Logistic Reggression

Load Data

path <- "/Users/pulkitbatra/Desktop/CACSC19/Unit-2 R Programming/Learning R/Assignment/Placement_Data_Full_Class.csv"



library(dplyr)
library(ggplot2)
location <- "../input/factors-affecting-campus-placement/Placement_Data_Full_Class.csv"
placement.df <- read.csv(path)
# select only relevant columns
placement.lr <- placement.df %>% select(ends_with("_p"), -etest_p, status)
table(placement.lr$status)

Not Placed     Placed 
        67        148 

placement.lr$status <- ifelse(placement.lr$status == "Not Placed", 1, 0)
table(placement.lr$status)

  0   1 
148  67 

library(caTools)

# Train and Test data
library(caTools) # to split data into train and test
set.seed(101)
sample <- sample.split(placement.lr$status, SplitRatio = 0.80)
train.lr = subset(placement.lr, sample == TRUE)
test.lr = subset(placement.lr, sample == FALSE)
#check the splits
prop.table(table(train.lr$status))

        0         1 
0.6860465 0.3139535 

prop.table(table(test.lr$status))

        0         1 
0.6976744 0.3023256 

# Train the model
model.lr <- glm(status ~ degree_p, family = binomial, data = train.lr)
summary(model.lr)

Call:
glm(formula = status ~ degree_p, family = binomial, data = train.lr)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) 11.43688    2.24817   5.087 3.63e-07 ***
degree_p    -0.18851    0.03509  -5.372 7.79e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 214.05  on 171  degrees of freedom
Residual deviance: 173.35  on 170  degrees of freedom
AIC: 177.35

Number of Fisher Scoring iterations: 5

# prediction
lr.pred <- predict(model.lr, newdata = test.lr, type = "response")
head(lr.pred)

        15         17         22         25         33         35 
0.88198047 0.28303502 0.01008494 0.03139780 0.25345579 0.83675747 

# The probabilities always refer to the class dummy-coded as “1”
head(test.lr$status)

[1] 1 0 0 0 0 1

# Classification Table
# categorize into groups based on the predicted probability
lr.pred.class <- ifelse(lr.pred>=0.5, 1, 0)
head(lr.pred.class)

15 17 22 25 33 35 
 1  0  0  0  0  1 

table(lr.pred.class)

lr.pred.class
 0  1 
34  9 

table(test.lr$status)

 0  1 
30 13 

conf.matrix <- table(test.lr$status, lr.pred.class)
conf.matrix

   lr.pred.class
     0  1
  0 30  0
  1  4  9

rownames(conf.matrix) <- c("Placed", "Not Placed")
colnames(conf.matrix) <- c("Placed", "Not Placed")
addmargins(conf.matrix)

            lr.pred.class
             Placed Not Placed Sum
  Placed         30          0  30
  Not Placed      4          9  13
  Sum            34          9  43

# model accuracy
mean((test.lr$status == lr.pred.class))

[1] 0.9069767

# different cut-off
lr.pred.class1 <- ifelse(lr.pred>=0.35, 1, 0)
conf.matrix1 <- table(test.lr$status, lr.pred.class1)
conf.matrix1

   lr.pred.class1
     0  1
  0 27  3
  1  2 11

Plots

ggplot(data = test.lr, aes(x = degree_p, y = status)) +
  geom_point() +
  geom_line(aes(y = lr.pred), color = "blue") +
  labs(title = "Logistic Regression Decision Boundary",
       x = "degree_p",
       y = "Probability of Placement")

install.packages("pROC")

Installing package into ‘/opt/homebrew/lib/R/4.3/site-library’
(as ‘lib’ is unspecified)
trying URL 'https://cran.rstudio.com/src/contrib/pROC_1.18.5.tar.gz'
Content type 'application/x-gzip' length 696162 bytes (679 KB)
==================================================
downloaded 679 KB

* installing *source* package ‘pROC’ ...
** package ‘pROC’ successfully unpacked and MD5 sums checked
** using staged installation
** libs
using C++ compiler: ‘Apple clang version 15.0.0 (clang-1500.0.40.1)’
using SDK: ‘MacOSX14.2.sdk’

clang++ -std=gnu++17 -I"/opt/homebrew/Cellar/r/4.3.2/lib/R/include" -DNDEBUG  -I'/opt/homebrew/lib/R/4.3/site-library/Rcpp/include' -I/opt/homebrew/opt/gettext/include -I/opt/homebrew/opt/readline/include -I/opt/homebrew/opt/xz/include -I/opt/homebrew/include    -fPIC  -g -O2  -c RcppExports.cpp -o RcppExports.o
clang++ -std=gnu++17 -I"/opt/homebrew/Cellar/r/4.3.2/lib/R/include" -DNDEBUG  -I'/opt/homebrew/lib/R/4.3/site-library/Rcpp/include' -I/opt/homebrew/opt/gettext/include -I/opt/homebrew/opt/readline/include -I/opt/homebrew/opt/xz/include -I/opt/homebrew/include    -fPIC  -g -O2  -c RcppVersion.cpp -o RcppVersion.o
clang++ -std=gnu++17 -I"/opt/homebrew/Cellar/r/4.3.2/lib/R/include" -DNDEBUG  -I'/opt/homebrew/lib/R/4.3/site-library/Rcpp/include' -I/opt/homebrew/opt/gettext/include -I/opt/homebrew/opt/readline/include -I/opt/homebrew/opt/xz/include -I/opt/homebrew/include    -fPIC  -g -O2  -c delong.cpp -o delong.o
clang++ -std=gnu++17 -I"/opt/homebrew/Cellar/r/4.3.2/lib/R/include" -DNDEBUG  -I'/opt/homebrew/lib/R/4.3/site-library/Rcpp/include' -I/opt/homebrew/opt/gettext/include -I/opt/homebrew/opt/readline/include -I/opt/homebrew/opt/xz/include -I/opt/homebrew/include    -fPIC  -g -O2  -c perfsAll.cpp -o perfsAll.o
clang++ -std=gnu++17 -dynamiclib -Wl,-headerpad_max_install_names -undefined dynamic_lookup -L/opt/homebrew/Cellar/r/4.3.2/lib/R/lib -L/opt/homebrew/opt/gettext/lib -L/opt/homebrew/opt/readline/lib -L/opt/homebrew/opt/xz/lib -L/opt/homebrew/lib -o pROC.so RcppExports.o RcppVersion.o delong.o perfsAll.o -L/opt/homebrew/Cellar/r/4.3.2/lib/R/lib -lR -lintl -Wl,-framework -Wl,CoreFoundation

installing to /opt/homebrew/lib/R/4.3/site-library/00LOCK-pROC/00new/pROC/libs
** R
** data
*** moving datasets to lazyload DB
** inst
** byte-compile and prepare package for lazy loading
** help
*** installing help indices
** building package indices
** testing if installed package can be loaded from temporary location
** checking absolute paths in shared objects and dynamic libraries
** testing if installed package can be loaded from final location
** testing if installed package keeps a record of temporary installation path
* DONE (pROC)

The downloaded source packages are in
    ‘/private/var/folders/gs/jr7fg_pj3kdbfx9sj3vfs7680000gn/T/RtmpLbjxS0/downloaded_packages’

library(pROC)

Type 'citation("pROC")' for a citation.

Attaching package: ‘pROC’

The following objects are masked from ‘package:stats’:

    cov, smooth, var

roc_curve <- roc(test.lr$status, lr.pred)

Setting levels: control = 0, case = 1
Setting direction: controls < cases

plot(roc_curve, main = "ROC Curve", col = "blue", lwd = 2)

library(ggplot2)

# Convert confusion matrix to a data frame
conf_matrix_df <- as.data.frame.matrix(conf.matrix)
conf_matrix_df <- cbind(Actual = rownames(conf_matrix_df), conf_matrix_df)

# Reshape data for ggplot
conf_matrix_long <- tidyr::gather(conf_matrix_df, key = "Predicted", value = "Frequency", -Actual)

# Create heatmap using ggplot2
ggplot(data = conf_matrix_long, aes(x = Predicted, y = Actual, fill = Frequency)) +
  geom_tile() +
  labs(title = "Confusion Matrix", x = "Predicted", y = "Actual") +
  scale_fill_gradient(low = "white", high = "blue") +
  theme_minimal()

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