This report was automatically generated with the R package knitr (version 1.5).

library(faraway)
require(MASS)
Loading required package: MASS
data(savings, package = "faraway")
lmod <- lm(sr ~ pop15 + pop75 + dpi + ddpi, savings)
boxcox(lmod, plotit = T)

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boxcox(lmod, plotit = T, lambda = seq(0.5, 1.5, by = 0.1))

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data(gala, package = "faraway")
lmod <- lm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent, gala)
boxcox(lmod, lambda = seq(-0.25, 0.75, by = 0.05), plotit = T)

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lmod <- lm(burntime ~ nitrogen + chlorine + potassium, leafburn)
logtrans(lmod, plotit = TRUE, alpha = seq(-min(leafburn$burntime) + 0.001, 0, 
    by = 0.01))

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lmod1 <- lm(sr ~ pop15, savings, subset = (pop15 < 35))
lmod2 <- lm(sr ~ pop15, savings, subset = (pop15 > 35))
plot(sr ~ pop15, savings, xlab = "Pop'n under 15", ylab = "Savings Rate")
abline(v = 35, lty = 5)
segments(20, lmod1$coef[1] + lmod1$coef[2] * 20, 35, lmod1$coef[1] + lmod1$coef[2] * 
    35)
segments(48, lmod2$coef[1] + lmod2$coef[2] * 48, 35, lmod2$coef[1] + lmod2$coef[2] * 
    35)
lhs <- function(x) ifelse(x < 35, 35 - x, 0)
rhs <- function(x) ifelse(x < 35, 0, x - 35)
lmod <- lm(sr ~ lhs(pop15) + rhs(pop15), savings)
x <- seq(20, 48, by = 1)
py <- lmod$coef[1] + lmod$coef[2] * lhs(x) + lmod$coef[3] * rhs(x)
lines(x, py, lty = 2)

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summary(lm(sr ~ ddpi, savings))

Call:
lm(formula = sr ~ ddpi, data = savings)

Residuals:
   Min     1Q Median     3Q    Max 
-8.553 -3.735  0.984  2.772  9.310 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)    7.883      1.011    7.80  4.5e-10
ddpi           0.476      0.215    2.22    0.031

Residual standard error: 4.31 on 48 degrees of freedom
Multiple R-squared:  0.0929,    Adjusted R-squared:  0.074 
F-statistic: 4.92 on 1 and 48 DF,  p-value: 0.0314
summary(lm(sr ~ ddpi + I(ddpi^2), savings))

Call:
lm(formula = sr ~ ddpi + I(ddpi^2), data = savings)

Residuals:
   Min     1Q Median     3Q    Max 
-8.560 -2.561  0.555  2.573  7.808 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   5.1304     1.4347    3.58  0.00082
ddpi          1.7575     0.5377    3.27  0.00203
I(ddpi^2)    -0.0930     0.0361   -2.57  0.01326

Residual standard error: 4.08 on 47 degrees of freedom
Multiple R-squared:  0.205, Adjusted R-squared:  0.171 
F-statistic: 6.06 on 2 and 47 DF,  p-value: 0.00456
summary(lm(sr ~ ddpi + I(ddpi^2) + I(ddpi^3), savings))

Call:
lm(formula = sr ~ ddpi + I(ddpi^2) + I(ddpi^3), data = savings)

Residuals:
   Min     1Q Median     3Q    Max 
-8.557 -2.557  0.562  2.576  7.798 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  5.145360   2.198606    2.34    0.024
ddpi         1.746017   1.380455    1.26    0.212
I(ddpi^2)   -0.090967   0.225598   -0.40    0.689
I(ddpi^3)   -0.000085   0.009374   -0.01    0.993

Residual standard error: 4.12 on 46 degrees of freedom
Multiple R-squared:  0.205, Adjusted R-squared:  0.153 
F-statistic: 3.95 on 3 and 46 DF,  p-value: 0.0137
savings <- data.frame(savings, mddpi = savings$ddpi - 10)
summary(lm(sr ~ mddpi + I(mddpi^2), savings))

Call:
lm(formula = sr ~ mddpi + I(mddpi^2), data = savings)

Residuals:
   Min     1Q Median     3Q    Max 
-8.560 -2.561  0.555  2.573  7.808 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  13.4070     1.4240    9.41  2.2e-12
mddpi        -0.1022     0.3027   -0.34    0.737
I(mddpi^2)   -0.0930     0.0361   -2.57    0.013

Residual standard error: 4.08 on 47 degrees of freedom
Multiple R-squared:  0.205, Adjusted R-squared:  0.171 
F-statistic: 6.06 on 2 and 47 DF,  p-value: 0.00456
lmod <- lm(sr ~ poly(ddpi, 4), savings)
sumary(lmod)
               Estimate Std. Error t value Pr(>|t|)
(Intercept)      9.6710     0.5846   16.54   <2e-16
poly(ddpi, 4)1   9.5590     4.1338    2.31    0.025
poly(ddpi, 4)2 -10.4999     4.1338   -2.54    0.015
poly(ddpi, 4)3  -0.0374     4.1338   -0.01    0.993
poly(ddpi, 4)4   3.6120     4.1338    0.87    0.387

n = 50, p = 5, Residual SE = 4.13, R-Squared = 0.22
lmod <- lm(sr ~ polym(pop15, ddpi, degree = 2), savings)
pop15r <- seq(20, 50, len = 10)
ddpir <- seq(0, 20, len = 10)
pgrid <- expand.grid(pop15 = pop15r, ddpi = ddpir)
pv <- predict(lmod, pgrid)
persp(pop15r, ddpir, matrix(pv, 10, 10), theta = 45, xlab = "Pop under 15", 
    ylab = "Growth", zlab = "Savings rate", ticktype = "detailed", shade = 0.25)

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funky <- function(x) sin(2 * pi * x^3)^3
x <- seq(0, 1, by = 0.01)
y <- funky(x) + 0.1 * rnorm(101)
matplot(x, cbind(y, funky(x)), type = "pl", ylab = "y", pch = 20, lty = 1, col = 1)

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g4 <- lm(y ~ poly(x, 4))
g12 <- lm(y ~ poly(x, 12))
matplot(x, cbind(y, g4$fit, g12$fit), type = "pll", ylab = "y", lty = c(1, 2), 
    pch = 20, col = 1)

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require(splines)
Loading required package: splines
knots <- c(0, 0, 0, 0, 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 0.85, 0.9, 1, 1, 1, 1)
bx <- splineDesign(knots, x)
lmodb <- lm(y ~ bx - 1)
matplot(x, bx, type = "l", col = 1)

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matplot(x, cbind(y, lmodb$fit), type = "pl", ylab = "y", pch = 20, lty = 1, 
    col = 1)

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ssf <- smooth.spline(x, y)
matplot(x, cbind(y, ssf$y), type = "pl", ylab = "y", lty = 1, pch = 20, col = 1)

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require(mgcv)
Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.7-29. For overview type 'help("mgcv-package")'.
gamod <- gam(sr ~ s(pop15) + s(pop75) + s(dpi) + s(ddpi), data = savings)
plot(gamod)

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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] splines   graphics  grDevices utils     datasets  methods   stats    
[8] base     

other attached packages:
[1] mgcv_1.7-29     nlme_3.1-117    MASS_7.3-31     faraway_1.0.6  
[5] 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       lattice_0.20-29   
[10] Matrix_1.1-3       munsell_0.4.2      plyr_1.8.1        
[13] proto_0.3-10       RColorBrewer_1.0-5 Rcpp_0.11.1       
[16] reshape2_1.2.2     scales_0.2.3       stringr_0.6.2     
[19] tools_3.1.0       
Sys.time()
[1] "2014-06-16 14:02:12 BST"