# Performing simple linear regression with statsmodels
import numpy as np
import statsmodels.api as sm
# Sample data: Hours studied and Exam scores
hours_studied = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])
exam_scores = np.array([51, 55, 60, 68, 72, 75, 78, 82, 85, 88, 90, 92, 94, 96, 97, 98, 99, 100, 101, 102])
# Adding a constant for the intercept term
X = sm.add_constant(hours_studied)
# Creating the model
model = sm.OLS(exam_scores, X)
# Fitting the model
results = model.fit()
# Making predictions
hours = 10 # Predicting the exam score for someone who studied 10 hours
predicted_score = results.predict([1, hours]) # The first element is the constant term
print(f"Predicted exam score for someone who studied {hours} hours: {predicted_score[0]}\n")
# Printing the summary of the model
print(results.summary())