bright: Brightness of de-inked newspaper

In EngrExpt: Data sets from "Introductory Statistics for Engineering Experimentation"

Description

One step of recycling newsprint is to "de-ink" the newsprint, that is to remove the ink. The brightness of the paper pulp after a de-inking process is a measure of how well the process to remove the ink worked. A half-fraction of a 2^5 factorial experiment experiment was run to test various factors on the ability to de-ink newsprint.

Usage

data(bright)

Format

A data frame with 16 observations on the following 6 variables.

type

type of alkali - an ordered factor with levels A < B

percent

percentage of alkali (25% or 75%)

time

time pulp is soaked (30 or 40 minutes)

hardness

water hardness (150 or 250)

speed

agitation rate - an ordered factor with levels S < F

bright

Brightness of pulp

References

Peter R. Nelson, Marie Coffin and Karen A. F. Copeland (2003), Introductory Statistics for Engineering Experimentation, Elsevier. (Appendix A)

Examples

str(bright)
options(contrasts = c("contr.treatment", "contr.helmert"))
summary(fm1 <- lm(bright ~ (type + percent + time + hardness + speed)^2,
                  bright))
qqmath(coef(fm1)[-1], aspect = 1,
       panel = function(...)
   {
       panel.grid(h = -1, v = -1)
       panel.qqmath(...)
       panel.qqmathline(..., alpha = 0.5, lty = 2)
   },
       xlab = "Standard normal quantiles",
       ylab = "First- and second-order effects")
summary(fm2 <- lm(bright ~ (type + hardness)^2, bright))
dotplot(type ~ bright, bright, groups = hardness,
        type = c("p", "a"), jitter.y = TRUE,
        xlab = "Brightness of pulp (lines and point styles are levels of water hardness)",
        ylab = "Alkali type", aspect = 0.4,
        auto.key = list(lines = TRUE, columns = 2))

Example output

Loading required package: lattice
'data.frame':	16 obs. of  6 variables:
 $ type    : Ord.factor w/ 2 levels "A"<"B": 1 2 1 2 1 2 1 2 1 2 ...
 $ percent : Ord.factor w/ 2 levels "0.25"<"0.75": 1 1 1 1 1 1 1 1 2 2 ...
 $ time    : Ord.factor w/ 2 levels "30"<"45": 1 1 1 1 2 2 2 2 1 1 ...
 $ hardness: Ord.factor w/ 2 levels "150"<"250": 1 1 2 2 1 1 2 2 1 1 ...
 $ speed   : Ord.factor w/ 2 levels "S"<"F": 1 2 2 1 2 1 1 2 2 1 ...
 $ bright  : num  53.6 57.4 54.8 57 53.4 ...

Call:
lm(formula = bright ~ (type + percent + time + hardness + speed)^2, 
    data = bright)

Residuals:
ALL 16 residuals are 0: no residual degrees of freedom!

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)
(Intercept)        55.86438         NA      NA       NA
type1               1.18687         NA      NA       NA
percent1            0.13188         NA      NA       NA
time1              -0.05313         NA      NA       NA
hardness1           0.49062         NA      NA       NA
speed1             -0.13063         NA      NA       NA
type1:percent1     -0.06562         NA      NA       NA
type1:time1        -0.10562         NA      NA       NA
type1:hardness1    -0.44687         NA      NA       NA
type1:speed1        0.12188         NA      NA       NA
percent1:time1     -0.06062         NA      NA       NA
percent1:hardness1 -0.01687         NA      NA       NA
percent1:speed1    -0.07812         NA      NA       NA
time1:hardness1     0.20563         NA      NA       NA
time1:speed1        0.01938         NA      NA       NA
hardness1:speed1   -0.16187         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:      1,	Adjusted R-squared:    NaN 
F-statistic:   NaN on 15 and 0 DF,  p-value: NA


Call:
lm(formula = bright ~ (type + hardness)^2, data = bright)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.8550 -0.2156 -0.0300  0.3069  0.4950 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)      55.8644     0.1105 505.570  < 2e-16 ***
type1             1.1869     0.1105  10.741 1.65e-07 ***
hardness1         0.4906     0.1105   4.440 0.000807 ***
type1:hardness1  -0.4469     0.1105  -4.044 0.001627 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.442 on 12 degrees of freedom
Multiple R-squared:  0.9266,	Adjusted R-squared:  0.9082 
F-statistic: 50.48 on 3 and 12 DF,  p-value: 4.447e-07

EngrExpt documentation built on May 1, 2019, 9:15 p.m.