An artificial data set which causes stepwise regression procedures to select a non-parsimonious model. The true model is a simple linear regression of y against x8.
data(artificialeg)A data frame with 50 observations on 10 variables.
Inspired by the pathoeg data set in the MPV pacakge.
data(artificialeg)
full.mod = lm(y~.,data=artificialeg)
step(full.mod)
#> Start: AIC=79.3
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9
#>
#> Df Sum of Sq RSS AIC
#> - x8 1 0.2423 163.94 77.374
#> - x3 1 0.6946 164.39 77.512
#> - x2 1 0.7107 164.41 77.517
#> - x6 1 1.3051 165.00 77.698
#> - x5 1 1.4425 165.14 77.739
#> - x9 1 1.6065 165.31 77.789
#> - x7 1 1.8835 165.58 77.873
#> - x1 1 3.4999 167.20 78.358
#> - x4 1 5.7367 169.44 79.023
#> <none> 163.70 79.301
#>
#> Step: AIC=77.37
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x9
#>
#> Df Sum of Sq RSS AIC
#> <none> 163.94 77.374
#> - x2 1 20.359 184.30 81.227
#> - x5 1 25.966 189.91 82.726
#> - x9 1 33.607 197.55 84.698
#> - x4 1 34.504 198.45 84.925
#> - x7 1 62.097 226.04 91.434
#> - x1 1 68.253 232.19 92.778
#> - x3 1 71.301 235.24 93.430
#> - x6 1 107.873 271.81 100.655
#>
#> Call:
#> lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x9, data = artificialeg)
#>
#> Coefficients:
#> (Intercept) x1 x2 x3 x4 x5
#> -0.1143 0.8019 0.4011 -0.8083 -0.3514 0.4927
#> x6 x7 x9
#> -0.7738 -0.5772 0.5478
#>
# generating model
n=50
set.seed(8) # a seed of 2 also works
x1 = rnorm(n,0.22,2)
x7 = 0.5*x1 + rnorm(n,0,sd=2)
x6 = -0.75*x1 + rnorm(n,0,3)
x3 = -0.5-0.5*x6 + rnorm(n,0,2)
x9 = rnorm(n,0.6,3.5)
x4 = 0.5*x9 + rnorm(n,0,sd=3)
x2 = -0.5 + 0.5*x9 + rnorm(n,0,sd=2)
x5 = -0.5*x2+0.5*x3+0.5*x6-0.5*x9+rnorm(n,0,1.5)
x8 = x1 + x2 -2*x3 - 0.3*x4 + x5 - 1.6*x6 - 1*x7 + x9 +rnorm(n,0,0.5)
y = 0.6*x8 + rnorm(n,0,2)
artificialeg = round(data.frame(x1,x2,x3,x4,x5,x6,x7,x8,x9,y),1)