Predicting Re-Exam Outcome with K-NN Using the Q5a Dataset (Student #9)

In this section, you’ll use your existing Q5a dataset (the same dataset you prepared in Q5a) to train a K-NN classifier and predict whether the overslept student will pass the re-exam.

We’ll treat the student record as a new query instance:

• ID: 9
• Cell No.: 93333-11109
• Language: C++
• Passed all Assignments: Yes
• GPA: 3.0
• Target (Passed Exam): unknown

Key idea

A k-NN classifier predicts the unknown label by finding the $k$ nearest neighbors in feature space and taking a vote (or average) of their labels. This requires careful preprocessing because your features include both categorical (Language, Passed all Assignments) and numeric (GPA, possibly others).

Assumption (based on typical coursework):
Your Q5a dataset contains rows with features similar to: Language, Passed all Assignments, GPA, and a target Passed Exam. If Q5a also included additional features (e.g., Cell No.), you should follow the exact same Q5a preprocessing pipeline for those features. If Cell No. is an identifier (not a meaningful predictor), it should be excluded from modeling.

Mathematical interpretation of the K-NN decision

Let the transformed training matrix be $\\mathbf{X} \\in \\mathbb{R}^{n\\times d}$ and the query point be \\mathbf{x}_\\* \\in \\mathbb{R}^{d} after preprocessing. For a chosen distance metric (commonly Minkowski distance), compute distances to all points:

Pick the set $\\mathcal{N}_k(\\mathbf{x}_\*)$ of the $k$ smallest distances. Then:

• Majority vote rule (classification):

This is how K-NN decides whether the student will pass.

Practical implementation (scikit-learn style)

Below is a template that matches the workflow you’d typically implement after Q5a.

Important

Because Q5a is not included in your prompt, the code shows the structure. You should align variable names and preprocessing steps with what you did in Q5a (e.g., which columns you dropped and how you encoded).

1import numpy as np
2import pandas as pd
3
4from sklearn.compose import ColumnTransformer
5from sklearn.preprocessing import OneHotEncoder, StandardScaler
6from sklearn.pipeline import Pipeline
7from sklearn.neighbors import KNeighborsClassifier
8
9# Assume df is your Q5a dataset
10# Target column:
11target_col = "Passed Exam"
12
13# Example feature columns (adjust to match Q5a)
14categorical_cols = ["Language", "Passed all Assignments"]
15numeric_cols = ["GPA"]
16# If Q5a kept Cell No. as a numeric/meaningful feature, include it in numeric_cols.
17# Otherwise drop it from features.
18
19X = df[categorical_cols + numeric_cols]
20y = df[target_col].astype(int)  # ensure 0/1
21
22preprocess = ColumnTransformer(
23    transformers=[
24        ("cat", OneHotEncoder(handle_unknown="ignore"), categorical_cols),
25        ("num", StandardScaler(), numeric_cols),
26    ]
27)
28
29knn = KNeighborsClassifier(n_neighbors=5)  # set k as decided in Q5a
30
31model = Pipeline(steps=[("preprocess", preprocess), ("knn", knn)])
32model.fit(X, y)
33
34# Query instance for ID=9
35query = pd.DataFrame([{
36    "Language": "C++",
37    "Passed all Assignments": "Yes",
38    "GPA": 3.0
39}])
40
41pred = model.predict(query)[0]
42proba = model.predict_proba(query)[0][pred]  # probability of predicted class
43
44print("Predicted Passed Exam:", pred)
45print("Confidence (prob of predicted class):", proba)