Linear Regression Interview Cheatsheet & Quick Reference

Machine Learning Interview Guide for Top Tech Roles (2025)

Linear Regression: Complete Interview Guide for Interviews

3 min read 480 words

🎯 Core Idea

Linear Regression models the relationship between input features and a continuous target by fitting the best straight line (or hyperplane) that minimizes prediction errors.

In a nutshell: Imagine drawing the “best possible straight line” through a cloud of points so that your guesses are as close as possible to reality.

🧠 How it Works: The Intuition

Linear Regression tries to find a mathematical equation (a line) that explains how inputs relate to outputs. It adjusts the slope and intercept so that the line best represents the observed data.

Step 1

Define a linear function that maps inputs (features) to outputs (predictions).

Step 2

Measure how far predictions are from actual values using a loss function (typically Mean Squared Error).

Step 3

Optimize the parameters (weights and bias) by minimizing this loss, often using the Normal Equation or Gradient Descent.

Step 4

Use the learned parameters to make predictions on new, unseen data.

📈 Mathematical Foundation & Complexity

This section contains the critical technical details for an interview setting.

🔍 View the Core Math & Equations

Hypothesis Function:
$$ \hat{y} = X\beta = \beta_0 + \beta_1 x_1 + \dots + \beta_n x_n $$
Loss Function (Mean Squared Error):
$$ J(\beta) = \frac{1}{2m} \sum_{i=1}^{m} \left( y^{(i)} - \hat{y}^{(i)} \right)^2 $$
Closed-form Solution (Normal Equation):
$$ \hat{\beta} = (X^T X)^{-1} X^T y $$
Gradient Descent Update Rule:
$$ \beta := \beta - \alpha \cdot \frac{1}{m} \sum_{i=1}^{m} ( \hat{y}^{(i)} - y^{(i)} ) x^{(i)} $$

ℹ️

Time Complexity:
- Closed-form (Normal Equation): O(n^3) due to matrix inversion.
- Gradient Descent: O(m·n·k) where m = samples, n = features, k = iterations.
Space Complexity: O(m·n) to store the dataset and O(n) for the parameters.

✅ Pros & ❌ Cons

A quick summary of the primary trade-offs.

Pro 1: Simple, interpretable, and easy to implement.
Pro 2: Fast training for small to medium datasets.
Pro 3: Provides insights into feature importance via coefficients.

Con 1: Assumes linear relationship between features and target.
Con 2: Sensitive to multicollinearity and outliers.
Con 3: Performance degrades with high-dimensional or non-linear data.

🛠️ Practical Application

Guidance on using the algorithm in a real-world project.

🔧 View Key Hyperparameters

fit_intercept: Whether to calculate the intercept (True by default).
normalize: Whether to normalize features before fitting (deprecated in some libraries, use preprocessing).
learning_rate (for Gradient Descent): Controls step size; too high causes divergence, too low slows convergence.
max_iter: Number of iterations for optimization methods like Gradient Descent.

⚠️ Interviewer’s Trap: Assumptions & Pitfalls

Key Assumption 1: Relationship between features and target is linear.

Key Assumption 2: Errors are normally distributed with constant variance (homoscedasticity).

Key Assumption 3: Features are not highly correlated (no strong multicollinearity).

Common Pitfall 1: Forgetting to scale features when using Gradient Descent.

Common Pitfall 2: Misinterpreting coefficients as causation instead of correlation.

Common Pitfall 3: Ignoring the impact of outliers, which can skew results.

Linear Regression Interview Study Roadmap (Practical Timeline)Linear Regression Coding Examples (Python & NumPy)