Linear regression

Foundations of Probability in Python

Alexander A. Ramírez M.

CEO @ Synergy Vision

Linear functions

Linear function plot

Linear function plot

$$ y = \color{red}{slope}*x + \color{blue}{intercept} $$

Linear function with random perturbations plot

$$ y = slope*x + intercept + \color{red}{random\_number} $$

Hours of study vs score plot

Fitting data with constant, linear, quadratic and logarithmic models

What would be the criteria to determine which is the best model?

Linear model animation plot

Residuals plot

Residuals plot and minimizing error

Linear model residuals plot

# Import LinearRegression
from sklearn.linear_model import LinearRegression

# sklearn linear model
model = LinearRegression()
model.fit(hours_of_study, scores)

# Get parameters
slope = model.coef_[0]
intercept = model.intercept_

# Print parameters
print(slope, intercept)

(1.496703900384545, 52.44845266434719)

# Score prediction
score = model.predict(np.array([[15]]))
print(score)

[74.89901117]

$$ $$

import matplotlib.pyplot as plt

plt.scatter(hours_of_study, scores)
plt.plot(hours_of_study_values, model.predict(hours_of_study_values))
plt.show()

Linear model fit plot

Foundations of Probability in Python