# [R] [FORGED] standard error for regression coefficients corresponding to factor levels

Rolf Turner r.turner at auckland.ac.nz
Fri Mar 17 00:41:31 CET 2017

```You have been posting to the R-help list long enough so that you should
have learned by now *not* to post in html.  Your code is mangled so as

(1) Your data frame "data1" seems to have a mysterious (and irrelevant?)
column named "data1" as well.

(2) The covariance matrix of your coefficient estimates is indeed (as
you hint) a constant multiple of (X^T X)^{-1}.  So do:

X <- model.matrix(~response*week,data=data1)
S <- solve(t(X)%*%X)
print(S)

and you will see the same pattern of constancy that your results exhibit.

(3) You could get the results you want much more easily, without all the
fooling around buried in your (illegible) code, by doing:

mod <- lm(response ~ (region - 1)/week,data=data1)
summary(mod)

cheers,

Rolf Turner

--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

On 17/03/17 07:26, li li wrote:
> Hi all,
>   I have the following data called "data1". After fitting the ancova model
> with different slopes and intercepts for each region, I calculated the
> regression coefficients and the corresponding standard error. The standard
> error (for intercept or for slope) are all the same for different regions.
> Is there something wrong?
>   I know the SE is related to (X^T X)^-1, where X is design matrix. So does
> this happen whenever each factor level has the same set of values for
> "week"?
>      Thanks.
>      Hanna
>
>
>
>> mod <- lm(response ~ region*week, data1)> tmp <- coef(summary(mod))> res <- matrix(NA, 5,4)> res[1,1:2] <- tmp[1,1:2]> res[2:5,1] <- tmp[1,1]+tmp[2:5,1]> res[2:5,2] <- sqrt(tmp[2:5,2]^2-tmp[1,2]^2)> res[1,3:4] <- tmp[6,1:2]> res[2:5,3] <- tmp[6,1]+tmp[7:10,1]> res[2:5,4] <- sqrt(tmp[7:10,2]^2-tmp[6,2]^2)
>
>> colnames(res) <- c("intercept", "intercept SE", "slope", "slope SE")> rownames(res) <- letters[1:5]> res   intercept intercept SE        slope   slope SE
> a 0.18404464   0.08976301 -0.018629310 0.01385073
> b 0.17605666   0.08976301 -0.022393789 0.01385073
> c 0.16754130   0.08976301 -0.022367770 0.01385073
> d 0.12554452   0.08976301 -0.017464385 0.01385073
> e 0.06153256   0.08976301  0.007714685 0.01385073
>
>
>
>
>
>
>
>> data1    week region     response
> 5      3      c  0.057325067
> 6      6      c  0.066723632
> 7      9      c -0.025317808
> 12     3      d  0.024692613
> 13     6      d  0.021761492
> 14     9      d -0.099820335
> 19     3      c  0.119559235
> 20     6      c -0.054456186
> 21     9      c  0.078811180
> 26     3      d  0.091667189
> 27     6      d -0.053400777
> 28     9      d  0.090754363
> 33     3      c  0.163818085
> 34     6      c  0.008959741
> 35     9      c -0.115410852
> 40     3      d  0.193920693
> 41     6      d -0.087738914
> 42     9      d  0.004987542
> 47     3      a  0.121332285
> 48     6      a -0.020202707
> 49     9      a  0.037295785
> 54     3      b  0.214304603
> 55     6      b -0.052346480
> 56     9      b  0.082501222
> 61     3      a  0.053540767
> 62     6      a -0.019182819
> 63     9      a -0.057629113
> 68     3      b  0.068592791
> 69     6      b -0.123298216
> 70     9      b -0.230671818
> 75     3      a  0.330741562
> 76     6      a  0.013902905
> 77     9      a  0.190620360
> 82     3      b  0.151002874
> 83     6      b  0.086177696
> 84     9      b  0.178982656
> 89     3      e  0.062974799
> 90     6      e  0.062035391
> 91     9      e  0.206200831
> 96     3      e  0.123102197
> 97     6      e  0.040181790
> 98     9      e  0.121332285
> 103    3      e  0.147557564
> 104    6      e  0.062035391
> 105    9      e  0.144965770
>
> 	[[alternative HTML version deleted]]

```