Import Package :

library(dplyr)       # Package for data manipulation
library(gtools)      # Utility functions for data manipulation and statistical analysis
library(ggplot2)     # Package for data visualization using the grammar of graphics
library(class)       # Package for classification, including K-nearest neighbors (KNN) classification
library(tidyr)       # Package for reshaping and tidying data
library(reshape2)    # Package for data reshaping and restructuring
library(caret)       # Comprehensive toolkit for machine learning
library(plotly)      # Interactive plotting library
library(knitr)       # Package for dynamic report generation

Import dataSet

water_potability <-read.csv("data_input/water_potability.csv", stringsAsFactors = T)
rmarkdown::paged_table(water_potability)

Finding NA Value

colSums(is.na(water_potability))

#>              ph        Hardness          Solids     Chloramines         Sulfate 
#>             491               0               0               0             781 
#>    Conductivity  Organic_carbon Trihalomethanes       Turbidity      Potability 
#>               0               0             162               0               0

We can see that there are a few null values in the columns ph, Sulfate, and Trihalomethanes. Given that there are only 3276 items in the dataset, we cannot afford to discard these data points. Alternatively, we might swap them out for the means of the corresponding columns.

So I’m Performing Mean & Median & Mode Imputation

# Replace missing values in 'ph' and 'Trihalomethanes' with the mean of the entire column
water_potability$ph[is.na(water_potability$ph)] <- mean(water_potability$ph, na.rm = TRUE)
water_potability$Trihalomethanes[is.na(water_potability$Trihalomethanes)] <- mean(water_potability$Trihalomethanes, na.rm = TRUE)

# Calculate mean values of 'Sulfate' based on potability
mean_sulfate_potable <- mean(water_potability$Sulfate[water_potability$Potability == 1], na.rm = TRUE)
mean_sulfate_non_potable <- mean(water_potability$Sulfate[water_potability$Potability == 0], na.rm = TRUE)

# Replace missing values in 'Sulfate' based on potability
water_potability$Sulfate[is.na(water_potability$Sulfate) & water_potability$Potability == 1] <- mean_sulfate_potable
water_potability$Sulfate[is.na(water_potability$Sulfate) & water_potability$Potability == 0] <- mean_sulfate_non_potable

Checking Range of our Dataframe

# explore with summary
summary(water_potability)

#>        ph            Hardness          Solids         Chloramines    
#>  Min.   : 0.000   Min.   : 47.43   Min.   :  320.9   Min.   : 0.352  
#>  1st Qu.: 6.278   1st Qu.:176.85   1st Qu.:15666.7   1st Qu.: 6.127  
#>  Median : 7.081   Median :196.97   Median :20927.8   Median : 7.130  
#>  Mean   : 7.081   Mean   :196.37   Mean   :22014.1   Mean   : 7.122  
#>  3rd Qu.: 7.870   3rd Qu.:216.67   3rd Qu.:27332.8   3rd Qu.: 8.115  
#>  Max.   :14.000   Max.   :323.12   Max.   :61227.2   Max.   :13.127  
#>     Sulfate       Conductivity   Organic_carbon  Trihalomethanes  
#>  Min.   :129.0   Min.   :181.5   Min.   : 2.20   Min.   :  0.738  
#>  1st Qu.:317.1   1st Qu.:365.7   1st Qu.:12.07   1st Qu.: 56.648  
#>  Median :334.6   Median :421.9   Median :14.22   Median : 66.396  
#>  Mean   :333.8   Mean   :426.2   Mean   :14.28   Mean   : 66.396  
#>  3rd Qu.:350.4   3rd Qu.:481.8   3rd Qu.:16.56   3rd Qu.: 76.667  
#>  Max.   :481.0   Max.   :753.3   Max.   :28.30   Max.   :124.000  
#>    Turbidity     Potability
#>  Min.   :1.450   0:1998    
#>  1st Qu.:3.440   1:1278    
#>  Median :3.955             
#>  Mean   :3.967             
#>  3rd Qu.:4.500             
#>  Max.   :6.739

Checking outlier in histogram of our Dataframe

water_potability %>%
  pivot_longer(cols = -Potability, names_to = "feature") %>%
  ggplot(aes(x = value)) +
  geom_histogram(bins = 30, aes(fill = feature)) +
  facet_wrap(vars(feature, Potability), ncol = 4, scales = "free") +
  scale_fill_brewer(palette = "Paired") +
  theme(
    legend.position = "none",
    strip.background = element_rect(fill = "lightblue"),
    strip.text = element_text(color = "black", face = "bold", size = 8)
  ) +
  labs(
    title = "Detect Outliers With Histogram",
    subtitle = "Plot, Histogram",
    caption = "Data source: Kaggle.com, Water Quality",
    x = NULL,
    y = NULL
  )

Nothing here seems crucial to me, and because the overall number of data is very big, I don’t think the outliers will have much of an impact.

Modelling

model_lr <- glm(formula = Potability ~ ., 
             family = "binomial", 
             data = water_potability_train)
# stepwise
model_steplr <- step(model_lr, direction = 'both')

#> Start:  AIC=3495
#> Potability ~ ph + Hardness + Solids + Chloramines + Sulfate + 
#>     Conductivity + Organic_carbon + Trihalomethanes + Turbidity
#> 
#>                   Df Deviance    AIC
#> - Turbidity        1   3475.0 3493.0
#> - Conductivity     1   3475.1 3493.1
#> - Hardness         1   3475.5 3493.5
#> - Trihalomethanes  1   3475.5 3493.5
#> - ph               1   3475.6 3493.6
#> - Sulfate          1   3476.6 3494.6
#> <none>                 3475.0 3495.0
#> - Solids           1   3477.3 3495.3
#> - Chloramines      1   3477.7 3495.7
#> - Organic_carbon   1   3482.2 3500.2
#> 
#> Step:  AIC=3493.02
#> Potability ~ ph + Hardness + Solids + Chloramines + Sulfate + 
#>     Conductivity + Organic_carbon + Trihalomethanes
#> 
#>                   Df Deviance    AIC
#> - Conductivity     1   3475.1 3491.1
#> - Hardness         1   3475.5 3491.5
#> - Trihalomethanes  1   3475.5 3491.5
#> - ph               1   3475.7 3491.7
#> - Sulfate          1   3476.6 3492.6
#> <none>                 3475.0 3493.0
#> - Solids           1   3477.3 3493.3
#> - Chloramines      1   3477.7 3493.7
#> + Turbidity        1   3475.0 3495.0
#> - Organic_carbon   1   3482.2 3498.2
#> 
#> Step:  AIC=3491.09
#> Potability ~ ph + Hardness + Solids + Chloramines + Sulfate + 
#>     Organic_carbon + Trihalomethanes
#> 
#>                   Df Deviance    AIC
#> - Hardness         1   3475.6 3489.6
#> - Trihalomethanes  1   3475.6 3489.6
#> - ph               1   3475.7 3489.7
#> - Sulfate          1   3476.7 3490.7
#> <none>                 3475.1 3491.1
#> - Solids           1   3477.3 3491.3
#> - Chloramines      1   3477.8 3491.8
#> + Conductivity     1   3475.0 3493.0
#> + Turbidity        1   3475.1 3493.1
#> - Organic_carbon   1   3482.3 3496.3
#> 
#> Step:  AIC=3489.59
#> Potability ~ ph + Solids + Chloramines + Sulfate + Organic_carbon + 
#>     Trihalomethanes
#> 
#>                   Df Deviance    AIC
#> - Trihalomethanes  1   3476.1 3488.1
#> - ph               1   3476.2 3488.2
#> - Sulfate          1   3477.0 3489.0
#> <none>                 3475.6 3489.6
#> - Solids           1   3478.0 3490.0
#> - Chloramines      1   3478.4 3490.4
#> + Hardness         1   3475.1 3491.1
#> + Conductivity     1   3475.5 3491.5
#> + Turbidity        1   3475.6 3491.6
#> - Organic_carbon   1   3482.8 3494.8
#> 
#> Step:  AIC=3488.13
#> Potability ~ ph + Solids + Chloramines + Sulfate + Organic_carbon
#> 
#>                   Df Deviance    AIC
#> - ph               1   3476.7 3486.7
#> - Sulfate          1   3477.6 3487.6
#> <none>                 3476.1 3488.1
#> - Solids           1   3478.4 3488.4
#> - Chloramines      1   3479.0 3489.0
#> + Trihalomethanes  1   3475.6 3489.6
#> + Hardness         1   3475.6 3489.6
#> + Conductivity     1   3476.1 3490.1
#> + Turbidity        1   3476.1 3490.1
#> - Organic_carbon   1   3483.5 3493.5
#> 
#> Step:  AIC=3486.7
#> Potability ~ Solids + Chloramines + Sulfate + Organic_carbon
#> 
#>                   Df Deviance    AIC
#> - Sulfate          1   3478.1 3486.1
#> <none>                 3476.7 3486.7
#> - Solids           1   3478.9 3486.9
#> - Chloramines      1   3479.4 3487.4
#> + ph               1   3476.1 3488.1
#> + Trihalomethanes  1   3476.2 3488.2
#> + Hardness         1   3476.3 3488.3
#> + Conductivity     1   3476.7 3488.7
#> + Turbidity        1   3476.7 3488.7
#> - Organic_carbon   1   3483.9 3491.9
#> 
#> Step:  AIC=3486.13
#> Potability ~ Solids + Chloramines + Organic_carbon
#> 
#>                   Df Deviance    AIC
#> <none>                 3478.1 3486.1
#> + Sulfate          1   3476.7 3486.7
#> - Chloramines      1   3480.8 3486.8
#> - Solids           1   3480.9 3486.9
#> + Trihalomethanes  1   3477.5 3487.5
#> + ph               1   3477.6 3487.6
#> + Hardness         1   3477.9 3487.9
#> + Conductivity     1   3478.1 3488.1
#> + Turbidity        1   3478.1 3488.1
#> - Organic_carbon   1   3485.5 3491.5

# Compare Value of AIC
model_lr$aic

#> [1] 3494.999

model_steplr$aic

#> [1] 3486.134

because the model_lr model has a higher AIC value then we will use model_lr

summary(model_steplr)

#> 
#> Call:
#> glm(formula = Potability ~ Solids + Chloramines + Organic_carbon, 
#>     family = "binomial", data = water_potability_train)
#> 
#> Deviance Residuals: 
#>     Min       1Q   Median       3Q      Max  
#> -1.1897  -0.9938  -0.9331   1.3560   1.5730  
#> 
#> Coefficients:
#>                    Estimate   Std. Error z value Pr(>|z|)   
#> (Intercept)    -0.470090403  0.278230522  -1.690  0.09111 . 
#> Solids          0.000007648  0.000004597   1.664  0.09616 . 
#> Chloramines     0.041921281  0.025629644   1.636  0.10191   
#> Organic_carbon -0.032817924  0.012080176  -2.717  0.00659 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for binomial family taken to be 1)
#> 
#>     Null deviance: 3490.6  on 2619  degrees of freedom
#> Residual deviance: 3478.1  on 2616  degrees of freedom
#> AIC: 3486.1
#> 
#> Number of Fisher Scoring iterations: 4

Interpretasi Model: * The greater the value of Organic Carbon, the better the chance that the water can be minimized

Prediction

Predict the potability probability for water_potability_test data and store it in a new column named pred_RiskLs. then I will Classify the loans.test data by pred_RiskLs and store it in a new column named pred_Label.

water_potability_test$pred_RiskLs <- predict(object = model_lr,
                                newdata = water_potability_test,
                                type = "response")

water_potability_test$pred_Label <- ifelse(water_potability_test$pred_RiskLs > 0.5, 1, 0)
head(water_potability_test)

#>          ph Hardness   Solids Chloramines  Sulfate Conductivity Organic_carbon
#> 1  7.080795 204.8905 20791.32    7.300212 368.5164     564.3087       10.37978
#> 3  8.099124 224.2363 19909.54    9.275884 334.5643     418.6062       16.86864
#> 16 6.347272 186.7329 41065.23    9.629596 364.4877     516.7433       11.53978
#> 18 9.181560 273.8138 24041.33    6.904990 398.3505     477.9746       13.38734
#> 36 5.115817 191.9527 19620.55    6.060713 323.8364     441.7484       10.96649
#> 42 5.331940 194.8741 16658.88    7.993830 316.6752     335.1204       10.18051
#>    Trihalomethanes Turbidity Potability pred_RiskLs pred_Label
#> 1         86.99097  2.963135          0   0.4032852          0
#> 3         66.42009  3.055934          0   0.3803156          0
#> 16        75.07162  4.376348          0   0.4530251          0
#> 18        71.45736  4.503661          0   0.3670449          0
#> 36        49.23823  3.902089          0   0.3805967          0
#> 42        59.57271  4.434820          0   0.4132216          0

Levels are used to choose the label in the logistic regression model that will become the number 1.

• class “0”,
  • “1” plus base = 0,
  • probabilities near 0 become 0 and
  • odds near 1 become 1.

Model Evaluation

head(water_potability_test %>% 
  select(Potability, pred_Label))

#>    Potability pred_Label
#> 1           0          0
#> 3           0          0
#> 16          0          0
#> 18          0          0
#> 36          0          0
#> 42          0          0

After making predictions using the model, there are still wrong predictions. In classification, we evaluate the model based on the confusion matrix:

confusionMatrix(data = as.factor(water_potability_test$pred_Label),
                reference = water_potability_test$Potability,
                positive = "1")

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction   0   1
#>          0 385 269
#>          1   0   2
#>                                              
#>                Accuracy : 0.5899             
#>                  95% CI : (0.5512, 0.6279)   
#>     No Information Rate : 0.5869             
#>     P-Value [Acc > NIR] : 0.4536             
#>                                              
#>                   Kappa : 0.0087             
#>                                              
#>  Mcnemar's Test P-Value : <0.0000000000000002
#>                                              
#>             Sensitivity : 0.007380           
#>             Specificity : 1.000000           
#>          Pos Pred Value : 1.000000           
#>          Neg Pred Value : 0.588685           
#>              Prevalence : 0.413110           
#>          Detection Rate : 0.003049           
#>    Detection Prevalence : 0.003049           
#>       Balanced Accuracy : 0.503690           
#>                                              
#>        'Positive' Class : 1                  
#> 

• Accuracy = how well my model correctly guesses target Y.
• Precision = of all the prediction results, how well can my model correctly guess the positive class.
• Re-call/Sensitivity = from all positive actual data, how well is the proportion of my model guessing correctly.
• Specificity = of all negative actual data, how well is my model’s proportion of the correct guess.

Accuracy <- (2+385)/nrow(water_potability_test)
Recall <- (2/(2 + 269))
Precision <- (2)/(2+0)
Specificity <- (385)/(385+0)
                
performanceLs <- cbind.data.frame(Accuracy, Recall, Precision, Specificity)
performanceLs

#>   Accuracy      Recall Precision Specificity
#> 1 0.589939 0.007380074         1           1

Model Tuning

after conducting further analysis and checking, it turns out that indeed our model needs to be tuned to improve the recall value. We want increase the recall / sensitiviy, We need the model to guesing correctly. So the first thing we do it’s to do upsampling

 water_potability_train <- upSample(
  x = water_potability_train %>% select(-Potability),
  y = water_potability_train$Potability,
  yname = "Potability"
 ) 
prop.table(table(water_potability_train$Potability))

#> 
#>   0   1 
#> 0.5 0.5

The provided code down below creates a logistic regression model in R using the glm() function. The model predicts the probability of water potability based on various input variables. The step() function is then used to perform stepwise variable selection, which automatically selects the best subset of predictors for the model based on a specified criterion. The resulting model with the selected predictors is stored in a variable called model_steplr.

model_lr <- glm(formula = Potability ~ ., 
             family = "binomial", 
             data = water_potability_train)
# stepwise
model_steplr <- step(model_lr, direction = 'both')

#> Start:  AIC=4472.37
#> Potability ~ ph + Hardness + Solids + Chloramines + Sulfate + 
#>     Conductivity + Organic_carbon + Trihalomethanes + Turbidity
#> 
#>                   Df Deviance    AIC
#> - ph               1   4452.4 4470.4
#> - Conductivity     1   4452.4 4470.4
#> - Turbidity        1   4452.8 4470.8
#> - Hardness         1   4453.2 4471.2
#> - Trihalomethanes  1   4453.2 4471.2
#> <none>                 4452.4 4472.4
#> - Chloramines      1   4455.2 4473.2
#> - Solids           1   4455.2 4473.2
#> - Sulfate          1   4455.9 4473.9
#> - Organic_carbon   1   4459.5 4477.5
#> 
#> Step:  AIC=4470.37
#> Potability ~ Hardness + Solids + Chloramines + Sulfate + Conductivity + 
#>     Organic_carbon + Trihalomethanes + Turbidity
#> 
#>                   Df Deviance    AIC
#> - Conductivity     1   4452.4 4468.4
#> - Turbidity        1   4452.8 4468.8
#> - Hardness         1   4453.2 4469.2
#> - Trihalomethanes  1   4453.2 4469.2
#> <none>                 4452.4 4470.4
#> - Chloramines      1   4455.2 4471.2
#> - Solids           1   4455.2 4471.2
#> - Sulfate          1   4455.9 4471.9
#> + ph               1   4452.4 4472.4
#> - Organic_carbon   1   4459.5 4475.5
#> 
#> Step:  AIC=4468.37
#> Potability ~ Hardness + Solids + Chloramines + Sulfate + Organic_carbon + 
#>     Trihalomethanes + Turbidity
#> 
#>                   Df Deviance    AIC
#> - Turbidity        1   4452.8 4466.8
#> - Hardness         1   4453.2 4467.2
#> - Trihalomethanes  1   4453.2 4467.2
#> <none>                 4452.4 4468.4
#> - Chloramines      1   4455.2 4469.2
#> - Solids           1   4455.2 4469.2
#> - Sulfate          1   4455.9 4469.9
#> + Conductivity     1   4452.4 4470.4
#> + ph               1   4452.4 4470.4
#> - Organic_carbon   1   4459.5 4473.5
#> 
#> Step:  AIC=4466.84
#> Potability ~ Hardness + Solids + Chloramines + Sulfate + Organic_carbon + 
#>     Trihalomethanes
#> 
#>                   Df Deviance    AIC
#> - Hardness         1   4453.6 4465.6
#> - Trihalomethanes  1   4453.7 4465.7
#> <none>                 4452.8 4466.8
#> - Solids           1   4455.7 4467.7
#> - Chloramines      1   4455.7 4467.7
#> - Sulfate          1   4456.4 4468.4
#> + Turbidity        1   4452.4 4468.4
#> + Conductivity     1   4452.8 4468.8
#> + ph               1   4452.8 4468.8
#> - Organic_carbon   1   4460.0 4472.0
#> 
#> Step:  AIC=4465.61
#> Potability ~ Solids + Chloramines + Sulfate + Organic_carbon + 
#>     Trihalomethanes
#> 
#>                   Df Deviance    AIC
#> - Trihalomethanes  1   4454.5 4464.5
#> <none>                 4453.6 4465.6
#> - Solids           1   4456.6 4466.6
#> - Chloramines      1   4456.7 4466.7
#> - Sulfate          1   4456.8 4466.8
#> + Hardness         1   4452.8 4466.8
#> + Turbidity        1   4453.2 4467.2
#> + ph               1   4453.6 4467.6
#> + Conductivity     1   4453.6 4467.6
#> - Organic_carbon   1   4460.8 4470.8
#> 
#> Step:  AIC=4464.46
#> Potability ~ Solids + Chloramines + Sulfate + Organic_carbon
#> 
#>                   Df Deviance    AIC
#> <none>                 4454.5 4464.5
#> - Solids           1   4457.5 4465.5
#> - Chloramines      1   4457.6 4465.6
#> + Trihalomethanes  1   4453.6 4465.6
#> + Hardness         1   4453.7 4465.7
#> - Sulfate          1   4457.7 4465.7
#> + Turbidity        1   4454.0 4466.0
#> + ph               1   4454.5 4466.5
#> + Conductivity     1   4454.5 4466.5
#> - Organic_carbon   1   4461.8 4469.8

water_potability_train$pred_RiskLs <- predict(model_steplr, 
                                            water_potability_train, 
                                            type = "response")

water_potability_train$pred_Label <- ifelse(water_potability_train$pred_RiskLs > 0.5, 1, 0)

confusionMatrix(data = as.factor(water_potability_train$pred_Label),
                reference = water_potability_train$Potability,
                positive = "1")

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction   0   1
#>          0 876 772
#>          1 737 841
#>                                           
#>                Accuracy : 0.5322          
#>                  95% CI : (0.5148, 0.5496)
#>     No Information Rate : 0.5             
#>     P-Value [Acc > NIR] : 0.0001334       
#>                                           
#>                   Kappa : 0.0645          
#>                                           
#>  Mcnemar's Test P-Value : 0.3814355       
#>                                           
#>             Sensitivity : 0.5214          
#>             Specificity : 0.5431          
#>          Pos Pred Value : 0.5330          
#>          Neg Pred Value : 0.5316          
#>              Prevalence : 0.5000          
#>          Detection Rate : 0.2607          
#>    Detection Prevalence : 0.4892          
#>       Balanced Accuracy : 0.5322          
#>                                           
#>        'Positive' Class : 1               
#> 

water_potability_test$pred_RiskLs <- predict(object = model_lr,
                                newdata = water_potability_test,
                                type = "response")

water_potability_test$pred_Label <- ifelse(water_potability_test$pred_RiskLs > 0.5, 1, 0)
head(water_potability_test)

#>          ph Hardness   Solids Chloramines  Sulfate Conductivity Organic_carbon
#> 1  7.080795 204.8905 20791.32    7.300212 368.5164     564.3087       10.37978
#> 3  8.099124 224.2363 19909.54    9.275884 334.5643     418.6062       16.86864
#> 16 6.347272 186.7329 41065.23    9.629596 364.4877     516.7433       11.53978
#> 18 9.181560 273.8138 24041.33    6.904990 398.3505     477.9746       13.38734
#> 36 5.115817 191.9527 19620.55    6.060713 323.8364     441.7484       10.96649
#> 42 5.331940 194.8741 16658.88    7.993830 316.6752     335.1204       10.18051
#>    Trihalomethanes Turbidity Potability pred_RiskLs pred_Label
#> 1         86.99097  2.963135          0   0.5262277          1
#> 3         66.42009  3.055934          0   0.4975655          0
#> 16        75.07162  4.376348          0   0.5637733          1
#> 18        71.45736  4.503661          0   0.4572410          0
#> 36        49.23823  3.902089          0   0.5068487          1
#> 42        59.57271  4.434820          0   0.5297354          1

confusionMatrix(data = as.factor(water_potability_test$pred_Label),
                reference = water_potability_test$Potability,
                positive = "1")

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction   0   1
#>          0 182 142
#>          1 203 129
#>                                           
#>                Accuracy : 0.4741          
#>                  95% CI : (0.4353, 0.5131)
#>     No Information Rate : 0.5869          
#>     P-Value [Acc > NIR] : 1.000000        
#>                                           
#>                   Kappa : -0.0496         
#>                                           
#>  Mcnemar's Test P-Value : 0.001237        
#>                                           
#>             Sensitivity : 0.4760          
#>             Specificity : 0.4727          
#>          Pos Pred Value : 0.3886          
#>          Neg Pred Value : 0.5617          
#>              Prevalence : 0.4131          
#>          Detection Rate : 0.1966          
#>    Detection Prevalence : 0.5061          
#>       Balanced Accuracy : 0.4744          
#>                                           
#>        'Positive' Class : 1               
#> 

Accuracy_tuning <- (129+182)/nrow(water_potability_test)
Recall_tuning <- 129/(129+142)
Precision_tuning <- (129)/(129+203)
Specificity_tuning <- (182)/(182+203)
                
performanceLs_Tuning <- cbind.data.frame(Accuracy_tuning, Recall_tuning, Precision_tuning, Specificity_tuning)
performanceLs_Tuning

#>   Accuracy_tuning Recall_tuning Precision_tuning Specificity_tuning
#> 1       0.4740854     0.4760148        0.3885542          0.4727273

# increase recall
water_potability_test$pred_Label_new <- ifelse(test = water_potability_test$pred_Risk > 0.45,
                                    yes = 1,
                                    no = 0)

confusionMatrix(data = as.factor(water_potability_test$pred_Label_new),
                reference = water_potability_test$Potability, 
                positive = "1")

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction   0   1
#>          0  27  28
#>          1 358 243
#>                                              
#>                Accuracy : 0.4116             
#>                  95% CI : (0.3736, 0.4503)   
#>     No Information Rate : 0.5869             
#>     P-Value [Acc > NIR] : 1                  
#>                                              
#>                   Kappa : -0.0281            
#>                                              
#>  Mcnemar's Test P-Value : <0.0000000000000002
#>                                              
#>             Sensitivity : 0.89668            
#>             Specificity : 0.07013            
#>          Pos Pred Value : 0.40433            
#>          Neg Pred Value : 0.49091            
#>              Prevalence : 0.41311            
#>          Detection Rate : 0.37043            
#>    Detection Prevalence : 0.91616            
#>       Balanced Accuracy : 0.48340            
#>                                              
#>        'Positive' Class : 1                  
#> 

Accuracy_tuning_Recall <- (243+27)/nrow(water_potability_test)
Recall_tuning_Recall <- 243/(243+28)
Precision_tuning_Recall <- (243)/(243+358)
Specificity_tuning_Recall <- (27)/(27+358)
                
performanceLs_Tuning_Recall <- cbind.data.frame(Accuracy_tuning_Recall, Recall_tuning_Recall, Precision_tuning_Recall, Specificity_tuning_Recall)
performanceLs_Tuning_Recall

#>   Accuracy_tuning_Recall Recall_tuning_Recall Precision_tuning_Recall
#> 1              0.4115854             0.896679               0.4043261
#>   Specificity_tuning_Recall
#> 1                0.07012987

for our next task is to apply it to our test model

# Find optimum k
sqrt(nrow(scaled_train_x))

#> [1] 51.18594

# Perform k-NN classification
water_potabilityKNN_pred <- knn(train = scaled_train_x,
                 test = scaled_test_x,
                 cl = water_potability_train_y,
                 k = 51)

# Convert the predicted values to factors
water_potabilityKNN_pred <- as.factor(water_potabilityKNN_pred)

# Set the levels of the test target variable
levels(water_potability_test_y) <- levels(water_potability_train_y)

# Create the confusion matrix
confusion_matrix <- confusionMatrix(data = water_potabilityKNN_pred,
                                    reference = water_potability_test_y,
                                    positive = "1")

# Print the confusion matrix
print(confusion_matrix)

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction   0   1
#>          0 375 241
#>          1  10  30
#>                                              
#>                Accuracy : 0.6174             
#>                  95% CI : (0.579, 0.6547)    
#>     No Information Rate : 0.5869             
#>     P-Value [Acc > NIR] : 0.0606             
#>                                              
#>                   Kappa : 0.097              
#>                                              
#>  Mcnemar's Test P-Value : <0.0000000000000002
#>                                              
#>             Sensitivity : 0.11070            
#>             Specificity : 0.97403            
#>          Pos Pred Value : 0.75000            
#>          Neg Pred Value : 0.60877            
#>              Prevalence : 0.41311            
#>          Detection Rate : 0.04573            
#>    Detection Prevalence : 0.06098            
#>       Balanced Accuracy : 0.54236            
#>                                              
#>        'Positive' Class : 1                  
#> 

The provided code conducts k-Nearest Neighbors (k-NN) classification to predict water potability. It uses a training dataset (scaled_train_x) with corresponding class labels (water_potability_train_y) to train the model. The predictions are made on a test dataset (scaled_test_x). The code then converts the predicted values to factors and ensures consistency in the levels between the test and training datasets. A confusion matrix is created to evaluate the performance of the k-NN model, and the results, including accuracy, precision, recall, and F1-score, are printed.

For our next task is to create Model Evaluation K-Nearest Neighbor :

Accuracy_knn <- (30+375)/nrow(water_potability_test)
recall_knn <- 30/(30+241)
Precision_knn <- (30)/(30+10)
Specificity_knn <- (375)/(375+10)
                
performanceLs_knn <- cbind.data.frame(Accuracy_knn, recall_knn, Precision_knn, Specificity_knn)
performanceLs_knn

#>   Accuracy_knn recall_knn Precision_knn Specificity_knn
#> 1     0.617378  0.1107011          0.75        0.974026

• According to the confusion matrix’s findings, the model’s accuracy in predicting target potability (both potability and nonpotability) is 61%.
• The algorithm was able to predict 11% of the actual data on water potability.
• The model was able to properly forecast the positive class for 75% of all prediction outcomes that it was able to estimate.
• The algorithm can predict 97% of the actual data for water that is unfit for human consumption.