Learn Challenge: Predict Student Scores Based on Study Hours | Probability, Statistics, and Simulation

Predicting student performance based on study habits is a practical application of regression analysis in education. By examining the relationship between the number of hours a student studies and their exam scores, you can model how changes in study time might affect outcomes. Linear regression is a statistical technique that fits a straight line to data points, allowing you to make predictions about one variable based on another. In this context, you will use Python's scikit-learn library to build a simple linear regression model, visualize the results using matplotlib, and predict the exam score for a student who studies a specific number of hours.


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import matplotlib.pyplot as plt
import numpy as np
from sklearn.linear_model import LinearRegression

# Example data: hours studied and corresponding exam scores
hours = [2, 3, 5, 6, 8, 10]
scores = [50, 55, 65, 70, 80, 90]

# Prepare the data for regression (reshape for sklearn)
X = np.array(hours).reshape(-1, 1)
y = np.array(scores)

# Fit the linear regression model
model = LinearRegression()
model.fit(X, y)

# Predict scores for the training data
predicted_scores = model.predict(X)

# Plot the data and the regression line
plt.scatter(hours, scores, color='blue', label='Actual Scores')
plt.plot(hours, predicted_scores, color='red', label='Regression Line')
plt.xlabel('Hours Studied')
plt.ylabel('Exam Score')
plt.title('Student Scores vs Study Hours')
plt.legend()
plt.show()

Task

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Write a function that performs linear regression on two lists, hours and scores, and predicts the exam score for a given number of study hours.

Fit a linear regression model using hours as the independent variable and scores as the dependent variable.
Plot the original data points and the regression line using matplotlib.
Predict the exam score for the value in predict_hours and print the predicted value.

Solution

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Section 3. Chapter 7

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import matplotlib.pyplot as plt
import numpy as np
from sklearn.linear_model import LinearRegression

# Example data: hours studied and corresponding exam scores
hours = [2, 3, 5, 6, 8, 10]
scores = [50, 55, 65, 70, 80, 90]

# Prepare the data for regression (reshape for sklearn)
X = np.array(hours).reshape(-1, 1)
y = np.array(scores)

# Fit the linear regression model
model = LinearRegression()
model.fit(X, y)

# Predict scores for the training data
predicted_scores = model.predict(X)

# Plot the data and the regression line
plt.scatter(hours, scores, color='blue', label='Actual Scores')
plt.plot(hours, predicted_scores, color='red', label='Regression Line')
plt.xlabel('Hours Studied')
plt.ylabel('Exam Score')
plt.title('Student Scores vs Study Hours')
plt.legend()
plt.show()