Campus Recruitment: A Classification Problem with Logistic Regression

Introduction

In this project, we will be focusing on data from India. And our goal is to create a predictive model, such as Logistic Regression, etc. so that when we give the characteristics of a candidate, the model can predict whether they will recruit.

The dataset revolves around the placement season of a Business School in India. The dataset has various factors on candidates, such as work experience, exam percentage, etc. Finally, it contains the status of recruitment and remuneration details.

Campus recruitment is a strategy for sourcing, engaging, and hiring young talent for internship and entry-level positions. It often involves working with university career services centers and attending career fairs to meet in person with college students and recent graduates.

This article was published as a part of the Data Science Blogathon.

Table of Contents

1. Steps Involved in Solving the Problem
2. Prepare Data
3. Build a Logistic Regression Model
4. Results of the Logistic Regression Model
5. Conclusion

Steps Involved in Solving the Problem

In this article, we will import that dataset, clean it, and then prepare it to build a logistic regression model. Our goals here are the following:

First, We’re going to prepare our data set for binary classification. Now, what do I mean? when we try to predict a continuous value, like the price of an apartment, it can be any number between zero and many million dollars. We call it a regression problem.

But in this project, things are a little bit different. Instead of predicting a continuous value, we have discrete groups or classes we are trying to predict between them.  So this is called a Classification problem, and because in our project, we will have only two groups that we’re trying to choose between, that makes it a binary classification.

The second goal is to create a logistic regression model to predict recruitment. And our third goal is to explain our model’s predictions using the odds ratio.

Now in terms of the machine learning workflow, the steps we will follow, and some of the new things, we will learn along the way. So in the import phase, we will prepare our data to work with a binary target. In the exploration phase, We will be looking at the class balance. So basically, what proportion of candidates was hird, and what proportions weren’t? and in the features encoding phase, we will do encoding to our categorical features. In the split part, we will do a randomized train test split.

For the model-building phase, firstly, we will set our baseline, and because we will use accuracy scores, we’ll talk more about what an accuracy score is and how to build a baseline when that’s the metric we’re interested in. Secondly, we will be doing logistic regression. And then last but not least, we will have the evaluation phase. We will again focus on the accuracy score. Finally, to communicate results, we will look at the odds ratio.

Lastly, Before diving into the work, let’s introduce ourselves to the libraries we will use throw the project. First, we will import our data to Google Colabe notebook into the io library. Then, as we’ll use a logistic regression model, we’ll import that from scikit-learn. After that, also from scikit-learn, we will import our performance metrics, the accuracy score, and the train-test-split.

We will use Matplotlib and seaborn for our visualization, and NumPy  will be just for little math.
We need pandas to manipulate our data, labelencoder to encode our categorical variables, and standard scaler to normalize the data. That’ll be the libraries that we need.

Let’s jump into preparing the data.

#import libraries
import io
import warnings

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
from sklearn.preprocessing import LabelEncoder
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

warnings.simplefilter(action="ignore", category=FutureWarning)

Prepare Data

Import

To start our preparing the data, let’s get our important work. First, we load our data file, and then we need to put them into a DataFrame `df.`

from google.colab import files
uploaded = files.upload()

# Read CSV file
df = pd.read_csv(io.BytesIO(uploaded["Placement_Data_Full_Class.csv"]))
print(df.shape)
df.head()

We can see our beautiful DataFrame, and we have 215 records and 15 columns that include the `status` attribute, our target. This is the description for all features.

Explore

Now we have all these features which we are going to explore. So let’s start our exploratory data analysis. First, let’s take a look at the info for this dataframe and see if any of them we may need to keep or if we maybe need to drop.

# Inspect DataFrame
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 215 entries, 0 to 214
Data columns (total 15 columns):
 #   Column          Non-Null Count  Dtype  
---  ------          --------------  -----  
 0   sl_no           215 non-null    int64  
 1   gender          215 non-null    object 
 2   ssc_p           215 non-null    float64
 3   ssc_b           215 non-null    object 
 4   hsc_p           215 non-null    float64
 5   hsc_b           215 non-null    object 
 6   hsc_s           215 non-null    object 
 7   degree_p        215 non-null    float64
 8   degree_t        215 non-null    object 
 9   workex          215 non-null    object 
 10  etest_p         215 non-null    float64
 11  specialisation  215 non-null    object 
 12  mba_p           215 non-null    float64
 13  status          215 non-null    object 
 14  salary          148 non-null    float64
dtypes: float64(6), int64(1), object(8)
memory usage: 25.3+ KB

Now when we look at `df` info, there are a couple of things that we’re looking for, we have 215 rows in our dataframe, and the question we want to ask ourselves is, is there any missing data? And if we look here, it seems we don’t have missing data except for the salary column, as expected, due to candidates who have not been hired.

Another concern for us here is, are there any leaky features that would give information to our model that it wouldn’t have if it deployed in the real world? Remember that we want our model to predict whether a candidate will place or not, and we want our model to make those predictions before the recruitment happens. So we don’t want to give any information about these candidates after the recruitment.

So, it’s pretty clear that this `salary` feature gives information about the salary offered by the corporate. And because this salary is for those accepted, this feature here constitutes leakage, and we have to drop it.

df.drop(columns="salary", inplace=True)

The second thing I want to look at is the data types for these different features. So, looking at these data types, we have eight categorical features with our target and seven numerical features, and everything is correct. So, now that we have these ideas let’s take some time to explore them more deeply.

We know that our target has two classes. We have placed candidates and not placed candidates. The question is, what is the relative proportion of those two classes? Are they about the same balance? Or is one a lot more than the other? That’s something that you need to take a look at when you’re doing classification problems. So this is a significant step in our EDA.

# Plot class balance
df["status"].value_counts(normalize=True).plot(
    kind="bar", xlabel="Class", ylabel="Relative Frequency", title="Class  Balance"
);

Our positive class ‘placed’ counts for more than 65% of our observations, and our negative class ‘Not Placed is around 30%. Now, if these were super imbalanced, like, if it were more like 80 or even more than that, I would say these are imbalanced classes. And we’d have to do some work to make sure our model is going to function in the right way. But this is an okay balance.

Let’s make another visualization to notice the connection between our features and the target. Let’s start with the numerical features.

First, we will see the individual distribution of the features using a distribution plot, and we will also see the relationship between the numerical features and our target by using a box plot.

fig,ax=plt.subplots(5,2,figsize=(15,35))
for index,i in enumerate(df.select_dtypes("number").drop(columns="sl_no")):
    plt.suptitle("Visualizing Distribution of Numerical Columns Indivualy and by Class",size=20)
    sns.histplot(data=df, x=i, kde=True, ax=ax[index,0])
    sns.boxplot(data=df, x='status', y=i, ax=ax[index,1]);

In the first column from our plot, we can see that all the distributions follow a normal distribution, and most of the candidate’s educational performances are between 60-80%.

In the second column, we have a double box plot with the ‘Placed’ class on the right and then the `Not Placed` class on the left. For the ‘etest_p’ and ‘mba_p’ features, there’s not a lot of difference in these two distributions from a model-building perspective. There is a significant overlap in the distribution over the classes, so these features would not be a good predictor of our target. As for the rest of the features, there are distinct enough to take them as potential good predictors of our target. Let’s move on to the categorical features. And to explore them, we will use a count plot.

fig,ax=plt.subplots(7,2,figsize=(15,35))
for index,i in enumerate(df.select_dtypes("object").drop(columns="status")):
    plt.suptitle("Visualizing Count of Categorical Columns",size=20)
    sns.countplot(data=df,x=i,ax=ax[index,0])
    sns.countplot(data=df,x=i,ax=ax[index,1],hue="status")

Looking at the plot, we see that we have more male candidates than females. And most of our candidates don’t have any work experience, but these candidates got hired more than the ones who had. We have candidates who did commerce as their ‘hsc’ course, and as well as an undergrad, the candidates with a science background are the second highest in both cases.

A little note on logistic regression models, although they are for classification, they’re in the same group as other linear models like linear regression, and for that reason, since they’re both linear models. We also need to worry about the issue of multicollinearity. So we need to create a correlation matrix, and then we need to plot it out in a heatmap. We don’t want to look at all the features here, we want to look just at the numerical features, and we don’t want to include our target. Since if our target correlates with some of our features, that is very good.

corr = df.select_dtypes("number").corr()
# Plot heatmap of `correlation`
plt.title('Correlation Matrix')
sns.heatmap(corr, vmax=1, square=True, annot=True, cmap='GnBu');

Here are the light blue, which means little to no correlation, and the dark blue, with which we have a higher correlation. So we want to be on the lookout for those dark blue. We can see a dark blue line, a diagonal line going down the middle of this plot. Those are the features that are correlated with themselves. And then, we see some dark squares. That means we have a bunch of correlations between features.

At the final step of our EDA, we need to check for high-low cardinality in the categorical features. Cardinality refers to the number of unique values in a categorical variable. High cardinality means that categorical features have a large number of unique values. There is no exact number of unique values that makes a feature high-cardinality. But if the value of the categorical feature is unique for almost all observations, it can usually be dropped.

# Check for high- and low-cardinality categorical features
df.select_dtypes("object").nunique()

gender            2
ssc_b             2
hsc_b             2
hsc_s             3
degree_t          3
workex            2
specialisation    2
status            2
dtype: int64

I don’t see any columns where the number of unique values is one or anything super high. But I think there’s one categorical type column that we’re missing here. And the reason is that it’s not encoded as an object but as an integer. The ‘sl_no’ column isn’t an integer in the sense we know. These candidates are ranked in some order. Just a unique name tag, and the name is like a category, right? So this is a categorical variable. And it doesn’t have any information, so we need to drop it.

df.drop(columns="sl_no", inplace=True)

Features Encoding

We finished our analysis, and the next thing we need to do is encode our categorical features, I will use the ‘LabelEncoder’. Label Encoding is a popular encoding technique for handling categorical variables. With using this technique, each label is assigned a unique integer based on alphabetical ordering.

lb = LabelEncoder ()

cat_data = ['gender', 'ssc_b', 'hsc_b', 'hsc_s', 'degree_t', 'workex', 'specialisation', 'status']
for i in cat_data:
    df[i] = lb.fit_transform(df[i])

df.head()

Split

We imported and cleaned our data. We’ve done a bit of exploratory data analysis, and now we need to split our data. We have two types of split: vertical split or features-target and horizontal split or train-test sets.Let’s start with the vertical one. We will Create our feature matrix ‘X’ and target vector ‘y’. Our target is “status.” Our features should be all the columns that remain in the ‘df.’

#vertical split
target = "status"
X = df.drop(columns = target)
y = df[target]

Models generally perform better when they have normalized data to train with, so what is normalization? Normalization is transforming the values of several variables into a similar range. Our target is to normalize our variables. So their value ranges will be from 0 to 1. Let’s do that, and I will use the `StandardScaler.`

scaler = StandardScaler()
X = scaler.fit_transform(X)

Now let’s do the horizontal split or train-test sets. We need to divide our data (X and y) into training and test sets using a randomized train-test split. our test set should be 20% of our total data. And we don’t forget to set a random_state for reproducibility.

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size = 0.2, random_state = 42
    )

print("X_train shape:", X_train.shape)
print("y_train shape:", y_train.shape)
print("X_test shape:", X_test.shape)
print("y_test shape:", y_test.shape)

X_train shape: (172, 12)
y_train shape: (172,)
X_test shape: (43, 12)
y_test shape: (43,)

Build a Logistic Regression Model

Baseline

So now we need to begin building our model, and we’ll need to start ordering to set our baseline. Remember that the type of problem we’re dealing with is a classification problem, and there are different metrics to evaluate classification models. The one I want to focus on is the accuracy score.

Now, what is the accuracy score? Accuracy score in machine learning is an evaluation metric that measures the number of correct predictions made by a model to the total number of predictions made. We calculate it by dividing the number of correct predictions by the total number of predictions. So what that means is that the accuracy score goes between 0 and 1. Zero is not good. That’s where you don’t want to be, and one is perfect. So Let’s keep that in mind and remember that the baseline is a model that gives one prediction over and over again, regardless of what the observation is, only one guess for us.

In our case, we have two classes, placed or not. So if we could make only one prediction, what would be our one guess? If you said the majority class. I think that makes sense, right? If we can only have one prediction, we should probably choose the one with the highest observations in our dataset. So, our baseline will use the percentage that the majority class shows up in the training data. If the model is not beating this baseline, the features are not adding valuable information to classify our observations.

We can use the ‘value_counts’ method with the `normalize = True` argument to calculate the baseline accuracy:

acc_baseline = y_train.value_counts(normalize=True).max()
print("Baseline Accuracy:", round(acc_baseline, 2))

Baseline Accuracy: 0.68

We can see that our baseline accuracy is 68% or 0.68 as a proportion. So to add value to be of use, we want to get above that number and get closer to one. That’s our goal, and now let’s start building our model.

Iterate

Now it’s time to build our model using Logistic Regression. We will use logistic regression, but before we do, let’s talk a little about what logistic regression is and how it works, and then we can do the coding stuff. And for that, here we have a little grid.

Along the x axis, let’s say I have the p_degrees of candidates in our data set. And as I move from right to left, the degrees get higher and higher, and then along the Y axis, I have the possible classes for placement:  zero and one.

So if we were to plot out our data points, what would it look like? Our analysis shows that a high `p_degree` candidate is more likely to be hired. So, it would probably look something like this, where the candidate with a small `p_degree` would be down at zero. And the candidate with a high `p_degree` would be up at one.

Now let’s say that we wanted to do linear regression with this. Let’s say we wanted to plot a line.
Now, if we did that, what would happen is that line would be plotted in such a way that it would try to be as close to all the points as possible. And so we would probably end up with a line that looked something like this. Would this be a good model?

Not really. What would happen is regardless of the p_degree of the candidate, we would always get a sort of value. And that’s not will help us because the numbers, in this context, don’t mean anything. This classification problem needs to either be zero or one. So, it’s not going to work that way.

On the other hand, because this is a line, what if we have a candidate with a very low p_degree? Well, all of a sudden, our estimate is a negative number. And again, this doesn’t make any sense. There is no negative number either needs to be zero or one. And in the same way, if we have a candidate with a very high p_degree, I might have a positive, something above one. And again, that doesn’t make any sense. We need to either have a zero or one.

So what we see here are some serious limitations to using linear regression for classification. So what do we need to do?  We need to create a model that number one: doesn’t go below zero or above one, so it needs to be bound between zero and one. And the number two, whatever comes out of that function, that equation that we create, we maybe shouldn’t treat it as the prediction per se but as a step towards making our final prediction.

Now, let me unpack what I just said, and let’s remind ourselves that when we’re doing our linear regression models, we end up with this linear equation, Which is the simplest form. And this is that equation or function that gives us that straight line.

There’s a way to bind that line between 0 and 1. And what we can do is take this function that we’ve just created and enclose it in another function, what’s called a sigmoid function.

So, I’m going to take the linear equation we just had, and I’m going to shrink it down in the sigmoid function and put it as the exponential.

What happens is instead of getting a straight line, we get a line that looks kind of like this. It’s stuck at one. It comes in and squiggles down. Then it is stuck at zero.

Right, that’s what the line looks like, and we can see that we’ve solved our first problem. Whatever we get out of this function will be between 0 and  1. In the second step, we will not treat whatever comes out of this equation as the ultimate prediction. Instead, we will treat it as a probability.

What do I mean? That means when I make a prediction, I will get some floating point value between 0 and 1. And what I will do is treat it as the probability that my prediction belongs to the positive class.

So I get a value up at 0.9999. I will say the probability that this candidate belongs to our positive, placed class is 99%. So I’m almost sure that it belongs to the positive class. Conversely, if it’s down at point 0.001 or whatever, I will say this number is low. The probability that this particular observation belongs to the positive, the placed class is almost zero. And so, I’m going to say it belongs to class zero.

So that makes sense for numbers that are close to one or close to zero. But you might ask yourself, what do I do with other values in between? The way that works is we put a cut off line right at 0.5, so any value I get below that line, I’ll put it at zero, so my prediction is no, and if it’s above that line, if it’s above point five, I will put this in the positive class, my prediction is one.

So, now I have a function that gives me a prediction between zero and one, and I treat that as a probability. And if that probability is above 0.5 or 50%, I say, okay, positive class one. And if it’s below 50%, I say, that’s negative class, zero. So that is the way that logistic regression works. And now we understand that, let’s code it up and fit it. I will set the hyperparameter ‘max_iter’ to 1000. This parameter refers to the maximum number of iterations for the solvers to converge.

# Build model
model = LogisticRegression(max_iter=1000)
    
# Fit model to training data
model.fit(X_train, y_train)

LogisticRegression(max_iter=1000)

Evaluate

Now it’s time to see how our model does. It’s time to evaluate the Logistic Regression model. So, let’s remember that this time, the performance metric we are interested in is the accuracy score, and we want an accurate one. And we want to beat the baseline of 0.68. Model accuracy can be calculated using the accuracy_score function. The function requires two arguments, the true labels and the predicted labels.

acc_train = accuracy_score(y_train, model.predict(X_train))
acc_test = model.score(X_test, y_test)

print("Training Accuracy:", round(acc_train, 2))
print("Test Accuracy:", round(acc_test, 2))

Training Accuracy: 0.9
Test Accuracy: 0.88

We can see our training accuracy at 90%. It’s beating the baseline. Our test accuracy was a little lower at 88%. It also beat the baseline and was very close to our training accuracy. So that’s good news because that means that our model isn’t overfitting or anything.

Results of the Logistic Regression Model

Remember that with logistic regression, we end up with these final predictions of zero or one. But underneath that prediction, there’s a probability of a floating point number between zero or one, and sometimes it can be helpful to see what those probability estimates are. Let’s look at our training predictions, and let’s look at the first five. The ‘predict’ method predicts the target of an unlabeled observation.

model.predict(X_train)[:5]

array([0, 1, 1, 1, 1])

So those were the final predictions, but what are the probabilities behind them? To get those, we need to do a slightly different code. Instead of using the `predict` method with our model, I will use the ‘predict_proba’ with our training data.

y_train_pred_proba = model.predict_proba(X_train)
print(y_train_pred_proba[:5])

[[0.92003219 0.07996781]
 [0.03202019 0.96797981]
 [0.00678421 0.99321579]
 [0.03889446 0.96110554]
 [0.00245525 0.99754475]]

We can see a kind of nested list with two different columns in it. The column on the left represents the probability that a candidate is not placed or our negative class ‘Not Placed’. The other column represents the positive class `Placed` or the probability that a candidate is placed. We will focus on the second column. If we look at the first probability estimate right, we can see that this is 0.07. So since that’s below 50%, our model says, my prediction is zero. And for the following predictions, we can see that those are all above 0.5, and that’s why our model predicted one in the end.

Now we want to extract the feature names and importance and put them in a series. And because we need to display the feature importance as odds ratios, we need to do just a little mathematical transformation by taking the exponential of our importance.

# Features names
features = ['gender', 'ssc_p', 'ssc_b', 'hsc_p', 'hsc_b', 'hsc_s', 'degree_p'
           ,'degree_t', 'workex', 'etest_p', 'specialisation', 'mba_p']
# Get importances
importances = model.coef_[0]
# Put importances into a Series
odds_ratios = pd.Series(np.exp(importances), index= features).sort_values()
# Review 
odds_ratios.head()

mba_p             0.406590
degree_t          0.706021
specialisation    0.850301
hsc_b             0.876864
etest_p           0.877831
dtype: float64

Before discussing the odds ratios and what they are, let’s get them on a horizontal bar chart. Let’s use pandas to make the plot, and remember that we will look for the five largest coefficients. And we don’t want to use all the odds ratios. So we want to use the tail.

# Horizontal bar chart, five largest coefficients
odds_ratios.tail().plot(kind="barh")
plt.xlabel("Odds Ratio")
plt.ylabel("Feature")
plt.title("High Importance Features");

Now I want you to imagine a vertical line right at 5, and I want to start by looking at it. Let’s talk about each of these individually or just the first couple. So let’s start here with the ‘ssc_p,’ which refers to the ‘Secondary Education percentage – 10th Grade’. And we can see that the odds ratio is at 30. Now, what does that mean? It means if a candidate has a high ‘ssc_p,’ the odds of their placement are six times greater than other candidates, all things being equal. So another way to think of it is when the candidate has `ssc_p,` the chance of the candidate’s recruitment increases six times.

So any odds ratio over five increases the odds that candidates are placed. And so that’s why we have that vertical line at five. And these five kinds of features are characteristics that are most associated with increased recruitment. So, that’s what our odds ratio is. Now, we’ve looked at the features that are most associated with an increase in recruitment. Let’s look at the features that are associated with it, the decrease in recruitment. So now it’s time to look at the smallest ones. So instead of looking at the tail, we will look at it.

odds_ratios.head().plot(kind="barh")
plt.xlabel("Odds Ratio")
plt.xlabel("Odds Ratio")
plt.ylabel("Feature")
plt.title("Low Importance Features");

The first thing we need to see here is that notice on the x-axis everything is one or below. Now, what does that mean? So let’s take a look at our smallest odds ratio here. It’s mba_p which refers to the MBA percentage. We can see that it’s ready at about 0.45. Now, what does that mean? Well, the difference between 0.45 and 1 is 0.55. All right? And what does that number mean? Those Candidates with MBA are less likely to be recruited by 55%, All other things being equal. All right? So it decreased the odds of recruitment by a factor of 0.55 or 55%. And that’s true for everything here.

Conclusion

So what did we learn? First, in the prepared data phase, we learned that we are working with classification, specifically binary classification, using Logistic Regression. In terms of exploring the data, we did a ton of stuff, but in terms of highlights, we looked at class balance, right? The proportion of our positive and negative classes. Then we split our data.

Since Logistic Regression is a classification model, we learned about a new performance metric, the accuracy score. Now, the accuracy score goes between 0 and 1. Zero is bad, and one is good. When we were iterating, we learned about logistic regression. That’s a magical way, where you can take a linear equation, a straight line, and put it inside another function, a sigmoid function, and an activation function, and get a probability estimate out of it and turn that probability estimate into prediction.

Finally, we learned about the odds ratio and the way we can interpret the coefficients to see if a given feature will increase the odds that we have recruited a candidate or not.

Project source code: https://github.com/SawsanYusuf/Campus-Recruitment.git

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