Correlation matrix for linear model regression coefficient

Question

Using cor(mtcars, method='pearson') produces a matrix showing the pearson's correlations for all variables in mtcars vs all other variables in mtcars . eg:

head(cor(mtcars, method='pearson'))
            mpg        cyl       disp         hp       drat         wt        qsec         vs         am       gear
mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684  0.6811719 -0.8676594  0.41868403  0.6640389  0.5998324  0.4802848
cyl  -0.8521620  1.0000000  0.9020329  0.8324475 -0.6999381  0.7824958 -0.59124207 -0.8108118 -0.5226070 -0.4926866
disp -0.8475514  0.9020329  1.0000000  0.7909486 -0.7102139  0.8879799 -0.43369788 -0.7104159 -0.5912270 -0.5555692
hp   -0.7761684  0.8324475  0.7909486  1.0000000 -0.4487591  0.6587479 -0.70822339 -0.7230967 -0.2432043 -0.1257043
drat  0.6811719 -0.6999381 -0.7102139 -0.4487591  1.0000000 -0.7124406  0.09120476  0.4402785  0.7127111  0.6996101
wt   -0.8676594  0.7824958  0.8879799  0.6587479 -0.7124406  1.0000000 -0.17471588 -0.5549157 -0.6924953 -0.5832870
           carb
mpg  -0.5509251
cyl   0.5269883
disp  0.3949769
hp    0.7498125
drat -0.0907898
wt    0.4276059

How can I get the same matrix above, except instead of each value being a pearson's correlation between each variable, it is the r.squared value from a linear model? So for example the first column, second row would be the same as summary(lm(mtcars$mpg~ mtcars$cyl))$r.squared . Thank you

Answer 1

library(tidyverse)

# kepp names of dataset
names = names(mtcars)

expand.grid(names, names, stringsAsFactors = F) %>%  # create pairs of names
  filter(Var1 != Var2) %>%                           # exclude same variables (creates warnings)
  rowwise() %>%                                      # for each row
  mutate(r = summary(lm(paste(Var1, "~" ,Var2), data = mtcars))$r.squared) %>%  # get the r squared
  spread(Var2, r)                                    # reshape

# # A tibble: 11 x 12
# Var1        am     carb    cyl   disp     drat    gear      hp    mpg
# <chr>    <dbl>    <dbl>  <dbl>  <dbl>    <dbl>   <dbl>   <dbl>  <dbl>
# 1 am    NA        0.00331  0.273  0.350  0.508    0.631   0.0591  0.360
# 2 carb   0.00331 NA        0.278  0.156  0.00824  0.0751  0.562   0.304
# 3 cyl    0.273    0.278   NA      0.814  0.490    0.243   0.693   0.726
# 4 disp   0.350    0.156    0.814 NA      0.504    0.309   0.626   0.718
# 5 drat   0.508    0.00824  0.490  0.504 NA        0.489   0.201   0.464
# 6 gear   0.631    0.0751   0.243  0.309  0.489   NA       0.0158  0.231
# 7 hp     0.0591   0.562    0.693  0.626  0.201    0.0158 NA       0.602
# 8 mpg    0.360    0.304    0.726  0.718  0.464    0.231   0.602  NA    
# 9 qsec   0.0528   0.431    0.350  0.188  0.00832  0.0452  0.502   0.175
# 10 vs     0.0283   0.324    0.657  0.505  0.194    0.0424  0.523   0.441
# 11 wt     0.480    0.183    0.612  0.789  0.508    0.340   0.434   0.753
# # ... with 3 more variables: qsec <dbl>, vs <dbl>, wt <dbl>

If you want to have row names instead of the first column (Var1) you can add at the end of the pipeline above

... %>%
  data.frame() %>%
  column_to_rownames("Var1")

That would be closer to the output you have from cor(mtcars, method='pearson')

Answer 2

I create a corlm function, which fills the entries with a for loop

corlm <- function(df){
mat <- matrix(NA, ncol(df), ncol(df), dimnames = list(colnames(df),colnames(df)))
suppressWarnings(for(i in 1:ncol(df)){
    for(j in 1:ncol(df)){
      mat[i,j] = summary(lm(df[,j]  ~ df[,i]))$r.squared}})
diag(mat) = NA; return(mat)
}

round(corlm(mtcars),3)
       mpg   cyl  disp    hp  drat    wt  qsec    vs    am  gear  carb
mpg     NA 0.726 0.718 0.602 0.464 0.753 0.175 0.441 0.360 0.231 0.304
cyl  0.726    NA 0.814 0.693 0.490 0.612 0.350 0.657 0.273 0.243 0.278
disp 0.718 0.814    NA 0.626 0.504 0.789 0.188 0.505 0.350 0.309 0.156
hp   0.602 0.693 0.626    NA 0.201 0.434 0.502 0.523 0.059 0.016 0.562
drat 0.464 0.490 0.504 0.201    NA 0.508 0.008 0.194 0.508 0.489 0.008
wt   0.753 0.612 0.789 0.434 0.508    NA 0.031 0.308 0.480 0.340 0.183
qsec 0.175 0.350 0.188 0.502 0.008 0.031    NA 0.554 0.053 0.045 0.431
vs   0.441 0.657 0.505 0.523 0.194 0.308 0.554    NA 0.028 0.042 0.324
am   0.360 0.273 0.350 0.059 0.508 0.480 0.053 0.028    NA 0.631 0.003
gear 0.231 0.243 0.309 0.016 0.489 0.340 0.045 0.042 0.631    NA 0.075
carb 0.304 0.278 0.156 0.562 0.008 0.183 0.431 0.324 0.003 0.075    NA