CODEWITHSUNDEEP
rlinear-regression
mrp
mrp

Reputation: 711

Running multiple, simple linear regressions from dataframe in R

I have a dataset (data frame) with 5 columns all containing numeric values.

I'm looking to run a simple linear regression for each pair in the dataset.

For example, If the columns were named A, B, C, D, E, I want to run lm(A~B), lm(A~C), lm(A~D), ...., lm(D~E),... and, then I want to plot the data for each pair along with the regression line.

I'm pretty new to R so I'm sort of spinning my wheels on how to actually accomplish this. Should I use ddply? or lapply? I'm not really sure how to tackle this.

Upvotes: 6

Views: 10328

Answers (3)

unique2
unique2

Reputation: 2302

I would recommend to also look at the correlation matrix (cor(DF)), which is usually the best way to discover linear relationships between variables. The correlation is tightly linked to the covariance and the slopes of a simple linear regression. The computation below exemplifies this link.

Sample data:

set.seed(1)
DF <- data.frame(
  A=rnorm(50, 100, 3),
  B=rnorm(50, 100, 3),
  C=rnorm(50, 100, 3),
  D=rnorm(50, 100, 3),
  E=rnorm(50, 100, 3)
)

The regression slope is cov(x, y) / var(x)

beta = cov(DF) * (1/diag(var(DF)))

            A            B           C           D           E
A  1.00000000 -0.045548503 0.028448192 -0.32982367  0.01800795
B -0.03354243  1.000000000 0.003298708 -0.02489518  0.04501362
C  0.02429041  0.003824755 1.000000000  0.24269838  0.15550116
D -0.22407592 -0.022967212 0.193107904  1.00000000 -0.08977834
E  0.01038445  0.035248685 0.105020194 -0.07620397  1.00000000

The intercept is mean(y) - beta * mean(x)

colMeans(DF) - beta * colMeans(DF)

             A         B         C         D         E
A 1.421085e-14 104.86992  97.44795 133.38310  98.49512
B 1.037180e+02   0.00000 100.02095 102.85026  95.83477
C 9.712461e+01  99.16182   0.00000  75.38373  84.06356
D 1.226899e+02 102.53263  80.87529   0.00000 109.22915
E 9.886859e+01  96.38451  89.41391 107.51930   0.00000

Upvotes: 2

Jilber Urbina
Jilber Urbina

Reputation: 61214

Here's one solution using combn 

 combn(names(DF), 2, function(x){lm(DF[, x])}, simplify = FALSE)

Example:

set.seed(1)
DF <- data.frame(A=rnorm(50, 100, 3),
                 B=rnorm(50, 100, 3),
                 C=rnorm(50, 100, 3),
                 D=rnorm(50, 100, 3),
                 E=rnorm(50, 100, 3))

Updated: adding @Henrik suggestion (see comments)

# only the coefficients
> results <- combn(names(DF), 2, function(x){coefficients(lm(DF[, x]))}, simplify = FALSE)
> vars <- combn(names(DF), 2)
> names(results) <- vars[1 , ] # adding names to identify variables in the reggression
> results
$A
 (Intercept)            B 
103.66739418  -0.03354243 

$A
(Intercept)           C 
97.88341555  0.02429041 

$A
(Intercept)           D 
122.7606103  -0.2240759 

$A
(Intercept)           E 
99.26387487  0.01038445 

$B
 (Intercept)            C 
99.971253525  0.003824755 

$B
 (Intercept)            D 
102.65399702  -0.02296721 

$B
(Intercept)           E 
96.83042199  0.03524868 

$C
(Intercept)           D 
 80.1872211   0.1931079 

$C
(Intercept)           E 
 89.0503893   0.1050202 

$D
 (Intercept)            E 
107.84384655  -0.07620397

Upvotes: 7

Metrics
Metrics

Reputation: 15458

Using combn for all combination of names of column (in the following example I assumed you want combination of two columns only) and Map for running over loops.

Example using mtcars data from R: 

colc<-names(mtcars)
colcc<-combn(colc,2)
colcc<-data.frame(colcc)
kk<-Map(function(x)lm(as.formula(paste(colcc[1,x],"~",paste(colcc[2,x],collapse="+"))),data=mtcars), as.list(1:nrow(colcc)))

 head(kk)
[[1]]

Call:
lm(formula = as.formula(paste(colcc[1, x], "~", paste(colcc[2, 
    x], collapse = "+"))), data = mtcars)

Coefficients:
(Intercept)          cyl  
     37.885       -2.876  


[[2]]

Call:
lm(formula = as.formula(paste(colcc[1, x], "~", paste(colcc[2, 
    x], collapse = "+"))), data = mtcars)

Coefficients:
(Intercept)         disp  
   29.59985     -0.04122  


[[3]]

Call:
lm(formula = as.formula(paste(colcc[1, x], "~", paste(colcc[2, 
    x], collapse = "+"))), data = mtcars)

Coefficients:
(Intercept)           hp  
   30.09886     -0.06823  


[[4]]

Call:
lm(formula = as.formula(paste(colcc[1, x], "~", paste(colcc[2, 
    x], collapse = "+"))), data = mtcars)

Coefficients:
(Intercept)         drat  
     -7.525        7.678  


[[5]]

Call:
lm(formula = as.formula(paste(colcc[1, x], "~", paste(colcc[2, 
    x], collapse = "+"))), data = mtcars)

Coefficients:
(Intercept)           wt  
     37.285       -5.344  


[[6]]

Call:
lm(formula = as.formula(paste(colcc[1, x], "~", paste(colcc[2, 
    x], collapse = "+"))), data = mtcars)

Coefficients:
(Intercept)         qsec  
     -5.114        1.412

Upvotes: 1

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