# [R] how to do linear regression when dimension is high

Douglas Bates bates at stat.wisc.edu
Tue Nov 16 18:20:44 CET 2010

```On Tue, Nov 16, 2010 at 10:30 AM, poko2000 <quan.poko2000 at gmail.com> wrote:

> Hi I am a newbie in R.
> I have data with dim of 20.
> How to use lm if i want to do regression with the whole design matrix? My y
> is the first column.
> the left are xs.
> Thanks a lot.

Do you have the data stored in a matrix or in a data frame?  If it is
in a data frame and the first column is named "y" then you can use a
call like

lm(y ~ ., mydata)

The '.' on the right hand side of the formula is expanded to a formula
incorporating of the columns in the data frame except for the
response.  For example

> summary(lm(Fertility ~ ., swiss))

Call:
lm(formula = Fertility ~ ., data = swiss)

Residuals:
Min       1Q   Median       3Q      Max
-15.2743  -5.2617   0.5032   4.1198  15.3213

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)      66.91518   10.70604   6.250 1.91e-07
Agriculture      -0.17211    0.07030  -2.448  0.01873
Examination      -0.25801    0.25388  -1.016  0.31546
Education        -0.87094    0.18303  -4.758 2.43e-05
Catholic          0.10412    0.03526   2.953  0.00519
Infant.Mortality  1.07705    0.38172   2.822  0.00734

Residual standard error: 7.165 on 41 degrees of freedom
Multiple R-squared: 0.7067,	Adjusted R-squared: 0.671
F-statistic: 19.76 on 5 and 41 DF,  p-value: 5.594e-10

```