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

li li hannah.hlx at gmail.com
Thu Mar 16 19:26:17 CET 2017

```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

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