# [R] Problem with lm Giving Wrong Results

Labone, Thomas |@bone @end|ng |rom em@||@@c@edu
Thu Dec 2 11:50:13 CET 2021

```In the code below the first and second plots should look pretty much the same, the only difference being that the first has n=1000 points and the second n=10000 points. On two of my Linux machines (info below) the second plot is a horizontal line (incorrect answer from lm), but on my Windows 10 machine and a third Linux machine it works as expected. The interesting thing is that the code works as expected for n <= 4095 but fails for n>=4096 (which equals 2^12). Can anyone else reproduce this problem? Any ideas on how to fix it?

set.seed(132)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# This works
n <- 1000# OK <= 4095
Z <- qnorm(ppoints(n))

k <- sort(rlnorm(n,log(2131),log(1.61)) / rlnorm(n,log(355),log(1.61)))

quantile(k,probs=c(0.025,0.5,0.975))
summary(k)

fit <- lm(log(k) ~ Z)
summary(fit)

gm <- exp(coef(fit)[1])
gsd <- exp(coef(fit)[2])
gm
gsd

plot(Z,k,log="y",xlim=c(-4,4),ylim=c(0.1,100))
lines(Z,gm*gsd^Z,col="red")

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#this does not
n <- 10000# fails >= 4096 = 2^12
Z <- qnorm(ppoints(n))

k <- sort(rlnorm(n,log(2131),log(1.61)) / rlnorm(n,log(355),log(1.61)))

quantile(k,probs=c(0.025,0.5,0.975))
summary(k)

fit <- lm(log(k) ~ Z)
summary(fit)

gm <- exp(coef(fit)[1])
gsd <- exp(coef(fit)[2])
gm
gsd

plot(Z,k,log="y",xlim=c(-4,4),ylim=c(0.1,100))
lines(Z,gm*gsd^Z,col="red")

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> sessionInfo() #for two Linux machines having problem
R version 4.1.2 (2021-11-01)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Linux Mint 20.2

Matrix products: default
BLAS/LAPACK: /usr/lib/x86_64-linux-gnu/libmkl_rt.so

locale:
[1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8
[6] LC_MESSAGES=en_US.UTF-8    LC_PAPER=en_US.UTF-8       LC_NAME=C                  LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

loaded via a namespace (and not attached):
[1] compiler_4.1.2  Matrix_1.3-4    tools_4.1.2     expm_0.999-6    grid_4.1.2      lattice_0.20-45

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> sessionInfo() # for a third Linux machine not having the problem
R version 4.1.1 (2021-08-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Linux Mint 19.3

Matrix products: default
BLAS/LAPACK: /opt/intel/compilers_and_libraries_2020.0.166/linux/mkl/lib/intel64_lin/libmkl_rt.so

locale:
[1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8
[4] LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
[10] LC_TELEPHONE=C             LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

loaded via a namespace (and not attached):
[1] compiler_4.1.1 tools_4.1.1

Thomas R. LaBone
PhD student
Department of Epidemiology and Biostatistics
Arnold School of Public Health
University of South Carolina
Columbia, South Carolina USA

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