsets of a data set. . . . . . . . . . . . . . . . . . . . . . . . 10
Other types of objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
A specific example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
The function tapply() and ragged arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Ordered factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Arrays and matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1
5.2
5.3
5.4
Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Array indexing. Subsections of an array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Index matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
The array() function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.4.1 Mixed vector and array arithmetic. The recycling rule . . . . . . . . . . . . . . . . . . . . . . . . 20
5.5 The outer product of two arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.6 Generalized transpose of an array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.7 Matrix facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.7.1 Matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
ii
5.7.2 Linear equations and inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.7.3 Eigenvalues and eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.7.4 Singular value decomposition and determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.7.5 Least squares fitting and the QR decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.8 Forming partitioned matrices, cbind() and rbind() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.9 The concatenation function, c(), with arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.10 Frequency tables from factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6
Lists and data frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.1
6.2
Lists. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Constructing and modifying lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.2.1 Concatenating lists. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.3 Data frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.3.1 Making data frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.3.2 attach() and detach() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.3.3 Working with data frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.3.4 Attaching arbitrary lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.3.5 Managing the search path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7
Reading data from files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.1
7.2
7.3
The read.table() function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
The scan() function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Accessing builtin datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.1 Loading data from other R packages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.4 Editing data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
8
Probability distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
8.1
8.2
8.3
9
R as a set of statistical tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Examining the distribution of a set of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
One- and two-sample tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Grouping, loops and conditional execution . . . . . . . . . . . . . . . . . 40
9.1
9.2
10
Grouped expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Control statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.2.1 Conditional execution: if statements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.2.2 Repetitive execution: for loops, repeat and while . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Writing your own functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
10.1 Simple examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
10.2 Defining new binary operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
10.3 Named arguments and defaults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
10.4 The ‘…’ argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
10.5 Assignments within functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
10.6 More advanced examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
10.6.1 Efficiency factors in block designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
10.6.2 Dropping all names in a printed array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
10.6.3 Recursive numerical integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
10.7 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
10.8 Customizing the environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
10.9 Classes, generic functions and object orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
iii
11
Statistical models in R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
11.1 Defining statistical models; formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
11.1.1 Contrasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
11.2 Linear models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
11.3 Generic functions for extracting model information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
11.4 Analysis of variance and model comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
11.4.1 ANOVA tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
11.5 Updating fitted models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
11.6 Generalized linear models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
11.6.1 Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
11.6.2 The glm() function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
11.7 Nonlinear least squares and maximum likelihood models . . . . . . . . . . . . . . . . . . . . . . . . . . 59
11.7.1 Least squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
11.7.2 Maximum likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
11.8 Some non-standard models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
12
Graphical procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
12.1 High-level plotting commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
12.1.1 The plot() function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
12.1.2 Displaying multivariate data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
12.1.3 Display graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
12.1.4 Arguments to high-level plotting functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
12.2 Low-level plotting commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
12.2.1 Mathematical annotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
12.2.2 Hershey vector fonts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
12.3 Interacting with graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
12.4 Using graphics parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
12.4.1 Permanent changes: The par() function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
12.4.2 Temporary changes: Arguments to graphics functions . . . . . . . . . . . . . . . . . . . . . . . 69
12.5 Graphics parameters list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
12.5.1 Graphical elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
12.5.2 Axes and tick marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
12.5.3 Figure margins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
12.5.4 Multiple figure environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
12.6 Device drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
12.6.1 PostScript diagrams for typeset documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
12.6.2 Multiple graphics devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
12.7 Dynamic graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
13
Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
13.1
13.2
13.3
14
Standard packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Contributed packages and CRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Namespaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
OS facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
14.1
14.2
14.3
14.4
Files and directories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Filepaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
System commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Compression and Archives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Appendix A
A sample session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
iv
Appendix B
B.1
B.2
B.3
B.4
Invoking R from the command line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Invoking R under Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Invoking R under macOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Scripting with R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Appendix C
C.1
C.2
C.3
Invoking R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
The command-line editor . . . . . . . . . . . . . . . . . . . . . . . . 92
Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Editing actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Command-line editor summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Appendix D Function and variable index . . . . . . . . . . . . . . . . . . . . . 94
Appendix E
Concept index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Appendix F
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
1
Preface
This introduction to R is derived from an original set of notes describing the S and S-Plus
environments written in 1990–2 by Bill Venables and David M. Smith when at the University
of Adelaide. We have made a number of small changes to reflect differences between the R and
S programs, and expanded some of the material.
We would like to extend warm thanks to Bill Venables (and David Smith) for granting
permission to distribute this modified version of the notes in this way, and for being a supporter
of R from way back.
Comments and corrections are always welcome. Please address email correspondence to
R-help@R-project.org.
Suggestions to the reader
Most R novices will start with the introductory session in Appendix A. This should give some
familiarity with the style of R sessions and more importantly some instant feedback on what
actually happens.
Many users will come to R mainly for its graphical facilities. See Chapter 12 [Graphics],
page 63, which can be read at almost any time and need not wait until all the preceding sections
have been digested.
2
1 Introduction and preliminaries
1.1 The R environment
R is an integrated suite of software facilities for data manipulation, calculation and graphical
display. Among other things it has
• an effective data handling and storage facility,
• a suite of operators for calculations on arrays, in particular matrices,
• a large, coherent, integrated collection of intermediate tools for data analysis,
• graphical facilities for data analysis and display either directly at the computer or on hardcopy, and
• a well developed, simple and effective programming language (called ‘S’) which includes
conditionals, loops, user defined recursive functions and input and output facilities. (Indeed
most of the system supplied functions are themselves written in the S language.)
The term “environment” is intended to characterize it as a fully planned and coherent system,
rather than an incremental accretion of very specific and inflexible tools, as is frequently the
case with other data analysis software.
R is very much a vehicle for newly developing methods of interactive data analysis. It has
developed rapidly, and has been extended by a large collection of packages. However, most
programs written in R are essentially ephemeral, written for a single piece of data analysis.
1.2 Related software and documentation
R can be regarded as an implementation of the S language which was developed at Bell Laboratories by Rick Becker, John Chambers and Allan Wilks, and also forms the basis of the S-Plus
systems.
The evolution of the S language is characterized by four books by John Chambers and
coauthors. For R, the basic reference is The New S Language: A Programming Environment
for Data Analysis and Graphics by Richard A. Becker, John M. Chambers and Allan R. Wilks.
The new features of the 1991 release of S are covered in Statistical Models in S edited by John
M. Chambers and Trevor J. Hastie. The formal methods and classes of the methods package are
based on those described in Programming with Data by John M. Chambers. See Appendix F
[References], page 99, for precise references.
There are now a number of books which describe how to use R for data analysis and statistics,
and documentation for S/S-Plus can typically be used with R, keeping the differences between
the S implementations in mind. See Section “What documentation exists for R?” in The R
statistical system FAQ.
1.3 R and statistics
Our introduction to the R environment did not mention statistics, yet many people use R as a
statistics system. We prefer to think of it of an environment within which many classical and
modern statistical techniques have been implemented. A few of these are built into the base R
environment, but many are supplied as packages. There are about 25 packages supplied with
R (called “standard” and “recommended” packages) and many more are available through the
CRAN family of Internet sites (via https://CRAN.R-project.org) and elsewhere. More details
on packages are given later (see Chapter 13 [Packages], page 77).
Most classical statistics and much of the latest methodology is available for use with R, but
users may need to be prepared to do a little work to find it.
Chapter 1: Introduction and preliminaries
3
There is an important difference in philosophy between S (and hence R) and the other
main statistical systems. In S a statistical analysis is normally done as a series of steps, with
intermediate results being stored in objects. Thus whereas SAS and SPSS will give copious
output from a regression or discriminant analysis, R will give minimal output and store the
results in a fit object for subsequent interrogation by further R functions.
1.4 R and the window system
The most convenient way to use R is at a graphics workstation running a windowing system.
This guide is aimed at users who have this facility. In particular we will occasionally refer to
the use of R on an X window system although the vast bulk of what is said applies generally to
any implementation of the R environment.
Most users will find it necessary to interact directly with the operating system on their
computer from time to time. In this guide, we mainly discuss interaction with the operating
system on UNIX machines. If you are running R under Windows or macOS you will need to
make some small adjustments.
Setting up a workstation to take full advantage of the customizable features of R is a straightforward if somewhat tedious procedure, and will not be considered further here. Users in difficulty should seek local expert help.
1.5 Using R interactively
When you use the R program it issues a prompt when it expects input commands. The default
prompt is ‘>’, which on UNIX might be the same as the shell prompt, and so it may appear that
nothing is happening. However, as we shall see, it is easy to change to a different R prompt if
you wish. We will assume that the UNIX shell prompt is ‘$’.
In using R under UNIX the suggested procedure for the first occasion is as follows:
1. Create a separate sub-directory, say work, to hold data files on which you will use R for
this problem. This will be the working directory whenever you use R for this particular
problem.
$ mkdir work
$ cd work
2. Start the R program with the command
$ R
3. At this point R commands may be issued (see later).
4. To quit the R program the command is
> q()
At this point you will be asked whether you want to save the data from your R session. On
some systems this will bring up a dialog box, and on others you will receive a text prompt
to which you can respond yes, no or cancel (a single letter abbreviation will do) to save
the data before quitting, quit without saving, or return to the R session. Data which is
saved will be available in future R sessions.
Further R sessions are simple.
1. Make work the working directory and start the program as before:
$ cd work
$ R
2. Use the R program, terminating with the q() command at the end of the session.
To use R under Windows the procedure to follow is basically the same. Create a folder as
the working directory, and set that in the Start In field in your R shortcut. Then launch R by
double clicking on the icon.
Chapter 1: Introduction and preliminaries
4
1.6 An introductory session
Readers wishing to get a feel for R at a computer before proceeding are strongly advised to work
through the introductory session given in Appendix A [A sample session], page 82.
1.7 Getting help with functions and features
R has an inbuilt help facility similar to the man facility of UNIX. To get more information on
any specific named function, for example solve, the command is
> help(solve)
An alternative is
> ?solve
For a feature specified by special characters, the argument must be enclosed in double or single
quotes, making it a “character string”: This is also necessary for a few words with syntactic
meaning including if, for and function.
> help(“[[“)
Either form of quote mark may be used to escape the other, as in the string “It’s
important”. Our convention is to use double quote marks for preference.
On most R installations help is available in HTML format by running
> help.start()
which will launch a Web browser that allows the help pages to be browsed with hyperlinks. On
UNIX, subsequent help requests are sent to the HTML-based help system. The ‘Search Engine
and Keywords’ link in the page loaded by help.start() is particularly useful as it is contains
a high-level concept list which searches though available functions. It can be a great way to get
your bearings quickly and to understand the breadth of what R has to offer.
The help.search command (alternatively ??) allows searching for help in various ways. For
example,
> ??solve
Try ?help.search for details and more examples.
The examples on a help topic can normally be run by
> example(topic)
Windows versions of R have other optional help systems: use
> ?help
for further details.
1.8 R commands, case sensitivity, etc.
Technically R is an expression language with a very simple syntax. It is case sensitive as are most
UNIX based packages, so A and a are different symbols and would refer to different variables.
The set of symbols which can be used in R names depends on the operating system and country
within which R is being run (technically on the locale in use). Normally all alphanumeric
symbols are allowed1 (and in some countries this includes accented letters) plus ‘.’ and ‘_’, with
the restriction that a name must start with ‘.’ or a letter, and if it starts with ‘.’ the second
character must not be a digit. Names are effectively unlimited in length.
Elementary commands consist of either expressions or assignments. If an expression is given
as a command, it is evaluated, printed (unless specifically made invisible), and the value is lost.
An assignment also evaluates an expression and passes the value to a variable but the result is
not automatically printed.
1
For portable R code (including that to be used in R packages) only A–Za–z0–9 should be used.
Chapter 1: Introduction and preliminaries
5
Commands are separated either by a semi-colon (‘;’), or by a newline. Elementary commands
can be grouped together into one compound expression by braces (‘{’ and ‘}’). Comments can
be put almost2 anywhere, starting with a hashmark (‘#’), everything to the end of the line is a
comment.
If a command is not complete at the end of a line, R will give a different prompt, by default
+
on second and subsequent lines and continue to read input until the command is syntactically
complete. This prompt may be changed by the user. We will generally omit the continuation
prompt and indicate continuation by simple indenting.
Command lines entered at the console are limited3 to about 4095 bytes (not characters).
1.9 Recall and correction of previous commands
Under many versions of UNIX and on Windows, R provides a mechanism for recalling and reexecuting previous commands. The vertical arrow keys on the keyboard can be used to scroll
forward and backward through a command history. Once a command is located in this way, the
cursor can be moved within the command using the horizontal arrow keys, and characters can
be removed with the DEL key or added with the other keys. More details are provided later: see
Appendix C [The command-line editor], page 92.
The recall and editing capabilities under UNIX are highly customizable. You can find out
how to do this by reading the manual entry for the readline library.
Alternatively, the Emacs text editor provides more general support mechanisms (via ESS,
Emacs Speaks Statistics) for working interactively with R. See Section “R and Emacs” in The
R statistical system FAQ.
1.10 Executing commands from or diverting output to a file
If commands4 are stored in an external file, say commands.R in the working directory work, they
may be executed at any time in an R session with the command
> source(“commands.R”)
For Windows Source is also available on the File menu. The function sink,
> sink(“record.lis”)
will divert all subsequent output from the console to an external file, record.lis. The command
> sink()
restores it to the console once again.
1.11 Data permanency and removing objects
The entities that R creates and manipulates are known as objects. These may be variables, arrays
of numbers, character strings, functions, or more general structures built from such components.
During an R session, objects are created and stored by name (we discuss this process in the
next section). The R command
> objects()
(alternatively, ls()) can be used to display the names of (most of) the objects which are currently
stored within R. The collection of objects currently stored is called the workspace.
2
not inside strings, nor within the argument list of a function definition
some of the consoles will not allow you to enter more, and amongst those which do some will silently discard
the excess and some will use it as the start of the next line.
4
of unlimited length.
3
Chapter 1: Introduction and preliminaries
6
To remove objects the function rm is available:
> rm(x, y, z, ink, junk, temp, foo, bar)
All objects created during an R session can be stored permanently in a file for use in future
R sessions. At the end of each R session you are given the opportunity to save all the currently
available objects. If you indicate that you want to do this, the objects are written to a file called
.RData5 in the current directory, and the command lines used in the session are saved to a file
called .Rhistory.
When R is started at later time from the same directory it reloads the workspace from this
file. At the same time the associated commands history is reloaded.
It is recommended that you should use separate working directories for analyses conducted
with R. It is quite common for objects with names x and y to be created during an analysis.
Names like this are often meaningful in the context of a single analysis, but it can be quite
hard to decide what they might be when the several analyses have been conducted in the same
directory.
5
The leading “dot” in this file name makes it invisible in normal file listings in UNIX, and in default GUI file
listings on macOS and Windows.
7
2 Simple manipulations; numbers and vectors
2.1 Vectors and assignment
R operates on named data structures. The simplest such structure is the numeric vector, which
is a single entity consisting of an ordered collection of numbers. To set up a vector named x,
say, consisting of five numbers, namely 10.4, 5.6, 3.1, 6.4 and 21.7, use the R command
> x 1/x
the reciprocals of the five values would be printed at the terminal (and the value of x, of course,
unchanged).
The further assignment
> y v s3
generates in s3 the vector c(-5.0, -4.8, -4.6, …, 4.6, 4.8, 5.0). Similarly
> s4 s5 s6 temp 13
sets temp as a vector of the same length as x with values FALSE corresponding to elements of x
where the condition is not met and TRUE where it is.
The logical operators are =, == for exact equality and != for inequality. In addition
if c1 and c2 are logical expressions, then c1 & c2 is their intersection (“and”), c1 | c2 is their
union (“or”), and !c1 is the negation of c1.
Logical vectors may be used in ordinary arithmetic, in which case they are coerced into
numeric vectors, FALSE becoming 0 and TRUE becoming 1. However there are situations where
logical vectors and their coerced numeric counterparts are not equivalent, for example see the
next subsection.
2.5 Missing values
In some cases the components of a vector may not be completely known. When an element
or value is “not available” or a “missing value” in the statistical sense, a place within a vector
may be reserved for it by assigning it the special value NA. In general any operation on an NA
becomes an NA. The motivation for this rule is simply that if the specification of an operation
is incomplete, the result cannot be known and hence is not available.
The function is.na(x) gives a logical vector of the same size as x with value TRUE if and
only if the corresponding element in x is NA.
> z Inf – Inf
Chapter 2: Simple manipulations; numbers and vectors
10
which both give NaN since the result cannot be defined sensibly.
In summary, is.na(xx) is TRUE both for NA and NaN values.
is.nan(xx) is only TRUE for NaNs.
To differentiate these,
Missing values are sometimes printed as when character vectors are printed without
quotes.
2.6 Character vectors
Character quantities and character vectors are used frequently in R, for example as plot labels.
Where needed they are denoted by a sequence of characters delimited by the double quote
character, e.g., “x-values”, “New iteration results”.
Character strings are entered using either matching double (“) or single (’) quotes, but are
printed using double quotes (or sometimes without quotes). They use C-style escape sequences,
using \ as the escape character, so \ is entered and printed as \\, and inside double quotes ”
is entered as \”. Other useful escape sequences are \n, newline, \t, tab and \b, backspace—see
?Quotes for a full list.
Character vectors may be concatenated into a vector by the c() function; examples of their
use will emerge frequently.
The paste() function takes an arbitrary number of arguments and concatenates them one by
one into character strings. Any numbers given among the arguments are coerced into character
strings in the evident way, that is, in the same way they would be if they were printed. The
arguments are by default separated in the result by a single blank character, but this can be
changed by the named argument, sep=string, which changes it to string, possibly empty.
For example
> labs y (x+1)[(!is.na(x)) & x>0] -> z
creates an object z and places in it the values of the vector x+1 for which the corresponding
value in x was both non-missing and positive.
3
paste(…, collapse=ss) joins the arguments into a single character string putting ss in between, e.g., ss
x[1:10]
selects the first 10 elements of x (assuming length(x) is not less than 10). Also
> c(“x”,”y”)[rep(c(1,2,2,1), times=4)]
(an admittedly unlikely thing to do) produces a character vector of length 16 consisting of
“x”, “y”, “y”, “x” repeated four times.
3. A vector of negative integral quantities. Such an index vector specifies the values to be
excluded rather than included. Thus
> y fruit names(fruit) lunch x[is.na(x)] y[y < 0] y z digits d e e[3] alpha length(alpha) attr(z, "dim") winter 4 A different style using ‘formal’ or ‘S4’ classes is provided in package methods. Chapter 3: Objects, their modes and attributes 15 will print it in data frame form, which is rather like a matrix, whereas > unclass(winter)
will print it as an ordinary list. Only in rather special situations do you need to use this facility,
but one is when you are learning to come to terms with the idea of class and generic functions.
Generic functions and classes will be discussed further in Section 10.9 [Object orientation],
page 48, but only briefly.
16
4 Ordered and unordered factors
A factor is a vector object used to specify a discrete classification (grouping) of the components
of other vectors of the same length. R provides both ordered and unordered factors. While the
“real” application of factors is with model formulae (see Section 11.1.1 [Contrasts], page 53), we
here look at a specific example.
4.1 A specific example
Suppose, for example, we have a sample of 30 tax accountants from all the states and territories
of Australia1 and their individual state of origin is specified by a character vector of state
mnemonics as
> state statef statef
[1] tas sa qld nsw nsw nt wa wa qld vic nsw vic qld qld sa
[16] tas sa nt wa vic qld nsw nsw wa sa act nsw vic vic act
Levels: act nsw nt qld sa tas vic wa
To find out the levels of a factor the function levels() can be used.
> levels(statef)
[1] “act” “nsw” “nt”
“qld” “sa”
“tas” “vic” “wa”
4.2 The function tapply() and ragged arrays
To continue the previous example, suppose we have the incomes of the same tax accountants in
another vector (in suitably large units of money)
> incomes incmeans stdError incster incster
act
nsw nt
qld
sa tas
vic
wa
1.5 4.3102 4.5 4.1061 2.7386 0.5 5.244 2.6575
As an exercise you may care to find the usual 95% confidence limits for the state mean
incomes. To do this you could use tapply() once more with the length() function to find
the sample sizes, and the qt() function to find the percentage points of the appropriate tdistributions. (You could also investigate R’s facilities for t-tests.)
The function tapply() can also be used to handle more complicated indexing of a vector
by multiple categories. For example, we might wish to split the tax accountants by both state
and sex. However in this simple instance (just one factor) what happens can be thought of as
follows. The values in the vector are collected into groups corresponding to the distinct entries
in the factor. The function is then applied to each of these groups individually. The value is a
vector of function results, labelled by the levels attribute of the factor.
The combination of a vector and a labelling factor is an example of what is sometimes called
a ragged array, since the subclass sizes are possibly irregular. When the subclass sizes are all
the same the indexing may be done implicitly and much more efficiently, as we see in the next
section.
4.3 Ordered factors
The levels of factors are stored in alphabetical order, or in the order they were specified to
factor if they were specified explicitly.
Sometimes the levels will have a natural ordering that we want to record and want our
statistical analysis to make use of. The ordered() function creates such ordered factors but
is otherwise identical to factor. For most purposes the only difference between ordered and
unordered factors is that the former are printed showing the ordering of the levels, but the
contrasts generated for them in fitting linear models are different.
18
5 Arrays and matrices
5.1 Arrays
An array can be considered as a multiply subscripted collection of data entries, for example
numeric. R allows simple facilities for creating and handling arrays, and in particular the
special case of matrices.
A dimension vector is a vector of non-negative integers. If its length is k then the array is
k-dimensional, e.g. a matrix is a 2-dimensional array. The dimensions are indexed from one up
to the values given in the dimension vector.
A vector can be used by R as an array only if it has a dimension vector as its dim attribute.
Suppose, for example, z is a vector of 1500 elements. The assignment
> dim(z) x x
[,1] [,2] [,3] [,4] [,5]
[1,]
1
5
9
13
17
[2,]
2
6
10
14
18
[3,]
3
7
11
15
19
[4,]
4
8
12
16
20
> i i
# i is a 3 by 2 index array.
[,1] [,2]
[1,]
1
3
[2,]
2
2
[3,]
3
1
> x[i]
# Extract those elements
[1] 9 6 3
> x[i] x
[,1] [,2] [,3] [,4] [,5]
[1,]
1
5
0
13
17
[2,]
2
0
10
14
18
[3,]
0
7
11
15
19
[4,]
4
8
12
16
20
>
Negative indices are not allowed in index matrices. NA and zero values are allowed: rows in the
index matrix containing a zero are ignored, and rows containing an NA produce an NA in the
result.
As a less trivial example, suppose we wish to generate an (unreduced) design matrix for a
block design defined by factors blocks (b levels) and varieties (v levels). Further suppose
there are n plots in the experiment. We could proceed as follows:
> Xb Xv ib iv Xb[ib] Xv[iv] X N N Z Z Z x %*% A %*% x
is a quadratic form.1
The function crossprod() forms “crossproducts”, meaning that crossprod(X, y) is the
same as t(X) %*% y but the operation is more efficient. If the second argument to crossprod()
is omitted it is taken to be the same as the first.
The meaning of diag() depends on its argument. diag(v), where v is a vector, gives a
diagonal matrix with elements of the vector as the diagonal entries. On the other hand diag(M),
where M is a matrix, gives the vector of main diagonal entries of M. This is the same convention
as that used for diag() in Matlab. Also, somewhat confusingly, if k is a single numeric value
then diag(k) is the k by k identity matrix!
5.7.2 Linear equations and inversion
Solving linear equations is the inverse of matrix multiplication. When after
> b solve(A,b)
solves the system, returning x (up to some accuracy loss). Note that in linear algebra, formally
x = A−1 b where A−1 denotes the inverse of A, which can be computed by
solve(A)
but rarely is needed. Numerically, it is both inefficient and potentially unstable to compute x
ev evals eigen(Sm)
is used by itself as a command the two components are printed, with their names. For large
matrices it is better to avoid computing the eigenvectors if they are not needed by using the
expression
> evals absdetM absdet ans Xplus b fit res X X vec vec statefr statefr factor(cut(incomes, breaks = 35+10*(0:7))) -> incomef
Then to calculate a two-way table of frequencies:
> table(incomef,statef)
statef
incomef
act nsw nt qld sa tas vic wa
(35,45]
1
1 0
1 0
0
1 0
(45,55]
1
1 1
1 2
0
1 3
(55,65]
0
3 1
3 2
2
2 1
(65,75]
0
1 0
0 0
0
1 0
Extension to higher-way frequency tables is immediate.
26
6 Lists and data frames
6.1 Lists
An R list is an object consisting of an ordered collection of objects known as its components.
There is no particular need for the components to be of the same mode or type, and, for
example, a list could consist of a numeric vector, a logical value, a matrix, a complex vector, a
character array, a function, and so on. Here is a simple example of how to make a list:
> Lst name$component_name
for the same thing.
This is a very useful convention as it makes it easier to get the right component if you forget
the number.
So in the simple example given above:
Lst$name is the same as Lst[[1]] and is the string “Fred”,
Lst$wife is the same as Lst[[2]] and is the string “Mary”,
Lst$child.ages[1] is the same as Lst[[4]][1] and is the number 4.
Additionally, one can also use the names of the list components in double square brackets,
i.e., Lst[[“name”]] is the same as Lst$name. This is especially useful, when the name of the
component to be extracted is stored in another variable as in
> x Lst Lst[5] list.ABC accountants attach(lentils)
places the data frame in the search path at position 2, and provided there are no variables u, v
or w in position 1, u, v and w are available as variables from the data frame in their own right.
At this point an assignment such as
> u lentils$u detach()
More precisely, this statement detaches from the search path the entity currently at
position 2. Thus in the present context the variables u, v and w would be no longer visible,
except under the list notation as lentils$u and so on. Entities at positions greater than 2
on the search path can be detached by giving their number to detach, but it is much safer to
always use a name, for example by detach(lentils) or detach(“lentils”)
Note: In R lists and data frames can only be attached at position 2 or above, and
what is attached is a copy of the original object. You can alter the attached values
via assign, but the original list or data frame is unchanged.
6.3.3 Working with data frames
A useful convention that allows you to work with many different problems comfortably together
in the same working directory is
• gather together all variables for any well defined and separate problem in a data frame
under a suitably informative name;
• when working with a problem attach the appropriate data frame at position 2, and use the
working directory at level 1 for operational quantities and temporary variables;
• before leaving a problem, add any variables you wish to keep for future reference to the
data frame using the $ form of assignment, and then detach();
• finally remove all unwanted variables from the working directory and keep it as clean of
left-over temporary variables as possible.
In this way it is quite simple to work with many problems in the same directory, all of which
have variables named x, y and z, for example.
6.3.4 Attaching arbitrary lists
attach() is a generic function that allows not only directories and data frames to be attached
to the search path, but other classes of object as well. In particular any object of mode “list”
may be attached in the same way:
> attach(any.old.list)
Anything that has been attached can be detached by detach, by position number or, preferably, by name.
Chapter 6: Lists and data frames
29
6.3.5 Managing the search path
The function search shows the current search path and so is a very useful way to keep track of
which data frames and lists (and packages) have been attached and detached. Initially it gives
> search()
[1] “.GlobalEnv”
“Autoloads”
“package:base”
where .GlobalEnv is the workspace.1
After lentils is attached we have
> search()
[1] “.GlobalEnv”
“lentils”
“Autoloads”
“package:base”
> ls(2)
[1] “u” “v” “w”
and as we see ls (or objects) can be used to examine the contents of any position on the search
path.
Finally, we detach the data frame and confirm it has been removed from the search path.
> detach(“lentils”)
> search()
[1] “.GlobalEnv”
“Autoloads”
“package:base”
1
See the on-line help for autoload for the meaning of the second term.
30
7 Reading data from files
Large data objects will usually be read as values from external files rather than entered during
an R session at the keyboard. R input facilities are simple and their requirements are fairly
strict and even rather inflexible. There is a clear presumption by the designers of R that you
will be able to modify your input files using other tools, such as file editors or Perl1 to fit in
with the requirements of R. Generally this is very simple.
If variables are to be held mainly in data frames, as we strongly suggest they should be, an
entire data frame can be read directly with the read.table() function. There is also a more
primitive input function, scan(), that can be called directly.
For more details on importing data into R and also exporting data, see the R Data Import/Export manual.
7.1 The read.table() function
To read an entire data frame directly, the external file will normally have a special form.
• The first line of the file should have a name for each variable in the data frame.
• Each additional line of the file has as its first item a row label and the values for each
variable.
If the file has one fewer item in its first line than in its second, this arrangement is presumed
to be in force. So the first few lines of a file to be read as a data frame might look as follows.

Input file form with names and row labels:
01
02
03
04
05
…
Price
52.00
54.75
57.50
57.50
59.75
Floor
111.0
128.0
101.0
131.0
93.0
Area
830
710
1000
690
900
Rooms
5
5
5
6
5
Age
6.2
7.5
4.2
8.8
1.9
Cent.heat
no
no
no
no
yes
By default numeric items (except row labels) are read as numeric variables and non-numeric
variables, such as Cent.heat in the example, as character variables. This can be changed if
necessary.
The function read.table() can then be used to read the data frame directly
> HousePrice HousePrice inp label