R Notebook

Linear Regression

iris = read.csv("../datasets/iris.csv")
iris

NA

library(ggplot2)

ggplot(iris, aes(x = petal.length, y = petal.width)) +
  geom_point() +
  geom_smooth(method = "lm")+
  theme_minimal()

ggplot(iris, aes(x = petal.length, y = petal.width, color = variety)) +
  geom_point() +
  geom_smooth(method = "lm")+
  theme_minimal()

lm_output = lm( petal.width~petal.length, data = iris)
summary(lm_output)

Call:
lm(formula = petal.width ~ petal.length, data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.56515 -0.12358 -0.01898  0.13288  0.64272 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.363076   0.039762  -9.131  4.7e-16 ***
petal.length  0.415755   0.009582  43.387  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2065 on 148 degrees of freedom
Multiple R-squared:  0.9271,    Adjusted R-squared:  0.9266 
F-statistic:  1882 on 1 and 148 DF,  p-value: < 2.2e-16

ggplot(iris, aes(x = sepal.length, y = sepal.width)) +
  geom_point() +
  geom_smooth(method = "lm")+
  theme_minimal()

lm_output = lm( sepal.width~sepal.length, data = iris)
summary(lm_output)

Call:
lm(formula = sepal.width ~ sepal.length, data = iris)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.1095 -0.2454 -0.0167  0.2763  1.3338 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.41895    0.25356   13.48   <2e-16 ***
sepal.length -0.06188    0.04297   -1.44    0.152    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4343 on 148 degrees of freedom
Multiple R-squared:  0.01382,   Adjusted R-squared:  0.007159 
F-statistic: 2.074 on 1 and 148 DF,  p-value: 0.1519

ggplot(iris, aes(x = petal.length, y = sepal.width)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y~poly(x, 1))+
  theme_minimal()

lm_output = lm( sepal.width~petal.length, data = iris)
summary(lm_output)

Call:
lm(formula = sepal.width ~ petal.length, data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.08463 -0.21537  0.02116  0.21587  1.10380 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.45487    0.07610  45.402  < 2e-16 ***
petal.length -0.10579    0.01834  -5.768 4.51e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3952 on 148 degrees of freedom
Multiple R-squared:  0.1836,    Adjusted R-squared:  0.178 
F-statistic: 33.28 on 1 and 148 DF,  p-value: 4.513e-08

ggplot(iris, aes(x = petal.length, y = sepal.width)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y~poly(x, 2))+
  theme_minimal()

lm_output = lm( sepal.width~I(petal.length)+I(petal.length^2), data = iris)
summary(lm_output)

Call:
lm(formula = sepal.width ~ I(petal.length) + I(petal.length^2), 
    data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.16966 -0.26002  0.02279  0.20965  1.02444 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        4.24920    0.13294  31.963  < 2e-16 ***
I(petal.length)   -0.71154    0.08929  -7.969 4.06e-13 ***
I(petal.length^2)  0.08608    0.01248   6.896 1.47e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3447 on 147 degrees of freedom
Multiple R-squared:  0.3831,    Adjusted R-squared:  0.3747 
F-statistic: 45.65 on 2 and 147 DF,  p-value: 3.8e-16

lm_output = lm( sepal.width~I(petal.length)+I(petal.length^5), data = iris)
summary(lm_output)

Call:
lm(formula = sepal.width ~ I(petal.length) + I(petal.length^5), 
    data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.11661 -0.24358  0.03151  0.20469  1.03151 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        3.731e+00  8.328e-02  44.805  < 2e-16 ***
I(petal.length)   -2.425e-01  2.855e-02  -8.493 2.04e-14 ***
I(petal.length^5)  9.624e-05  1.638e-05   5.877 2.69e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3568 on 147 degrees of freedom
Multiple R-squared:  0.3389,    Adjusted R-squared:  0.3299 
F-statistic: 37.68 on 2 and 147 DF,  p-value: 6.172e-14

ggplot(iris, aes(x = petal.length, y = sepal.width)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y~poly(x, 5))+
  theme_minimal()

ggplot(iris, aes(x = petal.length, y = sepal.length)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y~poly(x, 2))+
  theme_minimal()

lm_output = lm( sepal.length~I(petal.length)+I(petal.length^2), data = iris)
summary(lm_output)

Call:
lm(formula = sepal.length ~ I(petal.length) + I(petal.length^2), 
    data = iris)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.0684 -0.2348  0.0121  0.2049  0.9146 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        5.05833    0.14036  36.038  < 2e-16 ***
I(petal.length)   -0.16435    0.09427  -1.743   0.0834 .  
I(petal.length^2)  0.08146    0.01318   6.181 5.96e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3639 on 147 degrees of freedom
Multiple R-squared:  0.8095,    Adjusted R-squared:  0.8069 
F-statistic: 312.3 on 2 and 147 DF,  p-value: < 2.2e-16

ggplot(iris, aes(x = petal.length, y = sepal.length)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y~poly(x, 1))+
  theme_minimal()

lm_output = lm( sepal.length~I(petal.length), data = iris)
summary(lm_output)

Call:
lm(formula = sepal.length ~ I(petal.length), data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.24675 -0.29657 -0.01515  0.27676  1.00269 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)      4.30660    0.07839   54.94   <2e-16 ***
I(petal.length)  0.40892    0.01889   21.65   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4071 on 148 degrees of freedom
Multiple R-squared:   0.76, Adjusted R-squared:  0.7583 
F-statistic: 468.6 on 1 and 148 DF,  p-value: < 2.2e-16

Multivariate polynomial regression

lm_output = lm( sepal.length~I(petal.length)+I(petal.width), data = iris)
summary(lm_output)

Call:
lm(formula = sepal.length ~ I(petal.length) + I(petal.width), 
    data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.18534 -0.29838 -0.02763  0.28925  1.02320 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)      4.19058    0.09705  43.181  < 2e-16 ***
I(petal.length)  0.54178    0.06928   7.820 9.41e-13 ***
I(petal.width)  -0.31955    0.16045  -1.992   0.0483 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4031 on 147 degrees of freedom
Multiple R-squared:  0.7663,    Adjusted R-squared:  0.7631 
F-statistic:   241 on 2 and 147 DF,  p-value: < 2.2e-16

lm_output = lm( sepal.length~I(petal.width^2)+I(petal.length^3), data = iris)
summary(lm_output)

Call:
lm(formula = sepal.length ~ I(petal.width^2) + I(petal.length^3), 
    data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.95925 -0.25830 -0.01588  0.20670  0.97874 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        5.0371767  0.0455562 110.571   <2e-16 ***
I(petal.width^2)  -0.0356134  0.0370512  -0.961    0.338    
I(petal.length^3)  0.0101508  0.0008602  11.800   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3692 on 147 degrees of freedom
Multiple R-squared:  0.8039,    Adjusted R-squared:  0.8012 
F-statistic: 301.3 on 2 and 147 DF,  p-value: < 2.2e-16

Cluster

iris

iris[ , -5]

cluster_result = kmeans(iris[ , -5], centers = 3)
cluster_result

K-means clustering with 3 clusters of sizes 50, 38, 62

Cluster means:
  sepal.length sepal.width petal.length petal.width
1     5.006000    3.428000     1.462000    0.246000
2     6.850000    3.073684     5.742105    2.071053
3     5.901613    2.748387     4.393548    1.433871

Clustering vector:
  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 2 3 3 3
 [57] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 2 2 2 2 3 2 2 2 2 2
[113] 2 3 3 2 2 2 2 3 2 3 2 3 2 2 3 3 2 2 2 2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 3 2 2 3

Within cluster sum of squares by cluster:
[1] 15.15100 23.87947 39.82097
 (between_SS / total_SS =  88.4 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"    "size"        
[8] "iter"         "ifault"      

library(cluster)
clusplot(iris[, -5], cluster_result$cluster)

iris

library(e1071) #SVM - ML model
library(caret) # data processing

iris$variety = as.factor(iris$variety)
training_idx = createDataPartition(iris$variety, p=0.8, list = FALSE)
train_data = iris[training_idx, ]
test_data = iris[-training_idx, ]

# train_data -> ML (SVM) -> test_data



svm_model = svm(variety~sepal.length+sepal.width+petal.length+petal.width, data=train_data,kernel="linear")

test_data[1, -5]

predict(svm_model, newdata = test_data[1, -5])

     8 
Setosa 
Levels: Setosa Versicolor Virginica

test_data[19, ]

predict(svm_model, newdata = test_data[19, -5])

        98 
Versicolor 
Levels: Setosa Versicolor Virginica

predictions = predict(svm_model, newdata = test_data[ , -5])
predictions

         8         11         16         20         24         26         28         35         42         45 
    Setosa     Setosa     Setosa     Setosa     Setosa     Setosa     Setosa     Setosa     Setosa     Setosa 
        56         65         68         70         77         79         84         90         98         99 
Versicolor Versicolor Versicolor Versicolor Versicolor Versicolor  Virginica Versicolor Versicolor Versicolor 
       112        114        121        125        126        142        143        145        146        147 
 Virginica  Virginica  Virginica  Virginica  Virginica  Virginica  Virginica  Virginica  Virginica  Virginica 
Levels: Setosa Versicolor Virginica

conf_mat = confusionMatrix(predictions, test_data$variety)
conf_mat

Confusion Matrix and Statistics

            Reference
Prediction   Setosa Versicolor Virginica
  Setosa         10          0         0
  Versicolor      0          9         0
  Virginica       0          1        10

Overall Statistics
                                          
               Accuracy : 0.9667          
                 95% CI : (0.8278, 0.9992)
    No Information Rate : 0.3333          
    P-Value [Acc > NIR] : 2.963e-13       
                                          
                  Kappa : 0.95            
                                          
 Mcnemar's Test P-Value : NA              

Statistics by Class:

                     Class: Setosa Class: Versicolor Class: Virginica
Sensitivity                 1.0000            0.9000           1.0000
Specificity                 1.0000            1.0000           0.9500
Pos Pred Value              1.0000            1.0000           0.9091
Neg Pred Value              1.0000            0.9524           1.0000
Prevalence                  0.3333            0.3333           0.3333
Detection Rate              0.3333            0.3000           0.3333
Detection Prevalence        0.3333            0.3000           0.3667
Balanced Accuracy           1.0000            0.9500           0.9750