# cork: The Cork Dataset In ACSWR: A Companion Package for the Book "A Course in Statistics with R"

## Description

Thickness of cork borings in four directions of North, South, East, and West are measured for 28 trees. The problem here is to examine if the bark deposit is same in all the directions.

## Usage

 `1` ```data(cork) ```

## Format

A data frame with 28 observations on the following 4 variables.

`North`

thickness of cork boring in the North direction

`East`

thickness of cork boring in the East direction

`South`

thickness of cork boring in the South direction

`West`

thickness of cork boring in the West direction

## References

Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2e. J. Wiley.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```data(cork) corkcent <- cork*0 corkcent[,1] <- cork[,1]-mean(cork[,1]) corkcent[,2] <- cork[,2]-mean(cork[,2]) corkcent[,3] <- cork[,3]-mean(cork[,3]) corkcent[,4] <- cork[,4]-mean(cork[,4]) corkcentsvd <- svd(corkcent) t(corkcentsvd\$u)%*%corkcentsvd\$u t(corkcentsvd\$v)%*%corkcentsvd\$v round(corkcentsvd\$u %*% diag(corkcentsvd\$d) %*% t(corkcentsvd\$v),2) round(corkcent,2) corkcentsvd\$d ```

### Example output

```              [,1]          [,2]          [,3]          [,4]
[1,]  1.000000e+00  1.040834e-17  6.938894e-17 -1.252254e-16
[2,]  1.040834e-17  1.000000e+00 -1.387779e-16  1.812786e-16
[3,]  6.938894e-17 -1.387779e-16  1.000000e+00 -1.301043e-16
[4,] -1.252254e-16  1.812786e-16 -1.301043e-16  1.000000e+00
[,1]          [,2]          [,3]          [,4]
[1,]  1.000000e+00  0.000000e+00  5.551115e-17 -5.551115e-17
[2,]  0.000000e+00  1.000000e+00 -5.551115e-17  3.885781e-16
[3,]  5.551115e-17 -5.551115e-17  1.000000e+00 -1.387779e-16
[4,] -5.551115e-17  3.885781e-16 -1.387779e-16  1.000000e+00
[,1]   [,2]   [,3]   [,4]
[1,]  21.46  19.82  26.32  31.82
[2,]   9.46   6.82  16.32  17.82
[3,]   5.46  10.82  14.32  12.82
[4,]  -9.54 -17.18 -13.68  -7.18
[5,] -18.54 -14.18 -14.68  -9.18
[6,] -20.54 -11.18 -15.68 -19.18
[7,] -11.54  -7.18 -18.68 -18.18
[8,]  -8.54  -3.18 -18.68 -20.18
[9,] -13.54  -6.18 -18.68 -20.18
[10,] -17.54 -17.18 -22.68  -9.18
[11,] -18.54 -16.18 -15.68 -17.18
[12,]  12.46  -1.18  24.32  17.82
[13,]   3.46  -0.18  10.32   6.82
[14,]  -3.54   4.82   2.32  -2.18
[15,]  40.46  32.82  50.32  29.82
[16,]   5.46  21.82  -2.68   4.82
[17,]  28.46  18.82  20.32  15.82
[18,]  30.46  33.82  18.32  12.82
[19,]  27.46   8.82  17.32  14.82
[20,]  -4.54  -8.18 -12.68  -7.18
[21,] -11.54 -11.18 -15.68  -8.18
[22,] -18.54 -16.18 -19.68 -13.18
[23,]   9.46   3.82  17.32   8.82
[24,] -15.54  -9.18  -1.68  -6.18
[25,] -11.54 -10.18 -10.68 -14.18
[26,]  -0.54 -12.18 -12.68  -5.18
[27,]  -7.54  -9.18 -10.68   4.82
[28,]  -2.54   7.82   7.32  -2.18
North   East  South   West
1   21.46  19.82  26.32  31.82
2    9.46   6.82  16.32  17.82
3    5.46  10.82  14.32  12.82
4   -9.54 -17.18 -13.68  -7.18
5  -18.54 -14.18 -14.68  -9.18
6  -20.54 -11.18 -15.68 -19.18
7  -11.54  -7.18 -18.68 -18.18
8   -8.54  -3.18 -18.68 -20.18
9  -13.54  -6.18 -18.68 -20.18
10 -17.54 -17.18 -22.68  -9.18
11 -18.54 -16.18 -15.68 -17.18
12  12.46  -1.18  24.32  17.82
13   3.46  -0.18  10.32   6.82
14  -3.54   4.82   2.32  -2.18
15  40.46  32.82  50.32  29.82
16   5.46  21.82  -2.68   4.82
17  28.46  18.82  20.32  15.82
18  30.46  33.82  18.32  12.82
19  27.46   8.82  17.32  14.82
20  -4.54  -8.18 -12.68  -7.18
21 -11.54 -11.18 -15.68  -8.18
22 -18.54 -16.18 -19.68 -13.18
23   9.46   3.82  17.32   8.82
24 -15.54  -9.18  -1.68  -6.18
25 -11.54 -10.18 -10.68 -14.18
26  -0.54 -12.18 -12.68  -5.18
27  -7.54  -9.18 -10.68   4.82
28  -2.54   7.82   7.32  -2.18
[1] 163.03355  40.17752  25.40940  22.16929
```

ACSWR documentation built on May 2, 2019, 6:53 a.m.