bath: Electrical resistance after water bath

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

Description

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.

Format

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)

References

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

Examples

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))

Example output

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

EngrExpt documentation built on May 2, 2019, 5:53 p.m.