Description Usage Format References Examples

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.

1 |

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

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
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))
``` |

```
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
```

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