R：对所有变量重复线性回归并将结果保存在新的数据框中

我有一个名为“dat”的数据框，其中包含 10 个数值变量（var1、var2、var3、var4、var5、...var 10），每个变量都有多个观察结果...

dat

   var1 var2 var3 var4 var5 var6 var7 var8 var9 var10 
1    12    5   18   19   12 17   11   16   18   10
2     3    2   10    6   13 17   11   16   18   10
3    13   15   14   13    1 17   11   16   18   10
4    17   11   16   18   10 17   11   16   18   10
5     9   13    8    8    7 17   11   16   18   10
6    15    6   20   17    3 17   11   16   18   10
7    12    5   18   19   12 17   11   16   18   10
8     3    2   10    6   13 17   11   16   18   10
9    13   15   14   13    1 17   11   16   18   10

...

我想编写一段代码来对数据框中的所有变量（第一个变量除外）重复相同的函数。 该函数应使用 lm() 函数每次分析 var 1 与所有其他变量（var2、var3、var4、var5）之间的线性回归

例如 周期 1：var 1 和 var 2 之间的线性回归

lm(var1~var2, data=dat)

周期 2：var 1 和 var 3 之间的线性回归，

lm(var1~var3, data=dat)

周期 3：var 1 和 var 4 之间的线性回归

lm(var1~var4, data=dat)

等等…

我还希望每个周期的结果将保存在名为“结果”的新数据框中，具有以下结构

Var_tested  Correlation_coefficient         P_value_correlation     R_squared
Var2        corr_coeff_var2                 p_value_var2            R_sq_var2
Var3        corr_coeff_var3                 p_value_var3            R_sq_var3
Var4        corr_coeff_var4                 p_value_var4            R_sq_var4

每行报告数据每个相关的结果。 是否可以？

非常感谢你的帮助！

您可以尝试以下代码以获得所需的输出

data <- structure(list(var1 = c(12L, 3L, 13L, 17L, 9L, 15L, 12L, 3L, 
13L), var2 = c(5L, 2L, 15L, 11L, 13L, 6L, 5L, 2L, 15L), var3 = c(18L, 
10L, 14L, 16L, 8L, 20L, 18L, 10L, 14L), var4 = c(19L, 6L, 13L, 
18L, 8L, 17L, 19L, 6L, 13L), var5 = c(12L, 13L, 1L, 10L, 7L, 
3L, 12L, 13L, 1L), var6 = c(17L, 17L, 17L, 17L, 17L, 17L, 17L, 
17L, 17L), var7 = c(11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L
), var8 = c(16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L), var9 = c(18L, 
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L), var10 = c(10L, 10L, 
10L, 10L, 10L, 10L, 10L, 10L, 10L)), class = "data.frame", row.names = c(NA, 
-9L))

head(data,2)
#>   var1 var2 var3 var4 var5 var6 var7 var8 var9 var10
#> 1   12    5   18   19   12   17   11   16   18    10
#> 2    3    2   10    6   13   17   11   16   18    10

x = names(data[,-1])
out <- unlist(lapply(1, function(n) combn(x, 1, FUN=function(row) paste0("var1 ~ ", paste0(row, collapse = "+")))))
out
#> [1] "var1 ~ var2"  "var1 ~ var3"  "var1 ~ var4"  "var1 ~ var5" 
#> [5] "var1 ~ var6"  "var1 ~ var7"  "var1 ~ var8"  "var1 ~ var9" 
#> [9] "var1 ~ var10"

library(broom)
#> Warning: package 'broom' was built under R version 3.5.3

library(dplyr)
#> Warning: package 'dplyr' was built under R version 3.5.3
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union

#To have the regression coefficients
tmp1 = bind_rows(lapply(out, function(frml) {
 a = tidy(lm(frml, data=data))
 a$frml = frml
 return(a)
}))
head(tmp1)
#> # A tibble: 6 x 6
#>   term        estimate std.error statistic p.value frml       
#>   <chr>          <dbl>     <dbl>     <dbl>   <dbl> <chr>      
#> 1 (Intercept)    6.46      2.78      2.33  0.0529  var1 ~ var2
#> 2 var2           0.525     0.288     1.82  0.111   var1 ~ var2
#> 3 (Intercept)   -1.50      4.47     -0.335 0.748   var1 ~ var3
#> 4 var3           0.863     0.303     2.85  0.0247  var1 ~ var3
#> 5 (Intercept)    0.649     2.60      0.250 0.810   var1 ~ var4
#> 6 var4           0.766     0.183     4.18  0.00413 var1 ~ var4

#To have the regression results i.e. R2, AIC, BIC
tmp2 = bind_rows(lapply(out, function(frml) {
 a = glance(lm(frml, data=data))
 a$frml = frml
 return(a)
}))
head(tmp2)
#> # A tibble: 6 x 12
#>   r.squared adj.r.squared sigma statistic  p.value    df logLik   AIC   BIC
#>       <dbl>         <dbl> <dbl>     <dbl>    <dbl> <int>  <dbl> <dbl> <dbl>
#> 1     0.321         0.224  4.33      3.31  0.111       2  -24.8  55.7  56.3
#> 2     0.537         0.471  3.58      8.12  0.0247      2  -23.1  52.2  52.8
#> 3     0.714         0.673  2.81     17.5   0.00413     2  -20.9  47.9  48.5
#> 4     0.276         0.173  4.47      2.67  0.146       2  -25.1  56.2  56.8
#> 5     0             0      4.92     NA    NA           1  -26.6  57.2  57.6
#> 6     0             0      4.92     NA    NA           1  -26.6  57.2  57.6
#> # ... with 3 more variables: deviance <dbl>, df.residual <int>, frml <chr>

write.csv(tmp1, "Try_lm_coefficients.csv")
write.csv(tmp2, "Try_lm_results.csv")

^{Created on 2019-11-20 by the reprex package https://reprex.tidyverse.org (v0.3.0)}