Load data

EDA

Find/fit model

fit <- lm(logy ~ Color + Initial.concentration + Dosage + Temperature + Initial.pH,data=data[,c("logy",predictors)])

# Try stepwise
out <- step(object=fit,scope=list(lower="logy ~ 1",
                                  upper="logy ~ Color + Initial.concentration + Dosage + Temperature + Initial.pH +
                       Color:Initial.concentration + Color:Dosage + Color:Temperature + Color:Initial.pH +
                       Initial.concentration:Dosage + Initial.concentration:Temperature + Initial.concentration:Initial.pH + 
                       Dosage:Temperature + Dosage:Initial.pH + Temperature:Initial.pH +
                       I(Initial.concentration^2) + I(Dosage^2) + I(Temperature^2) + I(Initial.pH^2)"),direction="both")

Summary of model found

## 
## Call:
## lm(formula = logy ~ Color + Initial.concentration + Dosage + 
##     Temperature + Initial.pH + I(Initial.concentration^2) + I(Dosage^2) + 
##     I(Initial.pH^2) + Color:Dosage + Color:Temperature + Initial.concentration:Initial.pH + 
##     Color:Initial.pH, data = data[, c("logy", predictors)])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.283503 -0.058834  0.005754  0.055536  0.304671 
## 
## Coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       2.610e+00  2.061e-01  12.663  < 2e-16 ***
## ColorMalachite Green              1.738e+00  2.851e-01   6.095 2.60e-08 ***
## Initial.concentration             7.470e-03  2.808e-04  26.600  < 2e-16 ***
## Dosage                           -6.212e-01  4.543e-02 -13.674  < 2e-16 ***
## Temperature                       3.810e-02  6.798e-03   5.605 2.20e-07 ***
## Initial.pH                        2.197e-02  2.970e-02   0.740 0.461394    
## I(Initial.concentration^2)       -4.183e-06  2.268e-07 -18.442  < 2e-16 ***
## I(Dosage^2)                       5.417e-02  7.111e-03   7.618 2.35e-11 ***
## I(Initial.pH^2)                  -3.528e-03  2.196e-03  -1.606 0.111662    
## ColorMalachite Green:Dosage      -1.322e-01  1.715e-02  -7.706 1.55e-11 ***
## ColorMalachite Green:Temperature -4.375e-02  9.575e-03  -4.570 1.53e-05 ***
## Initial.concentration:Initial.pH -1.178e-04  3.279e-05  -3.592 0.000531 ***
## ColorMalachite Green:Initial.pH   2.127e-02  1.165e-02   1.825 0.071247 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1125 on 91 degrees of freedom
## Multiple R-squared:  0.9889, Adjusted R-squared:  0.9875 
## F-statistic: 678.4 on 12 and 91 DF,  p-value: < 2.2e-16

Plot of observed vs predicted

## [1] "Correlation"
## [1] 0.9783616
## [1] "mse"
## [1] 790.217
## [1] "mae"
## [1] 10.2917

Save requested files

Cross validation

## [1] "Correlation"
## [1] 0.9652492
## [1] "mse"
## [1] 1264.19
## [1] "mae"
## [1] 12.72066

Optimisation

##      97 
## 3.95186 
##      828 
## 6.539854 
##        1 
## 6.875889 
##        1 
## 6.875889 
##        1 
## 7.028773 
##        1 
## 7.028773 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116 
##      858 
## 7.032116

##      858 
## 7.032116

##      858 
## 7.032116

##      858 
## 7.032116

##      858 
## 7.032116

## [1] "Optimal experimental settings"
##               Color Initial.concentration Dosage Temperature Initial.pH
## 858 Malachite Green               864.965    0.5          27          2
## [1] "Predicted optimal adsorption"
##      858 
## 1132.424