Singular Value Decomposition in Regression Analysis

This data set can be used to demostrate the use of singular value decomposition in regression analysis.

svd.linreg

Format

A list with four elements ya, Xa, yb, and Xb. y* is a vector of length 8 and X* is an 8 by 3 matrix. ya and Xa correspond to Table 1 in Mandel (1982). yb and Xb correspond to Table 4 in Mandel (1982).

Source

Tables 1 and 4 in Mandel (1982)

References

Mandel, J. (1982). Use of the Singular Value Decomposition in Regression Analysis. The American Statistician, 36(1), 15-24. doi:10.1080/00031305.1982.10482771.

Examples

data(svd.linreg, package = "jeksterslabRdatarepo")
str(svd.linreg)
#> List of 4
#>  $ ya: num [1:8] 41.4 31 37.4 50 39.2 ...
#>  $ Xa: num [1:8, 1:3] 1 1 1 1 1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "x1" "x2" "x3"
#>  $ yb: num [1:8] 41.4 31 37.4 50 39.2 ...
#>  $ Xb: num [1:8, 1:3] 1 1 1 1 1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "x1" "x2" "x3"
head(svd.linreg)
#> $ya
#> [1] 41.38 31.01 37.41 50.05 39.17 38.86 46.14 44.47
#> 
#> $Xa
#>      x1    x2    x3
#> [1,]  1 16.85  1.46
#> [2,]  1 24.81 -4.61
#> [3,]  1 18.85 -0.21
#> [4,]  1 12.63  4.93
#> [5,]  1 21.38 -1.36
#> [6,]  1 18.78 -0.08
#> [7,]  1 15.58  2.98
#> [8,]  1 16.30  1.73
#> 
#> $yb
#> [1] 41.38 31.01 37.41 50.05 39.17 38.86 46.14 44.47
#> 
#> $Xb
#>      x1    x2      x3
#> [1,]  1 16.85  2.3625
#> [2,]  1 24.81 -3.6075
#> [3,]  1 18.85  0.8625
#> [4,]  1 12.63  5.5275
#> [5,]  1 21.38 -1.0350
#> [6,]  1 18.78  0.9150
#> [7,]  1 15.58  3.3150
#> [8,]  1 16.30  2.7750
#>