How to store the standard errors with the lm() function in R?

Question

All is in the title... I know how to store the estimates but I don't know how to store their standard errors... Thanks

> x <- runif(100)
> y <- 5 + 3 * x + rnorm(100, 0, 0.15)
> reg <- lm(y~x)
> 
> summary(reg)

Call:
lm(formula = y ~ x)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.32198 -0.12626  0.02584  0.10873  0.31411 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  5.00931    0.03087  162.25   <2e-16 ***
x            2.98162    0.05359   55.64   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.1499 on 98 degrees of freedom
Multiple R-squared: 0.9693,     Adjusted R-squared: 0.969 
F-statistic:  3096 on 1 and 98 DF,  p-value: < 2.2e-16 

> 
> reg$coef
(Intercept)           x 
   5.009309    2.981617

@user603: Thank you... but I am interested in the standard errors... not in the residuals... — user7064, Oct 26 '11 at 12:58

Joris Meys · Accepted Answer · 2011-10-26T13:37:13.453

12

Check the object that summary(reg) returns. You find then that

> str(summary(reg)$coef)
...
> X <- summary(reg)$coef
> X[,2]
(Intercept)           x 
 0.03325738  0.05558073

gives you what you want. Or, if you calculate them yourself (as @caracal showed in the comments) :

sqrt(diag(vcov(reg)))

edited Oct 26 '11 at 13:37

answered Oct 26 '11 at 12:57

Joris Meys

5,475
2
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6

Another way, based on the `lm()` fit alone: `sqrt(diag(vcov(reg)))` – caracal Oct 26 '11 at 13:20

score 6 · Answer 2 · answered Oct 26 '11 at 15:54

6

Somewhere Doug Bates once mentioned that accessor functions are preferable, so I'd do

R> example(lm)   ## to create lm.D9 object
[...]
R> coef(summary(lm.D9))
            Estimate Std. Error  t value    Pr(>|t|)
(Intercept)    5.032   0.220218 22.85012 9.54713e-15
groupTrt      -0.371   0.311435 -1.19126 2.49023e-01
R> str(coef(summary(lm.D9)))
 num [1:2, 1:4] 5.032 -0.371 0.22 0.311 22.85 ...
 - attr(*, "dimnames")=List of 2
  ..$ : chr [1:2] "(Intercept)" "groupTrt"
  ..$ : chr [1:4] "Estimate" "Std. Error" "t value" "Pr(>|t|)"
R> coef(summary(lm.D9))[,"Std. Error"]
(Intercept)    groupTrt 
   0.220218    0.311435 
R>

and the key is the coef() accessor for the summary object.

answered Oct 26 '11 at 15:54

Dirk Eddelbuettel

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Very true, accessors should be used preferably. I just always forget their names... – Joris Meys Oct 26 '11 at 16:59
Why is this preferable if it gives the same result as the method given by Joris? – mark999 Oct 26 '11 at 19:17
1

Better object-oriented behaviour---there are *lots* of modelling function returning differently organized objects. By providing `coef()`, you abstract that inner layer away. – Dirk Eddelbuettel Oct 26 '11 at 20:20

Ryan SY Kwan · Answer 3 · 2021-07-28T08:49:34.560

Following on @Joris Meys answer for how to calculate std. error manually.

#Std. Error = residual variance / variable variance =
sqrt(diag(vcov(reg)))

#where vcov(reg) = 
summary(reg)$cov.unscaled * summary(reg)$sigma^2

#where summary(reg)$cov.unscaled = 1/(variable variance) (diagonal of precision matrix) =
solve(t(x) %*% x)

#where summary(reg)$sigma = residual variance =
sqrt(sum(reg$residuals^2) / (nrow(x)-ncol(x)))

> x <- matrix(runif(200),nrow=100)
> y <- 5 + 3 * x[,1] + rnorm(100, 0, 0.15)
> reg <- lm(y~x)
> summary(reg)$coefficient[,'Std. Error']
(Intercept)          x1          x2 
 0.03842706  0.05494507  0.05243990 
> sqrt(diag(vcov(reg)))
(Intercept)          x1          x2 
 0.03842706  0.05494507  0.05243990 
> sqrt(diag( summary(reg)$sigma^2*summary(reg)$cov.unscaled ))
(Intercept)          x1          x2 
 0.03842706  0.05494507  0.05243990 
> x_ = cbind(rep(1,nrow(x)),x)
> sqrt(diag( sum(reg$residuals^2)/(nrow(x)-ncol(x)-1) * solve(t(x_) %*% x_) ))
[1] 0.03842706 0.05494507 0.05243990

For math detailed please check Standard Error for a Parameter in Ordinary Least Squares or How to derive variance-covariance matrix of coefficients in linear regression .

Although implementation is often mixed with substantive content in questions, we are supposed to be a site for providing information about statistics, machine learning, etc., not code. It can be good to provide code as well, but please elaborate your substantive answer in text for people who don't read this language well enough to recognize & extract the answer from the code. — gung - Reinstate Monica, Jan 29 '19 at 13:09

How to store the standard errors with the lm() function in R?

3 Answers3