Voicethread 10: RSM
x <- read.csv("~/Desktop/Listeria+Monocytogenes.csv")
x
## Run X1.Conc X2.Conc Time Listeria.count S.N.ratio
## 1 1 1 0 1 6.613 16.41
## 2 2 1 0 2 6.618 16.41
## 3 3 1 0 3 6.776 16.62
## 4 4 1 0 4 6.769 16.61
## 5 5 2 0 1 6.518 16.28
## 6 6 2 0 2 6.542 16.31
## 7 7 2 0 3 6.406 16.13
## 8 8 2 0 4 6.263 15.94
## 9 9 3 0 1 6.457 16.20
## 10 10 3 0 2 6.183 16.01
## 11 11 3 0 3 6.543 16.20
## 12 12 3 0 4 6.612 16.41
## 13 13 4 0 1 6.318 16.01
## 14 14 4 0 2 6.559 16.34
## 15 15 4 0 3 6.294 15.98
## 16 16 4 0 4 6.375 16.09
## 17 17 0 1 1 6.613 16.41
## 18 18 0 1 2 6.618 16.41
## 19 19 0 1 3 6.776 16.62
## 20 20 0 1 4 6.769 16.61
## 21 21 0 2 1 6.474 16.22
## 22 22 0 2 2 6.402 16.13
## 23 23 0 2 3 6.573 16.36
## 24 24 0 2 4 6.586 16.37
## 25 25 0 3 1 6.338 16.04
## 26 26 0 3 2 6.639 16.44
## 27 27 0 3 3 6.489 16.24
## 28 28 0 3 4 6.663 16.47
## 29 29 0 4 1 6.498 16.26
## 30 30 0 4 2 6.474 16.22
## 31 31 0 4 3 6.575 16.36
## 32 32 0 4 4 6.573 16.36
rsm1 <- rsm(Listeria.count ~ Time + FO(X1.Conc,X2.Conc), data = x)
summary(rsm1)
##
## Call:
## rsm(formula = Listeria.count ~ Time + FO(X1.Conc, X2.Conc), data = x)
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.6147 0.0710 93.13 < 2e-16 ***
## Time 0.0341 0.0192 1.78 0.08545 .
## X1.Conc -0.0850 0.0207 -4.11 0.00031 ***
## X2.Conc -0.0524 0.0207 -2.53 0.01724 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Multiple R-squared: 0.422, Adjusted R-squared: 0.36
## F-statistic: 6.8 on 3 and 28 DF, p-value: 0.00138
##
## Analysis of Variance Table
##
## Response: Listeria.count
## Df Sum Sq Mean Sq F value Pr(>F)
## Time 1 0.047 0.0466 3.18 0.0855
## FO(X1.Conc, X2.Conc) 2 0.253 0.1264 8.61 0.0012
## Residuals 28 0.411 0.0147
## Lack of fit 5 0.111 0.0223 1.71 0.1723
## Pure error 23 0.300 0.0130
##
## Direction of steepest ascent (at radius 1):
## X1.Conc X2.Conc
## -0.8514 -0.5245
##
## Corresponding increment in original units:
## X1.Conc X2.Conc
## -0.8514 -0.5245
contour(rsm1, ~X1.Conc+X2.Conc, image=TRUE, at=summary(rsm1$canonical$xs))
persp(rsm1, X1.Conc ~ X2.Conc, zlab="Listeria Count", contours = "colors", theta=65)
rsm2 <- rsm(Listeria.count ~ Time + SO(X1.Conc,X2.Conc), data = x)
summary(rsm2)
##
## Call:
## rsm(formula = Listeria.count ~ Time + SO(X1.Conc, X2.Conc), data = x)
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.8539 0.1207 56.78 <2e-16 ***
## Time 0.0341 0.0180 1.90 0.0689 .
## X1.Conc -0.3165 0.1066 -2.97 0.0063 **
## X2.Conc -0.2993 0.1066 -2.81 0.0093 **
## X1.Conc^2 0.0455 0.0220 2.07 0.0484 *
## X2.Conc^2 0.0502 0.0220 2.28 0.0309 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Multiple R-squared: 0.526, Adjusted R-squared: 0.435
## F-statistic: 5.77 on 5 and 26 DF, p-value: 0.00104
##
## Analysis of Variance Table
##
## Response: Listeria.count
## Df Sum Sq Mean Sq F value Pr(>F)
## Time 1 0.047 0.0466 3.60 0.06889
## FO(X1.Conc, X2.Conc) 2 0.253 0.1264 9.76 0.00069
## PQ(X1.Conc, X2.Conc) 2 0.074 0.0371 2.86 0.07528
## Residuals 26 0.337 0.0130
## Lack of fit 3 0.037 0.0124 0.95 0.43158
## Pure error 23 0.300 0.0130
##
## Stationary point of response surface:
## X1.Conc X2.Conc
## 3.476 2.984
##
## Eigenanalysis:
## $values
## [1] 0.05016 0.04553
##
## $vectors
## [,1] [,2]
## X1.Conc 0 -1
## X2.Conc 1 0
contour(rsm2, ~X1.Conc+X2.Conc, image=TRUE, at=summary(rsm2$canonical$xs))
persp(rsm2, X1.Conc ~ X2.Conc, zlab="Listeria Count", contours = "colors", theta=65)
