Data Science

Linear Regression

Arun Murali

Tags: data-science; ml-supervised; regression; linear-regression

🟪 1-Minute Summary

Linear regression models the relationship between independent variables (X) and a continuous dependent variable (y) using a straight line: y = β₀ + β₁x₁ + … + βₙxₙ. Finds coefficients that minimize error (typically using least squares). Assumptions: linearity, independence, homoscedasticity, normality of residuals. Evaluate with R², RMSE, MAE. Simple but powerful baseline model.

🟦 Core Notes (Must-Know)

What is Linear Regression?

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The Equation

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How It Works (Least Squares)

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Key Assumptions

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  1. Linearity
  2. Independence
  3. Homoscedasticity
  4. Normality of residuals
  5. No multicollinearity

When to Use

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Interpreting Coefficients

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🟨 Interview Triggers (What Interviewers Actually Test)

Common Interview Questions

  1. “Explain linear regression to a non-technical person”

    • [Answer: Drawing best-fit line through data points]

  2. “What are the assumptions of linear regression?”

    • [Answer: List 5 assumptions above]

  3. “How do you check if assumptions are violated?”

    • [Answer framework: Residual plots, VIF for multicollinearity]

  4. “What does a negative coefficient mean?”

    • [Answer: Inverse relationship]

🟥 Common Mistakes (Traps to Avoid)

Mistake 1: Using linear regression for non-linear relationships

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Mistake 2: Not checking assumptions

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Mistake 3: Ignoring multicollinearity

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🟩 Mini Example (Quick Application)

Scenario

[Predicting house prices based on square footage]

Solution

from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, r2_score

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🔗 Related Topics

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