Description Format References Examples
In a production process a rubber material is extruded in a continous ribbon (about 2 feet in width). In one step of the process the product passes through a water bath. In this experiment the time spent in the bath and the temperature of the bath were varied to determine their effect on the electrical resistance of the final product.
A data frame with 4 observations on the following 3 variables.
time
time in the bath (coded as levels -1 and 1)
temp
temperature in the bath (coded as levels -1 and 1)
er
electrical resistance of the final produce (ohm/m^2)
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 | str(bath)
dotplot(ordered(time) ~ er, bath, groups = temp, type = c("p","a"),
xlab = expression("Electrical resistance (ohm/" * m^2 * ")"),
ylab = "Time in bath (coded)",
auto.key = list(columns = 2, lines = TRUE))
summary(fm1 <- lm(er ~ time * temp, bath))
summary(fm2 <- lm(er ~ time + temp, bath))
summary(fm3 <- lm(er ~ temp, bath))
|
Loading required package: lattice
'data.frame': 4 obs. of 3 variables:
$ time: Ord.factor w/ 2 levels "-1"<"1": 1 2 1 2
$ temp: Ord.factor w/ 2 levels "-1"<"1": 1 2 2 1
$ er : int 36 47 43 41
Call:
lm(formula = er ~ time * temp, data = bath)
Residuals:
ALL 4 residuals are 0: no residual degrees of freedom!
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 41.750 NA NA NA
time.L 3.182 NA NA NA
temp.L 4.596 NA NA NA
time.L:temp.L -0.500 NA NA NA
Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: NaN
F-statistic: NaN on 3 and 0 DF, p-value: NA
Call:
lm(formula = er ~ time + temp, data = bath)
Residuals:
1 2 3 4
-0.25 -0.25 0.25 0.25
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 41.7500 0.2500 167 0.00381 **
time.L 3.1820 0.3536 9 0.07045 .
temp.L 4.5962 0.3536 13 0.04887 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5 on 1 degrees of freedom
Multiple R-squared: 0.996, Adjusted R-squared: 0.988
F-statistic: 125 on 2 and 1 DF, p-value: 0.06312
Call:
lm(formula = er ~ temp, data = bath)
Residuals:
1 2 3 4
-2.5 2.0 -2.0 2.5
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 41.750 1.601 26.08 0.00147 **
temp.L 4.596 2.264 2.03 0.17945
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.202 on 2 degrees of freedom
Multiple R-squared: 0.6733, Adjusted R-squared: 0.51
F-statistic: 4.122 on 1 and 2 DF, p-value: 0.1794
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