Girth, Height and Volume for Black Cherry Trees

Description

This data set provides measurements of the girth, height and volume of timber in 31 felled black cherry trees. Note that girth is the diameter of the tree (in inches) measured at 4 ft 6 in above the ground.

Usage

trees

Format

A data frame with 31 observations on 3 variables.

Source

Ryan, T. A., Joiner, B. L. and Ryan, B. F. (1976) The Minitab Student Handbook. Duxbury Press.

References

Atkinson, A. C. (1985) Plots, Transformations and Regression. Oxford University Press.

Examples

require(stats); require(graphics)
pairs(trees, panel = panel.smooth, main = "trees data")
plot(Volume ~ Girth, data = trees, log = "xy")
coplot(log(Volume) ~ log(Girth) | Height, data = trees,
       panel = panel.smooth)
summary(fm1 <- lm(log(Volume) ~ log(Girth), data = trees))
summary(fm2 <- update(fm1, ~ . + log(Height), data = trees))
step(fm2)
## i.e., Volume ~= c * Height * Girth^2  seems reasonable

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(datasets)
> png(filename="/home/ddbj/snapshot/RGM3/R_rel/result/datasets/trees.Rd_%03d_medium.png", width=480, height=480)
> ### Name: trees
> ### Title: Girth, Height and Volume for Black Cherry Trees
> ### Aliases: trees
> ### Keywords: datasets
> 
> ### ** Examples
> 
> require(stats); require(graphics)
> pairs(trees, panel = panel.smooth, main = "trees data")
> plot(Volume ~ Girth, data = trees, log = "xy")
> coplot(log(Volume) ~ log(Girth) | Height, data = trees,
+        panel = panel.smooth)
> summary(fm1 <- lm(log(Volume) ~ log(Girth), data = trees))

Call:
lm(formula = log(Volume) ~ log(Girth), data = trees)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.205999 -0.068702  0.001011  0.072585  0.247963 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.35332    0.23066  -10.20 4.18e-11 ***
log(Girth)   2.19997    0.08983   24.49  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.115 on 29 degrees of freedom
Multiple R-squared:  0.9539,	Adjusted R-squared:  0.9523 
F-statistic: 599.7 on 1 and 29 DF,  p-value: < 2.2e-16

> summary(fm2 <- update(fm1, ~ . + log(Height), data = trees))

Call:
lm(formula = log(Volume) ~ log(Girth) + log(Height), data = trees)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.168561 -0.048488  0.002431  0.063637  0.129223 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -6.63162    0.79979  -8.292 5.06e-09 ***
log(Girth)   1.98265    0.07501  26.432  < 2e-16 ***
log(Height)  1.11712    0.20444   5.464 7.81e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.08139 on 28 degrees of freedom
Multiple R-squared:  0.9777,	Adjusted R-squared:  0.9761 
F-statistic: 613.2 on 2 and 28 DF,  p-value: < 2.2e-16

> step(fm2)
Start:  AIC=-152.69
log(Volume) ~ log(Girth) + log(Height)

              Df Sum of Sq    RSS      AIC
<none>                     0.1855 -152.685
- log(Height)  1    0.1978 0.3832 -132.185
- log(Girth)   1    4.6275 4.8130  -53.743

Call:
lm(formula = log(Volume) ~ log(Girth) + log(Height), data = trees)

Coefficients:
(Intercept)   log(Girth)  log(Height)  
     -6.632        1.983        1.117  

> ## i.e., Volume ~= c * Height * Girth^2  seems reasonable
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>