This report was automatically generated with the R package knitr (version 1.5).
library(faraway)
data(gala, package = "faraway")
head(gala[, -2])
Species Area Elevation Nearest Scruz Adjacent
Baltra 58 25.09 346 0.6 0.6 1.84
Bartolome 31 1.24 109 0.6 26.3 572.33
Caldwell 3 0.21 114 2.8 58.7 0.78
Champion 25 0.10 46 1.9 47.4 0.18
Coamano 2 0.05 77 1.9 1.9 903.82
Daphne.Major 18 0.34 119 8.0 8.0 1.84
lmod <- lm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent, data = gala)
summary(lmod)
Call:
lm(formula = Species ~ Area + Elevation + Nearest + Scruz + Adjacent,
data = gala)
Residuals:
Min 1Q Median 3Q Max
-111.68 -34.90 -7.86 33.46 182.58
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.06822 19.15420 0.37 0.7154
Area -0.02394 0.02242 -1.07 0.2963
Elevation 0.31946 0.05366 5.95 3.8e-06
Nearest 0.00914 1.05414 0.01 0.9932
Scruz -0.24052 0.21540 -1.12 0.2752
Adjacent -0.07480 0.01770 -4.23 0.0003
Residual standard error: 61 on 24 degrees of freedom
Multiple R-squared: 0.766, Adjusted R-squared: 0.717
F-statistic: 15.7 on 5 and 24 DF, p-value: 6.84e-07
require(faraway)
sumary(lmod)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.06822 19.15420 0.37 0.7154
Area -0.02394 0.02242 -1.07 0.2963
Elevation 0.31946 0.05366 5.95 3.8e-06
Nearest 0.00914 1.05414 0.01 0.9932
Scruz -0.24052 0.21540 -1.12 0.2752
Adjacent -0.07480 0.01770 -4.23 0.0003
n = 30, p = 6, Residual SE = 60.98, R-Squared = 0.77
x <- model.matrix(~Area + Elevation + Nearest + Scruz + Adjacent, gala)
y <- gala$Species
xtxi <- solve(t(x) %*% x)
xtxi %*% t(x) %*% y
[,1]
(Intercept) 7.068221
Area -0.023938
Elevation 0.319465
Nearest 0.009144
Scruz -0.240524
Adjacent -0.074805
solve(crossprod(x, x), crossprod(x, y))
[,1]
(Intercept) 7.068221
Area -0.023938
Elevation 0.319465
Nearest 0.009144
Scruz -0.240524
Adjacent -0.074805
names(lmod)
[1] "coefficients" "residuals" "effects" "rank"
[5] "fitted.values" "assign" "qr" "df.residual"
[9] "xlevels" "call" "terms" "model"
lmodsum <- summary(lmod)
names(lmodsum)
[1] "call" "terms" "residuals" "coefficients"
[5] "aliased" "sigma" "df" "r.squared"
[9] "adj.r.squared" "fstatistic" "cov.unscaled"
sqrt(deviance(lmod)/df.residual(lmod))
[1] 60.98
lmodsum$sigma
[1] 60.98
xtxi <- lmodsum$cov.unscaled
sqrt(diag(xtxi)) * 60.975
(Intercept) Area Elevation Nearest Scruz Adjacent
19.15414 0.02242 0.05366 1.05413 0.21540 0.01770
lmodsum$coef[, 2]
(Intercept) Area Elevation Nearest Scruz Adjacent
19.15420 0.02242 0.05366 1.05414 0.21540 0.01770
qrx <- qr(x)
dim(qr.Q(qrx))
[1] 30 6
(f <- t(qr.Q(qrx)) %*% y)
[,1]
[1,] -466.842
[2,] 381.406
[3,] 256.250
[4,] 5.408
[5,] -119.498
[6,] 257.694
backsolve(qr.R(qrx), f)
[,1]
[1,] 7.068221
[2,] -0.023938
[3,] 0.319465
[4,] 0.009144
[5,] -0.240524
[6,] -0.074805
gala$Adiff <- gala$Area - gala$Adjacent
lmod <- lm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent + Adiff,
gala)
sumary(lmod)
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.06822 19.15420 0.37 0.7154
Area -0.02394 0.02242 -1.07 0.2963
Elevation 0.31946 0.05366 5.95 3.8e-06
Nearest 0.00914 1.05414 0.01 0.9932
Scruz -0.24052 0.21540 -1.12 0.2752
Adjacent -0.07480 0.01770 -4.23 0.0003
n = 30, p = 6, Residual SE = 60.98, R-Squared = 0.77
set.seed(123)
Adiffe <- gala$Adiff + 0.001 * (runif(30) - 0.5)
lmod <- lm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent + Adiffe,
gala)
sumary(lmod)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.30e+00 1.94e+01 0.17 0.87
Area -4.51e+04 4.26e+04 -1.06 0.30
Elevation 3.13e-01 5.39e-02 5.81 6.4e-06
Nearest 3.83e-01 1.11e+00 0.35 0.73
Scruz -2.62e-01 2.16e-01 -1.21 0.24
Adjacent 4.51e+04 4.26e+04 1.06 0.30
Adiffe 4.51e+04 4.26e+04 1.06 0.30
n = 30, p = 7, Residual SE = 60.82, R-Squared = 0.78
data(odor, package = "faraway")
odor
odor temp gas pack
1 66 -1 -1 0
2 39 1 -1 0
3 43 -1 1 0
4 49 1 1 0
5 58 -1 0 -1
6 17 1 0 -1
7 -5 -1 0 1
8 -40 1 0 1
9 65 0 -1 -1
10 7 0 1 -1
11 43 0 -1 1
12 -22 0 1 1
13 -31 0 0 0
14 -35 0 0 0
15 -26 0 0 0
cov(odor[, -1])
temp gas pack
temp 0.5714 0.0000 0.0000
gas 0.0000 0.5714 0.0000
pack 0.0000 0.0000 0.5714
lmod <- lm(odor ~ temp + gas + pack, odor)
summary(lmod, cor = T)
Call:
lm(formula = odor ~ temp + gas + pack, data = odor)
Residuals:
Min 1Q Median 3Q Max
-50.20 -17.14 1.18 20.30 62.93
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.2 9.3 1.63 0.13
temp -12.1 12.7 -0.95 0.36
gas -17.0 12.7 -1.34 0.21
pack -21.4 12.7 -1.68 0.12
Residual standard error: 36 on 11 degrees of freedom
Multiple R-squared: 0.334, Adjusted R-squared: 0.152
F-statistic: 1.84 on 3 and 11 DF, p-value: 0.199
Correlation of Coefficients:
(Intercept) temp gas
temp 0.00
gas 0.00 0.00
pack 0.00 0.00 0.00
lmod <- lm(odor ~ gas + pack, odor)
summary(lmod)
Call:
lm(formula = odor ~ gas + pack, data = odor)
Residuals:
Min 1Q Median 3Q Max
-50.20 -26.70 1.17 26.80 50.80
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.20 9.26 1.64 0.13
gas -17.00 12.68 -1.34 0.20
pack -21.37 12.68 -1.69 0.12
Residual standard error: 35.9 on 12 degrees of freedom
Multiple R-squared: 0.279, Adjusted R-squared: 0.159
F-statistic: 2.32 on 2 and 12 DF, p-value: 0.141
x <- 1:20
y <- x + rnorm(20)
The R session information (including the OS info, R version and all packages used):
sessionInfo()
R version 3.1.0 (2014-04-10)
Platform: x86_64-apple-darwin13.1.0 (64-bit)
locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8
attached base packages:
[1] graphics grDevices utils datasets methods stats base
other attached packages:
[1] faraway_1.0.6 knitr_1.5 ggplot2_0.9.3.1
loaded via a namespace (and not attached):
[1] colorspace_1.2-4 dichromat_2.0-0 digest_0.6.4
[4] evaluate_0.5.3 formatR_0.10 grid_3.1.0
[7] gtable_0.1.2 labeling_0.2 MASS_7.3-31
[10] munsell_0.4.2 plyr_1.8.1 proto_0.3-10
[13] RColorBrewer_1.0-5 Rcpp_0.11.1 reshape2_1.2.2
[16] scales_0.2.3 stringr_0.6.2 tools_3.1.0
Sys.time()
[1] "2014-06-16 14:01:04 BST"