DATA622_HW1
IR
2/7/2021
library(palmerpenguins)
library(tidyr)
library(dplyr)
library(ggplot2)
library(mlbench)
library(MASS)
library(pROC)
library(stringr)
library(ggplot2)1. Logistic Regression with a binary outcome. (40)
a.
The penguin dataset has ‘species’ column. Please check how many categories you have in the species column. Conduct whatever data manipulation you need to do to be able to build a logistic regression with binary outcome. Please explain your reasoning behind your decision as you manipulate the outcome/dependent variable (species).
There are three categories in the species column. From the summary statistic, there are missing values in the dataset, being displayed as NA’s and should be removed. Species is the binary dependent variable in this dataset with categories Adelie, Chinstrap and Gentoo. When the dependent variable has more than two categories, then it is a multinomial logistic regression. In this case we are trying to build a logistic regression with binary outcome therefore one category has to be removed.
## species island bill_length_mm bill_depth_mm
## Adelie :152 Biscoe :168 Min. :32.10 Min. :13.10
## Chinstrap: 68 Dream :124 1st Qu.:39.23 1st Qu.:15.60
## Gentoo :124 Torgersen: 52 Median :44.45 Median :17.30
## Mean :43.92 Mean :17.15
## 3rd Qu.:48.50 3rd Qu.:18.70
## Max. :59.60 Max. :21.50
## NA's :2 NA's :2
## flipper_length_mm body_mass_g sex year
## Min. :172.0 Min. :2700 female:165 Min. :2007
## 1st Qu.:190.0 1st Qu.:3550 male :168 1st Qu.:2007
## Median :197.0 Median :4050 NA's : 11 Median :2008
## Mean :200.9 Mean :4202 Mean :2008
## 3rd Qu.:213.0 3rd Qu.:4750 3rd Qu.:2009
## Max. :231.0 Max. :6300 Max. :2009
## NA's :2 NA's :2I will remove the species with the lowest quantity which is Chinstrap.
## Rows: 265
## Columns: 8
## $ species <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Ade…
## $ island <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgers…
## $ bill_length_mm <dbl> 39.1, 39.5, 40.3, 36.7, 39.3, 38.9, 39.2, 41.1, 38.…
## $ bill_depth_mm <dbl> 18.7, 17.4, 18.0, 19.3, 20.6, 17.8, 19.6, 17.6, 21.…
## $ flipper_length_mm <int> 181, 186, 195, 193, 190, 181, 195, 182, 191, 198, 1…
## $ body_mass_g <int> 3750, 3800, 3250, 3450, 3650, 3625, 4675, 3200, 380…
## $ sex <fct> male, female, female, female, male, female, male, f…
## $ year <int> 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 200…b.
Please make sure you are evaluating the independent variables appropriately in deciding which ones should be in the model.
Non-numeric columns, Island and Sex were removed along with Year. I reordered the columns to have the binary dependent variable, species as the last column.
newdata2 <-newdatat [, c(3,4,5,6,1)]
#newdata2 <-newdatat [, c(3,6,1)]
pnewdata <-newdata2 %>%
mutate_all(str_trim) %>%
mutate(bill_length_mm = bill_length_mm %>% as.numeric()) %>%
mutate(bill_depth_mm = bill_depth_mm %>% as.numeric()) %>%
mutate(flipper_length_mm= flipper_length_mm %>% as.numeric()) %>%
mutate(body_mass_g= body_mass_g %>% as.numeric()) %>%
arrange(body_mass_g) %>%
mutate_if(is.character,as.factor)
glimpse(pnewdata)## Rows: 265
## Columns: 5
## $ bill_length_mm <dbl> 36.5, 36.4, 34.5, 33.1, 38.6, 37.9, 37.0, 37.3, 35.…
## $ bill_depth_mm <dbl> 16.6, 17.1, 18.1, 16.1, 17.0, 18.6, 16.9, 16.8, 16.…
## $ flipper_length_mm <dbl> 181, 184, 187, 178, 188, 193, 185, 192, 190, 186, 1…
## $ body_mass_g <dbl> 2850, 2850, 2900, 2900, 2900, 2925, 3000, 3000, 305…
## $ species <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Ade…There are now four independent variables as indicated in the Descriptive statistics.
Changed data frame to matrix to handle the following error: Error in hist.default(newdata2[, i], main = colnames(newdata2)[i], xlab = colnames(newdata2)[i], : ‘x’ must be numeric
#newdata3 <-as.matrix(sapply(newdata2, as.numeric))
#head(newdata3)
pnewdata2 <-as.matrix(sapply(pnewdata, as.numeric))Analyze the distribution of each independent variable
par(mfrow = c(2,2))
for( i in 1:4){
hist(pnewdata2[,i], main = colnames(pnewdata)[i],xlab=colnames(pnewdata)[i], col = 'yellow')
}
For continuous independent variables, we can get more clarity on the distribution by analyzing it w.r.t. dependent variable.
par(mfrow = c(2,2))
boxplot(bill_length_mm~species, ylab="Bill Length (mm)", xlab= "Species", col="light blue",data = pnewdata)
boxplot(bill_depth_mm~species, ylab="Bill Depth (mm)", xlab= "Species", col="light blue",data = pnewdata)
boxplot(flipper_length_mm~species, ylab="Flipper Length (mm)", xlab= "Species", col="light blue",data = pnewdata)
boxplot(body_mass_g~species, ylab="Body Mass (g)", xlab= "Species", col="light blue",data = pnewdata)
## c. Provide variable interpretations in your model.
## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredAnalysis of Model Summary
##
## Call:
## glm(formula = species ~ ., family = binomial, data = pnewdata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.173e-05 -2.100e-08 -2.100e-08 2.100e-08 3.746e-05
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.435e+02 3.546e+05 0.000 1.000
## bill_length_mm -1.706e-01 5.586e+03 0.000 1.000
## bill_depth_mm -1.167e+01 1.048e+04 -0.001 0.999
## flipper_length_mm 1.265e+00 1.689e+03 0.001 0.999
## body_mass_g 1.848e-02 2.833e+01 0.001 0.999
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3.6461e+02 on 264 degrees of freedom
## Residual deviance: 5.8112e-09 on 260 degrees of freedom
## AIC: 10
##
## Number of Fisher Scoring iterations: 25For continuous variables, the interpretation is as follows: For every one unit increase in bill length(mm), the log odds of being species ‘Adelie’(versus being Species ‘Gentoo’) decreases by 1.706. Similarly, for one unit increase in bill depth(mm), the log odds of being species ‘Adelie’(versus being Species ‘Gentoo’) decreases by 1.167. For every one unit increase in flipper_length(mm), the log odds of being species ‘Adelie’(versus being Species ‘Gentoo’) increases by 1.265. Similarly, for one unit increase in body_mass(g), the log odds of being species ‘Adelie’(versus being Species ‘Gentoo’) increases by 1.848.
The model ‘logit_1’, might not be the best model with the given set of independent variables. There are multiple methodologies for variable selection. I will explore only the ‘stepAIC’ function. The ‘stepAIC’ function in R performs a stepwise model selection with an objective to minimize the AIC value.
## Start: AIC=10
## species ~ bill_length_mm + bill_depth_mm + flipper_length_mm +
## body_mass_g## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Df Deviance AIC
## - bill_length_mm 1 0.0000 8.000
## - body_mass_g 1 0.0000 8.000
## - flipper_length_mm 1 0.0000 8.000
## <none> 0.0000 10.000
## - bill_depth_mm 1 9.9544 17.954## Warning: glm.fit: algorithm did not converge
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred##
## Step: AIC=8
## species ~ bill_depth_mm + flipper_length_mm + body_mass_g## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Df Deviance AIC
## - body_mass_g 1 0.000 6.000
## - flipper_length_mm 1 0.000 6.000
## <none> 0.000 8.000
## - bill_depth_mm 1 15.388 21.388## Warning: glm.fit: algorithm did not converge
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred##
## Step: AIC=6
## species ~ bill_depth_mm + flipper_length_mm
##
## Df Deviance AIC
## <none> 0.000 6.000
## - bill_depth_mm 1 20.887 24.887
## - flipper_length_mm 1 79.317 83.317##
## Call:
## glm(formula = species ~ bill_depth_mm + flipper_length_mm, family = binomial,
## data = pnewdata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -7.598e-05 -2.100e-08 -2.100e-08 2.100e-08 7.092e-05
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -242.039 383506.606 -0.001 0.999
## bill_depth_mm -20.343 12032.046 -0.002 0.999
## flipper_length_mm 2.803 1489.552 0.002 0.998
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3.6461e+02 on 264 degrees of freedom
## Residual deviance: 1.1987e-08 on 262 degrees of freedom
## AIC: 6
##
## Number of Fisher Scoring iterations: 25After implementing ‘stepAIC’ function, I am now left with two independent variables — bill depth(mm) and flipper length(mm). Of all the possible models, this model (logit_2) has the minimum AIC value and these variables are highly significant.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0000 0.0000 0.4491 1.0000 1.0000## [1] 10## [1] 62. Provide: AUC, Accuracy, TPR, FPR, TNR, FNR (20)
Gentoo Confusion Matrix was zero so I will adjust the data set.
pennewdata <-na.omit(penguins)%>% filter(species !="Chinstrap")
#newdata2 <-newdatat [, c(3,4,5,6,1)]
pennewdata2 <-pennewdata [, c(3,6,1)]
pennewdata3 <-pennewdata2 %>%
mutate_all(str_trim) %>%
mutate(bill_length_mm = bill_length_mm %>% as.numeric()) %>%
#mutate(bill_depth_mm = bill_depth_mm %>% as.numeric()) %>%
#mutate(flipper_length_mm= flipper_length_mm %>% as.numeric()) %>%
mutate(body_mass_g= body_mass_g %>% as.numeric()) %>%
#arrange(body_mass_g) %>%
mutate_if(is.character,as.factor)
glimpse(pennewdata3)## Rows: 265
## Columns: 3
## $ bill_length_mm <dbl> 39.1, 39.5, 40.3, 36.7, 39.3, 38.9, 39.2, 41.1, 38.6, …
## $ body_mass_g <dbl> 3750, 3800, 3250, 3450, 3650, 3625, 4675, 3200, 3800, …
## $ species <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adelie…Train/Test Split
## ── Attaching packages ────────────────────────────────────── tidymodels 0.1.2 ──## ✓ broom 0.7.4 ✓ recipes 0.1.15
## ✓ dials 0.0.9 ✓ rsample 0.0.8
## ✓ infer 0.5.4 ✓ tibble 3.0.6
## ✓ modeldata 0.1.0 ✓ tune 0.1.2
## ✓ parsnip 0.1.5 ✓ workflows 0.2.1
## ✓ purrr 0.3.4 ✓ yardstick 0.0.7## ── Conflicts ───────────────────────────────────────── tidymodels_conflicts() ──
## x purrr::discard() masks scales::discard()
## x dplyr::filter() masks stats::filter()
## x recipes::fixed() masks stringr::fixed()
## x dplyr::lag() masks stats::lag()
## x MASS::select() masks dplyr::select()
## x recipes::step() masks stats::step()df_split <- initial_split(pennewdata3, prop=0.7)
df_train <- training(df_split)
df_test <- testing(df_split)Logistic regression model
lr_model <- logistic_reg() %>%
# using model classification
set_mode('classification') %>%
# use glm function
set_engine('glm') %>%
#fit training data
fit(species ~ ., df_train)Prediction on Training Data
lr_train_pred <- lr_model %>%
predict(df_train) %>%
# rename the prediction column
mutate(prediction = `.pred_class`) %>%
# merge the prediction result back to training data set
bind_cols(df_train) Confusion Matrix is a tabular representation of Observed vs Predicted values. It helps to quantify the efficiency (or accuracy) of the model.
lr_train_cm <- lr_train_pred %>%
#use only prediction values and actual label
dplyr::select(prediction, species) %>%
#construct confusion matrix
table() %>%
#display as matrix
as.matrix()
lr_train_cm## species
## prediction Adelie Gentoo
## Adelie 101 4
## Gentoo 4 77Accuracy is .946.
## # A tibble: 2 x 3
## .metric .estimator .estimate
## <chr> <chr> <dbl>
## 1 accuracy binary 0.957
## 2 kap binary 0.913tp<-lr_train_cm[1,1]
fp<-lr_train_cm[1,2]
fn<-lr_train_cm[2,1]
tn<-lr_train_cm[2,2]
accuracy <- (tp+tn)/(tp+tn+fp+fn) #accuracy=(TP+TN/P+N)
tpr <- tp/(tp+fn) #TPR=TP/(TP+FN)
fpr <- fp/(fp+tn) #FPR=FP/(FP+TN)
tnr <- tn/(tn+fp) #TNR=TN/(TN+FP)
fnr <- fn/(fn+tp) #FNR=FN/(FN+TP)
lr_pred_prob_tr <- lr_train_pred %>%
cbind(predict(lr_model, df_train, type='prob'))
lr_pred_prob_tr## .pred_class prediction bill_length_mm body_mass_g species .pred_Adelie
## 1 Adelie Adelie 39.1 3750 Adelie 9.993429e-01
## 2 Adelie Adelie 39.5 3800 Adelie 9.987914e-01
## 3 Adelie Adelie 40.3 3250 Adelie 9.999346e-01
## 4 Adelie Adelie 36.7 3450 Adelie 9.999831e-01
## 5 Adelie Adelie 39.3 3650 Adelie 9.995977e-01
## 6 Adelie Adelie 39.2 4675 Adelie 7.965891e-01
## 7 Adelie Adelie 38.7 3450 Adelie 9.999273e-01
## 8 Adelie Adelie 42.5 4500 Adelie 5.184427e-01
## 9 Adelie Adelie 34.4 3325 Adelie 9.999986e-01
## 10 Adelie Adelie 37.7 3600 Adelie 9.999088e-01
## 11 Adelie Adelie 35.9 3800 Adelie 9.999123e-01
## 12 Adelie Adelie 38.2 3950 Adelie 9.987824e-01
## 13 Adelie Adelie 35.3 3800 Adelie 9.999433e-01
## 14 Adelie Adelie 40.6 3550 Adelie 9.994510e-01
## 15 Adelie Adelie 40.5 3200 Adelie 9.999450e-01
## 16 Adelie Adelie 37.9 3150 Adelie 9.999940e-01
## 17 Adelie Adelie 40.5 3950 Adelie 9.935242e-01
## 18 Adelie Adelie 39.5 3250 Adelie 9.999635e-01
## 19 Adelie Adelie 37.2 3900 Adelie 9.995724e-01
## 20 Adelie Adelie 39.5 3300 Adelie 9.999498e-01
## 21 Adelie Adelie 40.9 3900 Adelie 9.936940e-01
## 22 Adelie Adelie 36.4 3325 Adelie 9.999939e-01
## 23 Adelie Adelie 39.2 4150 Adelie 9.910533e-01
## 24 Adelie Adelie 42.2 3550 Adelie 9.982398e-01
## 25 Adelie Adelie 37.6 3300 Adelie 9.999874e-01
## 26 Adelie Adelie 36.5 3150 Adelie 9.999978e-01
## 27 Adelie Adelie 40.8 3900 Adelie 9.941347e-01
## 28 Adelie Adelie 36.0 3100 Adelie 9.999989e-01
## 29 Gentoo Gentoo 44.1 4400 Adelie 3.879773e-01
## 30 Adelie Adelie 37.0 3000 Adelie 9.999988e-01
## 31 Adelie Adelie 39.6 4600 Adelie 8.250618e-01
## 32 Adelie Adelie 42.3 4150 Adelie 9.204034e-01
## 33 Adelie Adelie 39.6 3500 Adelie 9.998073e-01
## 34 Adelie Adelie 35.0 3450 Adelie 9.999951e-01
## 35 Adelie Adelie 42.0 4050 Adelie 9.645370e-01
## 36 Adelie Adelie 34.5 2900 Adelie 9.999999e-01
## 37 Adelie Adelie 39.0 3550 Adelie 9.998289e-01
## 38 Adelie Adelie 40.6 3800 Adelie 9.973093e-01
## 39 Adelie Adelie 37.6 3750 Adelie 9.997797e-01
## 40 Adelie Adelie 35.7 3150 Adelie 9.999988e-01
## 41 Adelie Adelie 37.6 3600 Adelie 9.999152e-01
## 42 Adelie Adelie 36.4 2850 Adelie 9.999997e-01
## 43 Adelie Adelie 41.1 4100 Adelie 9.744407e-01
## 44 Adelie Adelie 41.8 4450 Adelie 7.114362e-01
## 45 Adelie Adelie 33.5 3600 Adelie 9.999957e-01
## 46 Adelie Adelie 39.7 3900 Adelie 9.973608e-01
## 47 Adelie Adelie 39.6 3550 Adelie 9.997351e-01
## 48 Gentoo Gentoo 45.8 4150 Adelie 4.741790e-01
## 49 Adelie Adelie 40.9 3700 Adelie 9.982268e-01
## 50 Adelie Adelie 37.2 3900 Adelie 9.995724e-01
## 51 Adelie Adelie 36.2 3550 Adelie 9.999778e-01
## 52 Adelie Adelie 42.1 4000 Adelie 9.720391e-01
## 53 Adelie Adelie 34.6 3200 Adelie 9.999993e-01
## 54 Gentoo Gentoo 42.9 4700 Adelie 1.837642e-01
## 55 Adelie Adelie 36.7 3800 Adelie 9.998428e-01
## 56 Adelie Adelie 35.1 4200 Adelie 9.993754e-01
## 57 Adelie Adelie 37.3 3350 Adelie 9.999861e-01
## 58 Adelie Adelie 41.3 3550 Adelie 9.990859e-01
## 59 Adelie Adelie 36.3 3800 Adelie 9.998826e-01
## 60 Adelie Adelie 36.9 3500 Adelie 9.999731e-01
## 61 Adelie Adelie 38.3 3950 Adelie 9.986905e-01
## 62 Adelie Adelie 35.7 3550 Adelie 9.999846e-01
## 63 Adelie Adelie 41.1 4300 Adelie 9.143213e-01
## 64 Adelie Adelie 36.2 3300 Adelie 9.999955e-01
## 65 Adelie Adelie 40.8 4300 Adelie 9.299716e-01
## 66 Adelie Adelie 38.1 3700 Adelie 9.997693e-01
## 67 Adelie Adelie 40.3 4350 Adelie 9.329173e-01
## 68 Adelie Adelie 33.1 2900 Adelie 1.000000e+00
## 69 Adelie Adelie 43.2 4100 Adelie 8.918843e-01
## 70 Adelie Adelie 35.0 3725 Adelie 9.999718e-01
## 71 Adelie Adelie 37.7 3075 Adelie 9.999968e-01
## 72 Adelie Adelie 37.8 4250 Adelie 9.938878e-01
## 73 Adelie Adelie 37.9 2925 Adelie 9.999986e-01
## 74 Adelie Adelie 38.6 3750 Adelie 9.995435e-01
## 75 Adelie Adelie 38.1 3825 Adelie 9.994889e-01
## 76 Gentoo Gentoo 45.6 4600 Adelie 5.612102e-02
## 77 Adelie Adelie 39.7 3200 Adelie 9.999693e-01
## 78 Adelie Adelie 39.6 3900 Adelie 9.975459e-01
## 79 Adelie Adelie 42.7 4075 Adelie 9.330027e-01
## 80 Adelie Adelie 38.6 2900 Adelie 9.999980e-01
## 81 Adelie Adelie 35.7 3350 Adelie 9.999957e-01
## 82 Adelie Adelie 36.2 3150 Adelie 9.999983e-01
## 83 Adelie Adelie 37.7 3500 Adelie 9.999517e-01
## 84 Adelie Adelie 40.2 3450 Adelie 9.997829e-01
## 85 Adelie Adelie 41.4 3875 Adelie 9.922681e-01
## 86 Adelie Adelie 35.2 3050 Adelie 9.999996e-01
## 87 Adelie Adelie 38.8 3275 Adelie 9.999743e-01
## 88 Adelie Adelie 41.5 4300 Adelie 8.885495e-01
## 89 Adelie Adelie 44.1 4000 Adelie 8.900010e-01
## 90 Adelie Adelie 38.5 3325 Adelie 9.999716e-01
## 91 Adelie Adelie 43.1 3500 Adelie 9.975345e-01
## 92 Adelie Adelie 36.8 3500 Adelie 9.999750e-01
## 93 Adelie Adelie 37.5 4475 Adelie 9.797186e-01
## 94 Adelie Adelie 38.1 3425 Adelie 9.999599e-01
## 95 Adelie Adelie 41.1 3900 Adelie 9.927116e-01
## 96 Adelie Adelie 35.6 3175 Adelie 9.999987e-01
## 97 Adelie Adelie 40.2 3975 Adelie 9.938960e-01
## 98 Adelie Adelie 37.0 3400 Adelie 9.999847e-01
## 99 Adelie Adelie 39.7 4250 Adelie 9.760229e-01
## 100 Adelie Adelie 32.1 3050 Adelie 1.000000e+00
## 101 Adelie Adelie 40.7 3725 Adelie 9.982030e-01
## 102 Adelie Adelie 39.0 3650 Adelie 9.996767e-01
## 103 Adelie Adelie 39.2 4250 Adelie 9.832233e-01
## 104 Adelie Adelie 36.6 3475 Adelie 9.999815e-01
## 105 Adelie Adelie 36.0 3450 Adelie 9.999898e-01
## 106 Gentoo Gentoo 46.1 4500 Gentoo 7.240609e-02
## 107 Gentoo Gentoo 48.7 4450 Gentoo 1.587244e-02
## 108 Gentoo Gentoo 50.0 5700 Gentoo 2.187371e-06
## 109 Gentoo Gentoo 47.6 5400 Gentoo 8.494069e-05
## 110 Gentoo Gentoo 46.5 4550 Gentoo 4.069152e-02
## 111 Gentoo Gentoo 45.4 4800 Gentoo 1.889114e-02
## 112 Gentoo Gentoo 46.7 5200 Gentoo 5.845061e-04
## 113 Adelie Adelie 43.3 4400 Gentoo 5.317852e-01
## 114 Gentoo Gentoo 46.8 5150 Gentoo 7.469771e-04
## 115 Adelie Adelie 40.9 4650 Gentoo 5.707985e-01
## 116 Gentoo Gentoo 49.0 5550 Gentoo 1.178202e-05
## 117 Gentoo Gentoo 45.5 4650 Gentoo 4.445020e-02
## 118 Gentoo Gentoo 48.4 5850 Gentoo 2.702035e-06
## 119 Gentoo Gentoo 45.8 4200 Gentoo 3.961106e-01
## 120 Adelie Adelie 42.0 4150 Gentoo 9.350217e-01
## 121 Gentoo Gentoo 49.2 6300 Gentoo 8.594716e-08
## 122 Gentoo Gentoo 46.5 4400 Gentoo 9.928201e-02
## 123 Gentoo Gentoo 42.9 5000 Gentoo 3.226485e-02
## 124 Gentoo Gentoo 46.1 5100 Gentoo 1.708953e-03
## 125 Gentoo Gentoo 48.2 4600 Gentoo 8.856772e-03
## 126 Gentoo Gentoo 42.8 4700 Gentoo 1.949505e-01
## 127 Gentoo Gentoo 45.1 5050 Gentoo 4.854788e-03
## 128 Gentoo Gentoo 49.1 5150 Gentoo 1.397882e-04
## 129 Gentoo Gentoo 42.6 4950 Gentoo 5.396302e-02
## 130 Gentoo Gentoo 44.4 5250 Gentoo 2.269402e-03
## 131 Gentoo Gentoo 48.7 5350 Gentoo 5.237852e-05
## 132 Gentoo Gentoo 49.6 5700 Gentoo 2.927847e-06
## 133 Gentoo Gentoo 49.6 4750 Gentoo 1.237865e-03
## 134 Gentoo Gentoo 50.5 5550 Gentoo 3.947981e-06
## 135 Gentoo Gentoo 43.6 4900 Gentoo 3.645362e-02
## 136 Gentoo Gentoo 45.2 5300 Gentoo 9.225706e-04
## 137 Gentoo Gentoo 46.6 4850 Gentoo 5.806148e-03
## 138 Gentoo Gentoo 45.1 4400 Gentoo 2.342008e-01
## 139 Gentoo Gentoo 45.0 5050 Gentoo 5.219962e-03
## 140 Adelie Adelie 43.8 4300 Gentoo 5.985667e-01
## 141 Gentoo Gentoo 50.4 5550 Gentoo 4.246503e-06
## 142 Gentoo Gentoo 54.3 5650 Gentoo 1.308993e-07
## 143 Gentoo Gentoo 49.8 5700 Gentoo 2.530670e-06
## 144 Gentoo Gentoo 49.5 5800 Gentoo 1.666152e-06
## 145 Gentoo Gentoo 43.5 4700 Gentoo 1.269276e-01
## 146 Gentoo Gentoo 50.7 5550 Gentoo 3.412418e-06
## 147 Gentoo Gentoo 46.4 5000 Gentoo 2.593381e-03
## 148 Gentoo Gentoo 46.5 5200 Gentoo 6.761800e-04
## 149 Gentoo Gentoo 46.4 4700 Gentoo 1.725469e-02
## 150 Gentoo Gentoo 48.6 5800 Gentoo 3.210872e-06
## 151 Gentoo Gentoo 47.5 4600 Gentoo 1.466622e-02
## 152 Gentoo Gentoo 51.1 6000 Gentoo 1.452878e-07
## 153 Gentoo Gentoo 45.2 4750 Gentoo 2.971652e-02
## 154 Gentoo Gentoo 49.1 4625 Gentoo 3.939067e-03
## 155 Gentoo Gentoo 52.5 5450 Gentoo 1.736744e-06
## 156 Gentoo Gentoo 47.4 4725 Gentoo 7.172193e-03
## 157 Gentoo Gentoo 50.0 5350 Gentoo 2.030636e-05
## 158 Gentoo Gentoo 44.9 4750 Gentoo 3.671339e-02
## 159 Gentoo Gentoo 50.8 5600 Gentoo 2.307601e-06
## 160 Gentoo Gentoo 51.3 5300 Gentoo 1.082297e-05
## 161 Gentoo Gentoo 47.5 4875 Gentoo 2.577890e-03
## 162 Gentoo Gentoo 52.1 5550 Gentoo 1.229905e-06
## 163 Gentoo Gentoo 47.5 4950 Gentoo 1.600743e-03
## 164 Gentoo Gentoo 52.2 5400 Gentoo 2.971326e-06
## 165 Gentoo Gentoo 45.5 4750 Gentoo 2.401987e-02
## 166 Gentoo Gentoo 49.5 5650 Gentoo 4.329619e-06
## 167 Gentoo Gentoo 50.8 5200 Gentoo 2.945180e-05
## 168 Gentoo Gentoo 51.1 5250 Gentoo 1.721481e-05
## 169 Gentoo Gentoo 48.5 4850 Gentoo 1.459850e-03
## 170 Gentoo Gentoo 55.9 5600 Gentoo 5.606321e-08
## 171 Gentoo Gentoo 47.2 4975 Gentoo 1.698736e-03
## 172 Gentoo Gentoo 49.1 5500 Gentoo 1.505938e-05
## 173 Gentoo Gentoo 46.8 5500 Gentoo 8.051547e-05
## 174 Gentoo Gentoo 41.7 4700 Gentoo 3.506127e-01
## 175 Gentoo Gentoo 53.4 5500 Gentoo 6.555141e-07
## 176 Gentoo Gentoo 43.3 4575 Gentoo 2.715420e-01
## 177 Gentoo Gentoo 48.1 5500 Gentoo 3.121517e-05
## 178 Gentoo Gentoo 50.5 5000 Gentoo 1.309239e-04
## 179 Gentoo Gentoo 43.5 4650 Gentoo 1.665776e-01
## 180 Gentoo Gentoo 51.5 5500 Gentoo 2.618518e-06
## 181 Gentoo Gentoo 55.1 5850 Gentoo 2.045048e-08
## 182 Gentoo Gentoo 48.8 6000 Gentoo 7.768363e-07
## 183 Gentoo Gentoo 47.2 4925 Gentoo 2.333968e-03
## 184 Gentoo Gentoo 46.8 4850 Gentoo 5.022468e-03
## 185 Gentoo Gentoo 50.4 5750 Gentoo 1.188643e-06
## 186 Gentoo Gentoo 45.2 5200 Gentoo 1.742344e-03
## .pred_Gentoo
## 1 6.571414e-04
## 2 1.208622e-03
## 3 6.536434e-05
## 4 1.693198e-05
## 5 4.023388e-04
## 6 2.034109e-01
## 7 7.274688e-05
## 8 4.815573e-01
## 9 1.428896e-06
## 10 9.119625e-05
## 11 8.772878e-05
## 12 1.217553e-03
## 13 5.665214e-05
## 14 5.490003e-04
## 15 5.500639e-05
## 16 6.013383e-06
## 17 6.475835e-03
## 18 3.648389e-05
## 19 4.275828e-04
## 20 5.015803e-05
## 21 6.305955e-03
## 22 6.139449e-06
## 23 8.946655e-03
## 24 1.760154e-03
## 25 1.255690e-05
## 26 2.167349e-06
## 27 5.865255e-03
## 28 1.094968e-06
## 29 6.120227e-01
## 30 1.200815e-06
## 31 1.749382e-01
## 32 7.959665e-02
## 33 1.927155e-04
## 34 4.904014e-06
## 35 3.546297e-02
## 36 1.027004e-07
## 37 1.710929e-04
## 38 2.690715e-03
## 39 2.202929e-04
## 40 1.209698e-06
## 41 8.478582e-05
## 42 2.984015e-07
## 43 2.555925e-02
## 44 2.885638e-01
## 45 4.270118e-06
## 46 2.639198e-03
## 47 2.649296e-04
## 48 5.258210e-01
## 49 1.773152e-03
## 50 4.275828e-04
## 51 2.222867e-05
## 52 2.796090e-02
## 53 7.459342e-07
## 54 8.162358e-01
## 55 1.571681e-04
## 56 6.246249e-04
## 57 1.387259e-05
## 58 9.141336e-04
## 59 1.174236e-04
## 60 2.693158e-05
## 61 1.309496e-03
## 62 1.543951e-05
## 63 8.567871e-02
## 64 4.525789e-06
## 65 7.002839e-02
## 66 2.306924e-04
## 67 6.708266e-02
## 68 3.701524e-08
## 69 1.081157e-01
## 70 2.824171e-05
## 71 3.224326e-06
## 72 6.112236e-03
## 73 1.435545e-06
## 74 4.565236e-04
## 75 5.111223e-04
## 76 9.438790e-01
## 77 3.070233e-05
## 78 2.454121e-03
## 79 6.699735e-02
## 80 2.039340e-06
## 81 4.321724e-06
## 82 1.741644e-06
## 83 4.825085e-05
## 84 2.170700e-04
## 85 7.731918e-03
## 86 4.445329e-07
## 87 2.568222e-05
## 88 1.114505e-01
## 89 1.099990e-01
## 90 2.837313e-05
## 91 2.465513e-03
## 92 2.503837e-05
## 93 2.028143e-02
## 94 4.006514e-05
## 95 7.288436e-03
## 96 1.318691e-06
## 97 6.103955e-03
## 98 1.532614e-05
## 99 2.397713e-02
## 100 4.640354e-08
## 101 1.796988e-03
## 102 3.233379e-04
## 103 1.677670e-02
## 104 1.845751e-05
## 105 1.016517e-05
## 106 9.275939e-01
## 107 9.841276e-01
## 108 9.999978e-01
## 109 9.999151e-01
## 110 9.593085e-01
## 111 9.811089e-01
## 112 9.994155e-01
## 113 4.682148e-01
## 114 9.992530e-01
## 115 4.292015e-01
## 116 9.999882e-01
## 117 9.555498e-01
## 118 9.999973e-01
## 119 6.038894e-01
## 120 6.497834e-02
## 121 9.999999e-01
## 122 9.007180e-01
## 123 9.677352e-01
## 124 9.982910e-01
## 125 9.911432e-01
## 126 8.050495e-01
## 127 9.951452e-01
## 128 9.998602e-01
## 129 9.460370e-01
## 130 9.977306e-01
## 131 9.999476e-01
## 132 9.999971e-01
## 133 9.987621e-01
## 134 9.999961e-01
## 135 9.635464e-01
## 136 9.990774e-01
## 137 9.941939e-01
## 138 7.657992e-01
## 139 9.947800e-01
## 140 4.014333e-01
## 141 9.999958e-01
## 142 9.999999e-01
## 143 9.999975e-01
## 144 9.999983e-01
## 145 8.730724e-01
## 146 9.999966e-01
## 147 9.974066e-01
## 148 9.993238e-01
## 149 9.827453e-01
## 150 9.999968e-01
## 151 9.853338e-01
## 152 9.999999e-01
## 153 9.702835e-01
## 154 9.960609e-01
## 155 9.999983e-01
## 156 9.928278e-01
## 157 9.999797e-01
## 158 9.632866e-01
## 159 9.999977e-01
## 160 9.999892e-01
## 161 9.974221e-01
## 162 9.999988e-01
## 163 9.983993e-01
## 164 9.999970e-01
## 165 9.759801e-01
## 166 9.999957e-01
## 167 9.999705e-01
## 168 9.999828e-01
## 169 9.985402e-01
## 170 9.999999e-01
## 171 9.983013e-01
## 172 9.999849e-01
## 173 9.999195e-01
## 174 6.493873e-01
## 175 9.999993e-01
## 176 7.284580e-01
## 177 9.999688e-01
## 178 9.998691e-01
## 179 8.334224e-01
## 180 9.999974e-01
## 181 1.000000e+00
## 182 9.999992e-01
## 183 9.976660e-01
## 184 9.949775e-01
## 185 9.999988e-01
## 186 9.982577e-01
auc <- lr_pred_prob_tr %>%
roc_auc(species, c(.pred_Adelie)) %>%
.[1,3] %>%
as.numeric()
train_r1 <- data.frame(AUC = auc,
ACCURACY = accuracy,
TPR = tpr,
FPR = fpr,
TNR = tnr,
FNR = fnr)
library(kableExtra)
train_r1 %>%
kable(caption = 'Training')| AUC | ACCURACY | TPR | FPR | TNR | FNR |
|---|---|---|---|---|---|
| 0.9945914 | 0.9569892 | 0.9619048 | 0.0493827 | 0.9506173 | 0.0380952 |
lr_test_pred <- lr_model %>%
#make prediction on testing data
predict(df_test) %>%
# rename the prediction column
mutate(prediction = `.pred_class`) %>%
# merge the prediction result back to training data set
bind_cols(df_test)lr_test_cm <- lr_test_pred %>%
#use only prediction values and actual label
dplyr::select(prediction, species) %>%
#construct confusion matrix
table() %>%
#display as matrix
as.matrix()
lr_test_cm## species
## prediction Adelie Gentoo
## Adelie 38 1
## Gentoo 3 37## # A tibble: 2 x 3
## .metric .estimator .estimate
## <chr> <chr> <dbl>
## 1 accuracy binary 0.949
## 2 kap binary 0.899tp<-lr_test_cm[1,1]
fp<-lr_test_cm[1,2]
fn<-lr_test_cm[2,1]
tn<-lr_test_cm[2,2]
accuracy <- (tp+tn)/(tp+tn+fp+fn) #accuracy=(TP+TN/P+N)
tpr <- tp/(tp+fn) #TPR=TP/(TP+FN)
fpr <- fp/(fp+tn) #FPR=FP/(FP+TN)
tnr <- tn/(tn+fp) #TNR=TN/(TN+FP)
fnr <- fn/(fn+tp) #FNR=FN/(FN+TP)
lr_pred_prob_te <- lr_test_pred %>%
cbind(predict(lr_model, df_test, type='prob'))
lr_pred_prob_te %>%
roc_curve(species, c(.pred_Adelie)) %>%
autoplot()
auc <- lr_pred_prob_te %>%
roc_auc(species, c(.pred_Adelie)) %>%
.[1,3] %>%
as.numeric()
test_r1 <- data.frame(AUC = auc,
ACCURACY = accuracy,
TPR = tpr,
FPR = fpr,
TNR = tnr,
FNR = fnr)
test_r1 %>%
kable(caption = 'Testing')| AUC | ACCURACY | TPR | FPR | TNR | FNR |
|---|---|---|---|---|---|
| 0.9839538 | 0.9493671 | 0.9268293 | 0.0263158 | 0.9736842 | 0.0731707 |
3. Multinomial Logistic Regression. (40)
## # A tibble: 3 x 1
## species
## <fct>
## 1 Adelie
## 2 Gentoo
## 3 Chinstrapa.
Please fit it a multinomial logistic regression where your outcome variable is ‘species’.
From the summary statistic, there are missing values in the dataset, being displayed as NA’s and should be removed. Species has categories Adelie, Chinstrap and Gentoo. When the dependent variable has more than two categories, then it is a multinomial logistic regression.
## species island bill_length_mm bill_depth_mm
## Adelie :152 Biscoe :168 Min. :32.10 Min. :13.10
## Chinstrap: 68 Dream :124 1st Qu.:39.23 1st Qu.:15.60
## Gentoo :124 Torgersen: 52 Median :44.45 Median :17.30
## Mean :43.92 Mean :17.15
## 3rd Qu.:48.50 3rd Qu.:18.70
## Max. :59.60 Max. :21.50
## NA's :2 NA's :2
## flipper_length_mm body_mass_g sex year
## Min. :172.0 Min. :2700 female:165 Min. :2007
## 1st Qu.:190.0 1st Qu.:3550 male :168 1st Qu.:2007
## Median :197.0 Median :4050 NA's : 11 Median :2008
## Mean :200.9 Mean :4202 Mean :2008
## 3rd Qu.:213.0 3rd Qu.:4750 3rd Qu.:2009
## Max. :231.0 Max. :6300 Max. :2009
## NA's :2 NA's :2## species island bill_length_mm bill_depth_mm
## Adelie :146 Biscoe :163 Min. :32.10 Min. :13.10
## Chinstrap: 68 Dream :123 1st Qu.:39.50 1st Qu.:15.60
## Gentoo :119 Torgersen: 47 Median :44.50 Median :17.30
## Mean :43.99 Mean :17.16
## 3rd Qu.:48.60 3rd Qu.:18.70
## Max. :59.60 Max. :21.50
## flipper_length_mm body_mass_g sex year
## Min. :172 Min. :2700 female:165 Min. :2007
## 1st Qu.:190 1st Qu.:3550 male :168 1st Qu.:2007
## Median :197 Median :4050 Median :2008
## Mean :201 Mean :4207 Mean :2008
## 3rd Qu.:213 3rd Qu.:4775 3rd Qu.:2009
## Max. :231 Max. :6300 Max. :2009Non-numeric columns, Island and Sex were removed along with Year. I reordered the columns to have the binary dependent variable, species as the last column.
There are now four independent variables as indicated in the Descriptive statistics.
## bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
## Min. :32.10 Min. :13.10 Min. :172 Min. :2700
## 1st Qu.:39.50 1st Qu.:15.60 1st Qu.:190 1st Qu.:3550
## Median :44.50 Median :17.30 Median :197 Median :4050
## Mean :43.99 Mean :17.16 Mean :201 Mean :4207
## 3rd Qu.:48.60 3rd Qu.:18.70 3rd Qu.:213 3rd Qu.:4775
## Max. :59.60 Max. :21.50 Max. :231 Max. :6300
## species
## Adelie :146
## Chinstrap: 68
## Gentoo :119
##
##
## Changed data frame to matrix to handle the following error: Error in hist.default(newdata2[, i], main = colnames(newdata2)[i], xlab = colnames(newdata2)[i], : ‘x’ must be numeric
Analyze the distribution of each independent variable
par(mfrow = c(2,2))
for( i in 1:4){
hist(mnewdata2[,i], main = colnames(mnewdata2)[i],xlab=colnames(mnewdata2)[i], col = 'yellow')
}
For continuous independent variables, we can get more clarity on the distribution by analyzing it w.r.t. dependent variable.
par(mfrow = c(2,2))
boxplot(bill_length_mm~species, ylab="Bill Length (mm)", xlab= "Species", col="light blue",data = mnewdata1)
boxplot(bill_depth_mm~species, ylab="Bill Depth (mm)", xlab= "Species", col="light blue",data = mnewdata1)
boxplot(flipper_length_mm~species, ylab="Flipper Length (mm)", xlab= "Species", col="light blue",data = mnewdata1)
boxplot(body_mass_g~species, ylab="Body Mass (g)", xlab= "Species", col="light blue",data = mnewdata1)
New data frame of relevant modeling variables.
mnewdata4 <- mnewdata2[,c("species", "bill_length_mm", "bill_depth_mm", "flipper_length_mm", "body_mass_g")]#b. Please be sure to evaluate the independent variables appropriately to fit your best parsimonious model.
Implementation of Logistic Regression to predict the binary outcome — species in the dataset “newdata4”.
## # weights: 18 (10 variable)
## initial value 365.837892
## iter 10 value 16.321214
## iter 20 value 3.754897
## iter 30 value 1.631859
## iter 40 value 0.012427
## iter 50 value 0.001125
## iter 60 value 0.001108
## iter 70 value 0.001006
## iter 80 value 0.000906
## iter 90 value 0.000498
## iter 100 value 0.000498
## final value 0.000498
## stopped after 100 iterationsc.
Please be sure to interpret your variables in the model.
Analysis of Model Summary
## Call:
## multinom(formula = species ~ ., data = mnewdata1)
##
## Coefficients:
## (Intercept) bill_length_mm bill_depth_mm flipper_length_mm
## Chinstrap -34.60273 58.94543 -84.81399 -2.643720
## Gentoo -4.70502 43.75912 -91.60364 -1.639715
## body_mass_g
## Chinstrap -0.132491128
## Gentoo 0.007448619
##
## Std. Errors:
## (Intercept) bill_length_mm bill_depth_mm flipper_length_mm
## Chinstrap 4.4008386318 73.52088725 51.084116136 15.71457598
## Gentoo 0.0003319148 0.01602115 0.006439479 0.06591798
## body_mass_g
## Chinstrap 0.3479725
## Gentoo 1.4739115
##
## Residual Deviance: 0.0009955954
## AIC: 20.001A one-unit increase in the variable body mass(g) is associated with the decrease in the log odds of being Chinstrap species vs. Adelie in the amount of .013. A one-unit increase in the variable body mass(g) is associated with the increase in the log odds of being Gentoo species vs. Adelie in the amount of .001. A one-unit increase in the variable flipper length(mm) is associated with the decrease in the log odds of being Chinstrap species vs. Adelie in the amount of 2.644. A one-unit increase in the variable body mass(g) is associated with the decrease in the log odds of being Gentoo species vs. Adelie in the amount of 1.640. A one-unit increase in the variable bill depth(mm) is associated with the decrease in the log odds of being Chinstrap species vs. Adelie in the amount of 84.814. A one-unit increase in the variable bill depth(mm) is associated with the decrease in the log odds of being Gentoo species vs. Adelie in the amount of 91.604. A one-unit increase in the variable bill length(mm) is associated with the increase in the log odds of being Chinstrap species vs. Adelie in the amount of 58.945. A one-unit increase in the variable bill length(mm) is associated with the increase in the log odds of being Gentoo species vs. Adelie in the amount of 43.759.
#4. Extra credit
What would be some of the fit statistics you would want to evaluate for your model in question #3? Feel free to share whatever you can provide. (10)
Naive Bayes computes the conditional a-posterior probabilities of a categorical class variable given independent predictor variables using the Bayes rule. Naive Bayes is a Supervised Machine Learning algorithm based on the Bayes Theorem that is used to solve classification problems by following a probabilistic approach.
FALSE
FALSE Naive Bayes Classifier for Discrete Predictors
FALSE
FALSE Call:
FALSE naiveBayes.default(x = X, y = Y, laplace = laplace)
FALSE
FALSE A-priori probabilities:
FALSE Y
FALSE Adelie Gentoo
FALSE 0.5645161 0.4354839
FALSE
FALSE Conditional probabilities:
FALSE bill_length_mm
FALSE Y [,1] [,2]
FALSE Adelie 38.68762 2.698137
FALSE Gentoo 47.68395 3.167430
FALSE
FALSE body_mass_g
FALSE Y [,1] [,2]
FALSE Adelie 3681.667 446.5179
FALSE Gentoo 5119.753 480.0019nb_train_pred <- nb_model %>%
#make prediction on training data
predict(df_train) %>%
data.frame(prediction = .) %>%
# merge the prediction result back to training data set
bind_cols(df_train)
nb_train_pred## prediction bill_length_mm body_mass_g species
## 1 Adelie 39.1 3750 Adelie
## 2 Adelie 39.5 3800 Adelie
## 3 Adelie 40.3 3250 Adelie
## 4 Adelie 36.7 3450 Adelie
## 5 Adelie 39.3 3650 Adelie
## 6 Adelie 39.2 4675 Adelie
## 7 Adelie 38.7 3450 Adelie
## 8 Gentoo 42.5 4500 Adelie
## 9 Adelie 34.4 3325 Adelie
## 10 Adelie 37.7 3600 Adelie
## 11 Adelie 35.9 3800 Adelie
## 12 Adelie 38.2 3950 Adelie
## 13 Adelie 35.3 3800 Adelie
## 14 Adelie 40.6 3550 Adelie
## 15 Adelie 40.5 3200 Adelie
## 16 Adelie 37.9 3150 Adelie
## 17 Adelie 40.5 3950 Adelie
## 18 Adelie 39.5 3250 Adelie
## 19 Adelie 37.2 3900 Adelie
## 20 Adelie 39.5 3300 Adelie
## 21 Adelie 40.9 3900 Adelie
## 22 Adelie 36.4 3325 Adelie
## 23 Adelie 39.2 4150 Adelie
## 24 Adelie 42.2 3550 Adelie
## 25 Adelie 37.6 3300 Adelie
## 26 Adelie 36.5 3150 Adelie
## 27 Adelie 40.8 3900 Adelie
## 28 Adelie 36.0 3100 Adelie
## 29 Gentoo 44.1 4400 Adelie
## 30 Adelie 37.0 3000 Adelie
## 31 Adelie 39.6 4600 Adelie
## 32 Adelie 42.3 4150 Adelie
## 33 Adelie 39.6 3500 Adelie
## 34 Adelie 35.0 3450 Adelie
## 35 Adelie 42.0 4050 Adelie
## 36 Adelie 34.5 2900 Adelie
## 37 Adelie 39.0 3550 Adelie
## 38 Adelie 40.6 3800 Adelie
## 39 Adelie 37.6 3750 Adelie
## 40 Adelie 35.7 3150 Adelie
## 41 Adelie 37.6 3600 Adelie
## 42 Adelie 36.4 2850 Adelie
## 43 Adelie 41.1 4100 Adelie
## 44 Adelie 41.8 4450 Adelie
## 45 Adelie 33.5 3600 Adelie
## 46 Adelie 39.7 3900 Adelie
## 47 Adelie 39.6 3550 Adelie
## 48 Gentoo 45.8 4150 Adelie
## 49 Adelie 40.9 3700 Adelie
## 50 Adelie 37.2 3900 Adelie
## 51 Adelie 36.2 3550 Adelie
## 52 Adelie 42.1 4000 Adelie
## 53 Adelie 34.6 3200 Adelie
## 54 Gentoo 42.9 4700 Adelie
## 55 Adelie 36.7 3800 Adelie
## 56 Adelie 35.1 4200 Adelie
## 57 Adelie 37.3 3350 Adelie
## 58 Adelie 41.3 3550 Adelie
## 59 Adelie 36.3 3800 Adelie
## 60 Adelie 36.9 3500 Adelie
## 61 Adelie 38.3 3950 Adelie
## 62 Adelie 35.7 3550 Adelie
## 63 Adelie 41.1 4300 Adelie
## 64 Adelie 36.2 3300 Adelie
## 65 Adelie 40.8 4300 Adelie
## 66 Adelie 38.1 3700 Adelie
## 67 Adelie 40.3 4350 Adelie
## 68 Adelie 33.1 2900 Adelie
## 69 Adelie 43.2 4100 Adelie
## 70 Adelie 35.0 3725 Adelie
## 71 Adelie 37.7 3075 Adelie
## 72 Adelie 37.8 4250 Adelie
## 73 Adelie 37.9 2925 Adelie
## 74 Adelie 38.6 3750 Adelie
## 75 Adelie 38.1 3825 Adelie
## 76 Gentoo 45.6 4600 Adelie
## 77 Adelie 39.7 3200 Adelie
## 78 Adelie 39.6 3900 Adelie
## 79 Adelie 42.7 4075 Adelie
## 80 Adelie 38.6 2900 Adelie
## 81 Adelie 35.7 3350 Adelie
## 82 Adelie 36.2 3150 Adelie
## 83 Adelie 37.7 3500 Adelie
## 84 Adelie 40.2 3450 Adelie
## 85 Adelie 41.4 3875 Adelie
## 86 Adelie 35.2 3050 Adelie
## 87 Adelie 38.8 3275 Adelie
## 88 Adelie 41.5 4300 Adelie
## 89 Adelie 44.1 4000 Adelie
## 90 Adelie 38.5 3325 Adelie
## 91 Adelie 43.1 3500 Adelie
## 92 Adelie 36.8 3500 Adelie
## 93 Adelie 37.5 4475 Adelie
## 94 Adelie 38.1 3425 Adelie
## 95 Adelie 41.1 3900 Adelie
## 96 Adelie 35.6 3175 Adelie
## 97 Adelie 40.2 3975 Adelie
## 98 Adelie 37.0 3400 Adelie
## 99 Adelie 39.7 4250 Adelie
## 100 Adelie 32.1 3050 Adelie
## 101 Adelie 40.7 3725 Adelie
## 102 Adelie 39.0 3650 Adelie
## 103 Adelie 39.2 4250 Adelie
## 104 Adelie 36.6 3475 Adelie
## 105 Adelie 36.0 3450 Adelie
## 106 Gentoo 46.1 4500 Gentoo
## 107 Gentoo 48.7 4450 Gentoo
## 108 Gentoo 50.0 5700 Gentoo
## 109 Gentoo 47.6 5400 Gentoo
## 110 Gentoo 46.5 4550 Gentoo
## 111 Gentoo 45.4 4800 Gentoo
## 112 Gentoo 46.7 5200 Gentoo
## 113 Gentoo 43.3 4400 Gentoo
## 114 Gentoo 46.8 5150 Gentoo
## 115 Adelie 40.9 4650 Gentoo
## 116 Gentoo 49.0 5550 Gentoo
## 117 Gentoo 45.5 4650 Gentoo
## 118 Gentoo 48.4 5850 Gentoo
## 119 Gentoo 45.8 4200 Gentoo
## 120 Adelie 42.0 4150 Gentoo
## 121 Gentoo 49.2 6300 Gentoo
## 122 Gentoo 46.5 4400 Gentoo
## 123 Gentoo 42.9 5000 Gentoo
## 124 Gentoo 46.1 5100 Gentoo
## 125 Gentoo 48.2 4600 Gentoo
## 126 Gentoo 42.8 4700 Gentoo
## 127 Gentoo 45.1 5050 Gentoo
## 128 Gentoo 49.1 5150 Gentoo
## 129 Gentoo 42.6 4950 Gentoo
## 130 Gentoo 44.4 5250 Gentoo
## 131 Gentoo 48.7 5350 Gentoo
## 132 Gentoo 49.6 5700 Gentoo
## 133 Gentoo 49.6 4750 Gentoo
## 134 Gentoo 50.5 5550 Gentoo
## 135 Gentoo 43.6 4900 Gentoo
## 136 Gentoo 45.2 5300 Gentoo
## 137 Gentoo 46.6 4850 Gentoo
## 138 Gentoo 45.1 4400 Gentoo
## 139 Gentoo 45.0 5050 Gentoo
## 140 Gentoo 43.8 4300 Gentoo
## 141 Gentoo 50.4 5550 Gentoo
## 142 Gentoo 54.3 5650 Gentoo
## 143 Gentoo 49.8 5700 Gentoo
## 144 Gentoo 49.5 5800 Gentoo
## 145 Gentoo 43.5 4700 Gentoo
## 146 Gentoo 50.7 5550 Gentoo
## 147 Gentoo 46.4 5000 Gentoo
## 148 Gentoo 46.5 5200 Gentoo
## 149 Gentoo 46.4 4700 Gentoo
## 150 Gentoo 48.6 5800 Gentoo
## 151 Gentoo 47.5 4600 Gentoo
## 152 Gentoo 51.1 6000 Gentoo
## 153 Gentoo 45.2 4750 Gentoo
## 154 Gentoo 49.1 4625 Gentoo
## 155 Gentoo 52.5 5450 Gentoo
## 156 Gentoo 47.4 4725 Gentoo
## 157 Gentoo 50.0 5350 Gentoo
## 158 Gentoo 44.9 4750 Gentoo
## 159 Gentoo 50.8 5600 Gentoo
## 160 Gentoo 51.3 5300 Gentoo
## 161 Gentoo 47.5 4875 Gentoo
## 162 Gentoo 52.1 5550 Gentoo
## 163 Gentoo 47.5 4950 Gentoo
## 164 Gentoo 52.2 5400 Gentoo
## 165 Gentoo 45.5 4750 Gentoo
## 166 Gentoo 49.5 5650 Gentoo
## 167 Gentoo 50.8 5200 Gentoo
## 168 Gentoo 51.1 5250 Gentoo
## 169 Gentoo 48.5 4850 Gentoo
## 170 Gentoo 55.9 5600 Gentoo
## 171 Gentoo 47.2 4975 Gentoo
## 172 Gentoo 49.1 5500 Gentoo
## 173 Gentoo 46.8 5500 Gentoo
## 174 Gentoo 41.7 4700 Gentoo
## 175 Gentoo 53.4 5500 Gentoo
## 176 Gentoo 43.3 4575 Gentoo
## 177 Gentoo 48.1 5500 Gentoo
## 178 Gentoo 50.5 5000 Gentoo
## 179 Gentoo 43.5 4650 Gentoo
## 180 Gentoo 51.5 5500 Gentoo
## 181 Gentoo 55.1 5850 Gentoo
## 182 Gentoo 48.8 6000 Gentoo
## 183 Gentoo 47.2 4925 Gentoo
## 184 Gentoo 46.8 4850 Gentoo
## 185 Gentoo 50.4 5750 Gentoo
## 186 Gentoo 45.2 5200 Gentoonb_train_cm <- nb_train_pred %>%
#use only prediction values and actual label
dplyr::select(prediction, species) %>%
#construct confusion matrix
table() %>%
#display as matrix
as.matrix()
nb_train_cm## species
## prediction Adelie Gentoo
## Adelie 100 2
## Gentoo 5 79## # A tibble: 2 x 3
## .metric .estimator .estimate
## <chr> <chr> <dbl>
## 1 accuracy binary 0.962
## 2 kap binary 0.924kNN k-nearest neighbour classification for test set from training set. For each row of the test set, the k nearest (in Euclidean distance) training set vectors are found, and the classification is decided by majority vote, with ties broken at random. If there are ties for the kth nearest vector, all candidates are included in the vote.
# kNN model with k=3
knn3_model <- nearest_neighbor(neighbors = 3) %>%
set_mode('classification') %>%
set_engine('kknn') %>%
fit(species ~ ., df_train)
knn3_model## parsnip model object
##
## Fit time: 46ms
##
## Call:
## kknn::train.kknn(formula = species ~ ., data = data, ks = min_rows(3, data, 5))
##
## Type of response variable: nominal
## Minimal misclassification: 0.06451613
## Best kernel: optimal
## Best k: 3knn3_train_pred <- knn3_model %>%
#make prediction on training data
predict(df_train) %>%
rename(prediction = `.pred_class`) %>%
# merge the prediction result back to training data set
bind_cols(df_train)knn3_train_cm <- knn3_train_pred %>%
#use only prediction values and actual label
dplyr::select(prediction, species) %>%
#construct confusion matrix
table() %>%
#display as matrix
as.matrix()
knn3_train_cm## species
## prediction Adelie Gentoo
## Adelie 105 0
## Gentoo 0 81## # A tibble: 2 x 3
## .metric .estimator .estimate
## <chr> <chr> <dbl>
## 1 accuracy binary 1
## 2 kap binary 1Refrences
https://stackoverflow.com/questions/16518428/right-way-to-convert-data-frame-to-a-numeric-matrix-when-df-also-contains-strin https://stackoverflow.com/questions/24111835/incorrect-number-of-dimensions-and-incorrect-number-of-subscripts-in-array http://www.sthda.com/english/wiki/reordering-data-frame-columns-in-r https://towardsdatascience.com/implementing-binary-logistic-regression-in-r-7d802a9d98fe http://r-statistics.co/Multinomial-Regression-With-R.html https://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/ https://datasciencebeginners.com/2018/12/20/multinomial-logistic-regression-using-r/ https://www.rdocumentation.org/packages/e1071/versions/1.7-3/topics/naiveBayes https://towardsdatascience.com/k-nearest-neighbors-algorithm-with-examples-in-r-simply-explained-knn-1f2c88da405c https://www.rdocumentation.org/packages/class/versions/7.3-17/topics/knn