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The Method S01 - Hardcoded Eng Subs - Sno
There are many methods to achieve unique values without repetition. The Fisher-Yates is one great way to prevent getting the same number twice by shuffling the sequence. Math.random will select a value from the shuffled array of a finite sequence demonstrated by the code snippet below.
R is very much a vehicle for newly developing methods of interactivedata analysis. It has developed rapidly, and has been extended by alarge collection of packages. However, most programs written inR are essentially ephemeral, written for a single piece of dataanalysis.
The evolution of the S language is characterized by four books byJohn Chambers and coauthors. For R, the basic reference is TheNew S Language: A Programming Environment for Data Analysis andGraphics by Richard A. Becker, John M. Chambers and Allan R.Wilks. The new features of the 1991 release of Sare covered in Statistical Models in S edited by John M.Chambers and Trevor J. Hastie. The formal methods and classes of themethods package are based on those described in Programmingwith Data by John M. Chambers. See References, for precisereferences.
There is an important difference in philosophy between S (and henceR) and the other main statistical systems. In S a statisticalanalysis is normally done as a series of steps, with intermediateresults being stored in objects. Thus whereas SAS and SPSS will givecopious output from a regression or discriminant analysis, R willgive minimal output and store the results in a fit object for subsequentinterrogation by further R functions.
on second and subsequent lines and continue to read input until thecommand is syntactically complete. This prompt may be changed by theuser. We will generally omit the continuation promptand indicate continuation by simple indenting.
Logical vectors may be used in ordinary arithmetic, in which case theyare coerced into numeric vectors, FALSE becoming 0and TRUE becoming 1. However there are situations wherelogical vectors and their coerced numeric counterparts are notequivalent, for example see the next subsection.
Subsets of the elements of a vector may be selected by appending to thename of the vector an index vector in square brackets. Moregenerally any expression that evaluates to a vector may have subsets ofits elements similarly selected by appending an index vector in squarebrackets immediately after the expression.
An array can be considered as a multiply subscripted collection of dataentries, for example numeric. R allows simple facilities forcreating and handling arrays, and in particular the special case ofmatrices.
More generally, subsections of an array may be specified by giving asequence of index vectors in place of subscripts; howeverif any index position is given an empty index vector, then thefull range of that subscript is taken.
Also, if an array name is given with just one subscript or indexvector, then the corresponding values of the data vector only are used;in this case the dimension vector is ignored. This is not the case,however, if the single index is not a vector but itself an array, as wenext discuss.
As well as an index vector in any subscript position, a matrix may beused with a single index matrix in order either to assign a vectorof quantities to an irregular collection of elements in the array, or toextract an irregular collection as a vector.
At this point dim(Z) stands for the dimension vectorc(3,4,2), and Z[1:24] stands for the data vector as it wasin h, and Z[] with an empty subscript or Z with nosubscript stands for the entire array as an array.
In particular the outer product of two ordinary vectors is a doublysubscripted array (that is a matrix, of rank at most 1). Notice thatthe outer product operator is of course non-commutative. Defining yourown R functions will be considered further in Writing your own functions.
As noted above, a matrix is just an array with two subscripts. Howeverit is such an important special case it needs a separate discussion.R contains many operators and functions that are available only formatrices. For example t(X) is the matrix transpose function, asnoted above. The functions nrow(A) and ncol(A) give thenumber of rows and columns in the matrix A respectively.
Components are always numbered and may always be referred to assuch. Thus if Lst is the name of a list with four components,these may be individually referred to as Lst[[1]],Lst[[2]], Lst[[3]] and Lst[[4]]. If, further,Lst[[4]] is a vector subscripted array then Lst[[4]][1] isits first entry.
Conversely the number of classes a generic function can handle can alsobe quite large. For example the plot() function has a defaultmethod and variants for objects of classes "data.frame","density", "factor", and more. A complete list can be gotagain by using the methods() function:
This section presumes the reader has some familiarity with statisticalmethodology, in particular with regression analysis and the analysis ofvariance. Later we make some rather more ambitious presumptions, namelythat something is known about generalized linear models and nonlinearregression.
Two factor non-additive model of y on A and B. Thefirst two specify the same crossed classification and the second twospecify the same nested classification. In abstract terms all fourspecify the same model subspace.
These assumptions are loose enough to encompass a wide class of modelsuseful in statistical practice, but tight enough to allow thedevelopment of a unified methodology of estimation and inference, atleast approximately. The reader is referred to any of the currentreference works on the subject for full details, such as McCullagh &Nelder (1989) or Dobson (1990).
One way to fit a nonlinear model is by minimizing the sum of the squarederrors (SSE) or residuals. This method makes sense if the observederrors could have plausibly arisen from a normal distribution.
There are thousands of contributed packages for R, written by manydifferent authors. Some of these packages implement specializedstatistical methods, others give access to data or hardware, and othersare designed to complement textbooks. Some (the recommendedpackages) are distributed with every binary distribution of R. Mostare available for download from CRAN( -project.org/ and its mirrors) and otherrepositories such as Bioconductor ( ).The R FAQcontains a list of CRAN packages current at the time of release, but thecollection of available packages changes very frequently.
There are two ways to run R under Windows. Within a terminal window(e.g. cmd.exe or a more capable shell), the methods described inthe previous section may be used, invoking by R.exe or moredirectly by Rterm.exe. For interactive use, there is aconsole-based GUI (Rgui.exe).
There are two ways to run R under macOS. Within a Terminal.appwindow by invoking R, the methods described in the firstsubsection apply. There is also console-based GUI (R.app) that bydefault is installed in the Applications folder on yoursystem. It is a standard double-clickable macOS application.
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